Underwater Acoustics

with a Focus on Underwater Reverb Spaces
Under Different Surface Conditions


Diploma Thesis
by Willem van den Bos
SAE Hamburg 2004


Table of Contents

1. Introduction

2. Underwater Acoustics - A Short History

3. Underwater Acoustics - An Introduction

3.1 The Definition of Sound
3.2 Water as a Medium for Sound
3.3 Boundary Behaviour
3.4 Underwater Reverb
3.5 Surface Scattering

4. Listening Underwater: Hydrophones

4.1 Impedance Matching
4.2 Hearing Underwater: Bone Conduction
4.3 Transduction Techniques for Hydrophones

5. The Speed of Sound in Water: A Practical Experiment

6. Convolution: The E-Magic Space Designer

6.1 Algorhitmic Reverb
6.2 Convolved Reverb
6.3 Impulse or Sweep?
6.4 Linearity and Time-invariance
6.5 The Sound Source

7. Sampling Underwater Spaces

7.1 The Bathtub
7.2 Bigger and More Challenging Waters
7.3 Problems Encountered
7.4 About Sampling
7.5 The ISO 3382:1997 Standard

8. Summary and Conclusion

9. Sources


1. Introduction

Generally, there seems to be not much understanding for 'listening underwater'. The 'Amt für Geoinformation und Vermessung' in Hamburg declared me crazy on my request for a map of the Aussenalster for the purpose of measuring the speed of sound in water. Curious locals of Zarrentin, at the Schaalsee, were merely amused and wanted to know if I was listening to singing fish... The words 'sound engineer', 'scientific experiment' and 'SAE Hamburg' worked wonders though, and gave me the acceptance that I needed to go about my business.

Doing outdoor experiments was fun, and required a lot of preparation. It was a good learning experience, especially for clarity of communication with my assistants.

As a starting point I wanted to measure the speed of sound in water, pretty much like Daniel Colladon and Charles Sturm did it way back in 1826, using a ship's bell as the sound source.

In Paul C. Etter's book 'Underwater Acoustic Modelling' I learned that the US Navy are running a special research project on deep ocean reverberation. They designated an area on the northern Mid-Atlantic Ridge as a natural laboratory for studying underwater acoustics. The area is an ideal natural reverberation site, because its steep rocky slopes, deep surface structures and sediment structure provide opportunities to study many aspects of deep sea reverberation.

Bearing this in mind, I realized that the best way to sample underwater soundscapes would be in a submarine equipped with a powerful active SONAR system. For naval and navigational purposes SONAR reverberation is a curse; for an aspiring sound engineer who is looking for great and unusual sound effects, a dream. I know that one day I will get out there!

For now, in the framework of this thesis and well within the limits of my budget, I will stick to more modest sound sources, such as click frogs and ship's bells. I can't complain. After all, Colladon and Sturm did not have cellphones, DAT recorders and Powerbooks equipped with state-of-the-art acoustic software.

Willem van den Bos
Hamburg, 8 April 2004


2. Underwater Acoustics - A Short History

Acoustics as a science started with Pythagoras, a Greek mathematician, who lived from 569 BC till about 475 BC. He is not only known for the Pythagorean Theorem that we may remember from our school days.(1) He also studied harmony in music, which he related to cosmic unity. He called it 'harmony of the spheres'.

The word 'acoustics' is derived from Greek 'AKOUZ' which means 'to listen'. This is a well chosen term, since one of the aspects of sound is the subjective experience resulting from listening.

The first scientific observation of underwater acoustics came much later. The Italian scientist, inventor and artist Leonardo da Vinci wrote in 1490:

"If you cause your ship to stop and place the head of a long tube in the water and place the outer extremity to your ear, you will hear ships at a great distance from you." [Urick, page 2]

This provided a simple method for listening underwater, and the technique was widely used, way till World War I. It had a few drawbacks: hearing through one tube does not enable the listener to determine the direction of the sound. Moreover, the transmission of sound from water to air is poor because of the big difference in acoustic properties of air and water. This will be discussed in chapter 3.

The Swiss physicist Daniel Colladon and the French mathematician Charles Sturm performed the first quantitative measurement of sound speed in water in Lake Geneva in Switzerland in 1827(2). They measured the time elapsing between a flash of light and the sound of a submerged ship's bell picked up by a listening horn over a distance of 17 kilometers. Their results were quite accurate. They measured 1,435 meters per second (m/s) in water of 8,1 degrees Celsius, not far from the speed accepted today. [Urick, page 112]

The invention of the carbon-button microphone in 1878, and the discovery of piezoelectricity() by Jacques and Pierre Curie in 1880, where crucial to the development of hydrophones in the twentieth century. Hydrophones are discussed in more detail in chapter 4.

The history of underwater acoustics is one with many gaps; there were long periods where apparently nothing new was discovered. Had underwater acoustics been taken more seriously by 1912, 'Titanic' might have been able to avoid the iceberg that sent her to the bottom of the ocean, taking the lives of 1.522 passengers and crew.

It was this tragic event however that inspired the development of tools for echolocation, the technique of detecting distant objects by sending out pulses of sound and listening for the return echo. As a matter of fact, a patent application for airborne echolocation was filed five days after the tragedy. A month later followed the application for a patent for its underwater analog. The first really functioning echo ranger, however, was patented in the United States in 1914 by Reginald A. Fessenden. (3)

It was not until World War I, when submarines started to be deployed on a big scale, that underwater sound got studied in great detail. War time gave rise to a feverish development and refinement of military devices, such as SONAR (sound navigation and ranging), both active (echo ranging) and passive (acoustic detection of enemy vessels), acoustic mines (explosive contraptions that are sensitive to the subsonic vibrations of passing ships), torpedos, and other such useful things.

"The ominous Trident ballistic missile submarine prowls the ocean depths in silence, carrying out its global mission of nuclear deterrence. It relies on stealth to avoid detection. And it relies on long-range ITC hydrophones as primary bow sensors to warn of those who seek its presence. The most powerful ship in the world's most advanced navy, the Trident is crewed by professionals aware of its strategic importance. They trust ITC. So can you." [ITC]

The ocean is divided into horizontal layers in which the speed of sound is influenced more strongly by temperature in the upper regions and by pressure in the lower regions. In between the upper and lower regions, at a depth between 600 and 1200 meter there is an equilibrium zone where sound gets caught in a kind of channel, which allows it to travel unhindered for long distances across the oceans.(4)

This so-called 'Deep Sound Channel' was discovered in 1943 The phenomenon is also called 'Sound Fixing and Ranging', or SOFAR. See chapter 3.3 for a detailed explanation.

As one might have guessed, the SOFAR channel has been used extensively for military applications. In 1951, Bell Telephone Labs started a secret project for the US Navy with the code name 'Jezebel'. They placed a network of hydrophone arrays (called 'passive' or 'listening' sonar) within the SOFAR Channel along the continental slopes and seamounts, connected to onshore processing centers. (See fig 1) Making use of the quietness of the environment, they were able to acoustically monitor enemy naval activity from far away. The system, known as SOSUS (Sound Surveillance System), can detect even relatively quiet sounds over distances of thousands of kilometers.

After the Cold War ended, the Navy permitted civilian use of this amazing device.


[Fig 1: Illustration credit - Naval Research Laboratory; from: www.pmel.noaa.gov/vents/acoustics/sosus.html ] (5)

There are many peaceful uses of underwater sound today. It is used for purposes such as mapping the ocean's floor, tracking and monitoring marine life, detecting underwater volcanic eruptions and earthquakes, and monitoring climatic changes.


3. Underwater Acoustics – An Introduction

3.1 The Definition of Sound

The Concise Oxford Dictionary of Current English(18), describes sound as:


a. "The sensation produced through the ear",
which is a subjective human experience

b. "What is or may be heard",
which indicates the assumption that sound does indeed exist independent from the listener.

c. "Vibrations causing this sensation".
It is these vibrations that are the subject of this chapter.

A vibration is a cyclic movement, which means that it that periodically repeats itself around a zero point, from zero to maximum, back to zero to the opposite maximum and back to zero. The distance of the moving object from the zero point is called elongation, measured in meters, indicated by the symbol [e]. The maximum elongation is called amplitude. The greater the amplitude, the stronger (louder) the sound.

When a vibration reproduces itself through an elastic medium, it forms a wave moving away from its source. A sound wave has a length in time, called 'period', measured by seconds, indicated by the symbol [T]; it has a length in space, called 'wavelength', measured in meters, indicated by the symbol [Lambda]; it has a certain number of periods over a certain length of time: the number of periods or cycles that occur each second is called 'frequency', measured by a unit called Hertz (=cycles per second), indicated by the symbol [f]. A sound wave propagates with a certain speed: a certain distance in space over a period of time, measured in meters per second (m/s), indicated by the symbol [c].

These parameters are related as follows:

Lambda = c/f

f = 1/T

What is it that is moving?

It is the particles of which the medium consists. Their velocity is measured in m/s, indicated by the symbol [u].

What is it that is propagating?

It is not the particles, but the periodic movement performed by the particles. One vibrating particle excites the next, which excites the next, and so on. The movement propagation results in patterns of increased and decreased pressure in the medium. When the distance between the particles is bigger, there is decreased pressure (rarefaction); when the distance between the particles becomes smaller, there is an increase in pressure (compression).

"A propagating sound wave consists of alternating compressions and rarefactions which are detected by a receiver as changes in pressure. Structures in our ears, and most man-made receptors are sensitive to these changes in sound pressure." [Fox]

Where does the energy come from that is needed to maintain the movement?

This energy must come from a source. Without source, there can be no sound. (6) Without medium there can be no sound. Without a listener there can be no sound. (7)

Air is an excellent medium for sound. Human beings live in it, breathe it and hear in it. Naturally, the major part of modern day acoustics is about sound in air.

However, water is an excellent medium for sound as well.


3.2 Water as a Medium for Sound

What is it that makes water different as a medium for sound?

Water is considerably denser than air: its molecules are closer together: there are more molecules per cubic unity. Density is indicated by the symbol [þ].

There is more energy (pressure, indicated by the symbol [p]) needed to initiate a sound wave in water; the sound wave will have less intensity than sound of equal pressure in air.

Once the sound wave is initiated in water, it propagates faster because the closer molecules are together, the easier they excite each other. (8)


This is illustrated in the following equations:

p = þ.c.u (pressure = density x sound speed x particle velocity)

I = p.p /þ.c (intensity = pressure squared / density x sound speed)

The acoustic impedance (or: resistance) of the medium is its density multiplied by the speed of the sound waves:


The acoustic impedance of water: þ.cwater = 1.5 x 105 g/(cm2)(s)

The acoustic impedance of air: þ.cair = 42 g/(cm2)(s)

[Urick, pages 11-13]

The impedance of water is 1.5 x 105 / 42 = 3571 times that of air!

At this point it is important to realize that "impedance should not be confused with attenuation or transmission loss". [Maurer] Sound travels with a greater speed and therefore with greater wavelengths, which are less likely to be obstructed by possible objects in the water.

The agreed (approximate) speed of sound in air is 340 m/s and that in water is 1450 m/s.


3.3 Boundary Behaviour

The end of a medium through which sound travels is called boundary. The behaviour of a sound wave at a boundary is called its boundary behaviour. "There are essentially four possible boundary behaviours by which a sound wave could behave:

* reflection (the bouncing off the boundary),
* diffraction (the bending around the obstacle without crossing over the boundary),
* transmission (the crossing of the boundary into the new material or obstacle), and
* refraction (occurs along with transmission and is charcterized by the subsequent change in speed and direction)." [the Physics Classroom]

Diffraction and Reflection

When a propagating sound wave encounters an object smaller than its wavelength, it diffracts around the object, and continues its path unhindered. When the encountered object is bigger than its wavelength, the sound wave will either be reflected, when the object surface is hard, or absorbed to a varying degree, when the object's surface is soft or spongy. When the surface is rough, the sound is reflected and scattered.

A sound with a frequency of 1000 Hertz has a wavelength of = c/f = 340/1000 = 0,34 m in air and a wavelength of 1450/1000 = 1,45 m in water. That means that sound underwater can diffract (deflect) around objects more than four times (1,45/0,34 = 4,26 x) bigger than in air, so sound can travel potentially more unhindered in water than in air.

Reflection of sound can lead to two subjective phenomena: (9)

Echo: The human brain 'holds' a sound for about 0,1 seconds. When the reflected sound hits the ear more than 0,1 seconds after the initial sound, it is perceived as a separate sound: an echo.

Reverberation: When the reflected sound hits the ear less than 0,1 seconds after the initial sound, it is perceived as a prolongation of the sound. Many such reflections together are perceived as reverberation.

Transmission and Refraction

Just as light is refracted when it passes from one medium to another, sound waves are refracted: they change speed and direction.

Sound waves traveling in the ocean will encounter changes in temperature and pressure in different layers of water. When the sound wave passes into a layer of water with a different temperature, its path gets bent in the following possible ways:

lower temperature - sound slows down - downward refraction
higher temperature - sound speeds up - upward refraction
lower pressure - sound slows down - downward refraction
higher pressure - sound speeds up - upward refraction

At a depth between 600 and 1200 meter an equilibrium between the effects of temperature and pressure happens and results in a phenomenon, called 'Sound Fixing and Ranging' or SOFAR.

The ocean consists of different layers of water, as shown in fig 2:


[Fig. 2 - Illustration credit: Willem van den Bos]

Until a depth of 600 to 1200 meter, the falling temperature in the thermocline slows the sound down and bends it downwards; below 1200 meter, the temperature remains constant, while the increasing pressure causes the sound to travel faster and therefore to bend upwards, until it reaches the thermocline again, where it will again be bent downwards. The sound gets bent continuously "towards the depth of minimum velocity" [Urick, page 159] This results in a kind of sound pipeline. Sound traveling through this pipeline does not interact with bottom or surface and can traverse big distances.


3.4 Underwater Reverb

As sound in water deflects, reflects, gets absorbed and refracted pretty much like in air, underwater reverb is not fundamentally different than reverb in air. There is one major difference, though, and that is that water has a distinct surface - unlike air, which gradually gets thinner as the distance from the earth's surface increases.

Water consists of the elements hydrogen and oxygen bound together in the ratio 2:1 – two hydrogen (H+) ions bound to one oxygen ion (O2-), forming H2O, which physically looks like this:


[Fig 3 - Illustration credit: W. van den Bos]

The positively charged hydrogen ions (which are in effect two protons without electrons) on the one side of the water molecule and the oxygen ion on the other side, which still contains four electrons make that the whole is more positive on one side and more negative on the other: water is a bipolar molecule. The consequences of this bipolarity are many. One which may be important in our context is the fact that on the surface the negative sides of the molecules attract the positive sides, forming a 'surface tension', which allows for instance insects to walk on water.

A quiet water surface reflects sound just like a hard surface does. When the surface reflects more, sound will be transmitted into the water to a lesser degree. When the surface reflects less, the sound will be transmitted into the water more and will be perceived as louder underwater.

As washing powder is known to break the water's surface tension, I performed the following bathtub experiment:

A sound source in the form of a ghettoblaster was placed on a soft, non-resonating surface in the form of a pillow. It was played outside the water. The sound was recorded through a hydrophone underwater. Then, as the ghetto blaster was playing, a little washing powder was added to the water, to break the surface tension. The result was a clear increase in loudness of the sound recorded underwater. (10)

The 'hard' water surface, moreover, has the capability to move, change shape and fluctuate, which can produce some interesting effects, which account for the unique nature of underwater sound, and which, I imagine, are the most dramatic in the sea, where the surface movement is big.

Sound scattering

When a sound wave hits a concave surface or a surface that is very rough, it gets scattered in all directions.


[Fig 4 - Illustration credit: W. van den Bos]

Reverberation is heard as "an irregular, quivering, slowly decaying tone". "Within the smooth decay there appear onsets of increased reverberation whenever the emitted sound intercepts with the sea surface and bottom, as well as blobs of reverberation of roughly the same duration as that of the pulse". [Urick, page 281]

Underwater reverberation can be seen, or, rather, heard as the sum result of sound scattering caused by three major factors.

Possible objects, air bubbles and life-forms (like fish, shrimp and plankton) distributed in and moving through the volume of the water. This is called volume reverberation, or volume scattering, which has well-marked increases at certain depths. "The depth of increased volume scattering is called deep scattering layer (DSL)" [Etter, page 202]. It is an ever changing, complex and fairly unpredictable factor, although many efforts have been and are being made to create mathematical models. Fishery data could for instance provide useful information concerning where, when and at which depth certain fish can be expected. However, species that are not favoured by the fish catching industry are likely to be ignored in such data, and volume reverberation cannot be dependent on the commercial value of fish!

The bottom has a reflecting and scattering effect, naturally depending on its composition and layeredness. Bottom reverberation is a science in itself, and a vast amount of research data has become available through for instance the Acoustic Reverberation Special Research Project of the US Navy.(11) These data can be purchased from 'Storming Media: Pentagon Reports and Documents' [www.stormingmedia.us] Unfortunately, these are merely technical data. I have not been able to find any sound samples in the form of WAV files. The focus of the Navy is not on appreciating the possible beauty of deep sea reverberation, but on how to suppress or avoid it, so that it does not interfere with the measuring results of their sensitive SONAR equipment.

The water surface has a major scattering effect, which has been found to vary in intensity with the angle in which the sound hits the surface (grazing angle), the sound frequency, and the roughness of the surface. [Urick, page 263]


3.5 Surface Scattering

Some special surface scattering effects are:

Fluctuating amplitude: When the sound source is near to the surface, the intensity of the sound is variable, due to early reflections from the moving surface. This results in an irregular sound field, which does not decay smoothly. [Urick, page 130]

Frequency smearing: The vertical motion of the surface superimposes itself on the frequency of the sound and produces upper and lower sidebands in the spectrum of the reflected sound that are duplicates of the frequency spectrum of the surface motion. [Urick, page 129]

Doppler effects: Water waves on the surface cause doppler effects, such as a shift in center frequency of the sound signal, while smaller waves within the bigger wave cause a spreading out of the frequency band of the sound signal. [Urick, page 282-284]


4. Listening Underwater: Hydrophones

Just like microphones, hydrophones are transducers: devices that transform the energy of sound waves into analog electrical waves and vice versa. Analog is not the opposite of digital. Analog means that the electrical waves are a more or less exact translation of the acoustic waves. Once transduced to electricity, the acoustic signal can be digitalized, processed and stored.


4.1 Impedance Matching

As we have seen in chapter 3, there is a big difference in acoustic impedance between water and air. Transducers that can very well transmit and receive sound in air, like soft-coned loudspeakers and soft-membraned microphones, do not function very well in the much more resistant medium of water. Underwater transducers need hard ceramics with a displacement big enough to transmit their kinetic energy to the water. "The better the 'impedance match' between the transmitting medium (i.e. ceramic) and the propagation medium (i.e. water), the higher the energy transfer." [Maurer]

Because of the big impedance mismatch between air and water, sound does not get transmitted very well between the two media. Leonardo da Vinci's listening tube was a genius idea, but it was not a very sensitive device.


4.2 Hearing underwater: Bone Conduction

This brings us first to the question: how do human beings hear underwater? Do we use our ears? The eardrums that connect the outer to the inner ear are too soft to be able to pick up sound underwater. We hear underwater sounds through a phenomenon called 'bone conduction'. [Maurer]


[Fig 5 – Illustration credit: The Physics Classroom - www.physicsclassroom.com]

The neck and skull bones are hard enough to pick up the sound, which is then transmitted directly to the inner ear, which is filled with fluid. Underwater, the outer and the middle ear (filled with air) are bypassed.

Because the skull provides only one source of transmission, stereo reception is not possible.(12) We cannot determine the direction from which sound comes underwater: we hear 'omniphonically': sound seems to come from all directions at once.

Another aspect of bone conduction is that it filters out low frequencies as well as ambient noises, which are simply not strong enough to resonate in the body.

Another interesting fact is that it is not possible to stop listening when one is immersed in water. Closing the ears will have no effect. The only way to escape from hearing sound underwater is to stick one's head above the surface.


4.3 Transduction Techniques for Hydrophones

Carbon-button Transducers

"The earliest, and still probably the most sensitive" [Urick, page 3], hydrophone for underwater sound is the carbon-button microphone. The membrane is elastically fixed over a closed capsule filled with an electrically charged layer of carbon grains. This layer reacts to the changes in pressure with changes in electrical resistance. The electrical tension at the output changes analog to the changes in resistance. A wonderful device, that works well also in water. It does not work in great depths, where the static pressure is so big that the membrane cannot move anymore.


[Fig 6 - Illustration adapted from Goerne]

Piezoelectric Transducers

A piezoelectric microphone uses the pressure-electric effect of various crystals, ceramics and synthetic materials such as quartz, bariumtitanate and polyvinylfluorid. When a piezo-electric substance is put under stress, it creates an electrical tension across its surface, due to the displacement of ions inside the crystal.

Piezoelectric microphones are simple in design, easy to build and because of their hardness, very suitable for underwater use.

For my experiments I acquired a piezo-electric hydrophone, the DolphinEar/PRO.


[Fig 7 - Illustration credit: Goodson]

Above the water it sounds like nothing; underwater its sensitivity is indeed surprising. I did my first underwater recording near the Hamburg Harbour by Oevelgoenne. Although it did not reveal a particularly appealing soundscape, it picked up a spectrum of noise, ranging from 20 – 5000 Hz, with a thick layer of noise between 380 and 1380 Hz, peaking around 1200 Hz. Very deep, almost subsonic rumblings near 20 Hz became audible only after filtering out this 'carpet'.

Magnetostrictive Transducers

A third type of transducer suitable for underwater purposes is called magnetostrictive. In a magnetostrictive microphone, changes of shape in a magnetic substance, such as nickel, placed inside a magnetic field, causes that magnetic field to change and an electric charge to be induced.


5. The Speed of Sound in Water: A Practical Experiment

To be able to stay close at home, I chose the Aussenalster in Hamburg as a medium in which to conduct the experiment. The water near the shores is generally too shallow to be useful. One cannot sound a bell in ankle deep water. Conveniently though, around the Aussenalster there are a great number of ramps and bridges, which make it possible to access deeper water without having to wade in it.(13)

From the Schwanenwikbrücke on the eastern shore to the Rabenstrasse 'Alsterdampfer' ramp on the western shore is 990 meter, measured on the map I acquired from the Amt für Geoinformation und Vermessung in Hamburg. The scale of this map is 1:5000 – 100 millimeter on the map equals 500 meter. The measured distance on the map was 198 millimeter, which is 500 x 198/100 = 990 meter.

The Alster is up to 2,5 meter deep. Across the distance there must have been several X-factors. The water is known to be littered with a multitude of garbage objects.

As sound source I chose a ship's bell (acquired through eBay). As recording device a DAT recorder, with a piezoceramic hydrophone and a regular condenser microphone. The experiment was carried out, with the indispensable help of an assistant, as follows:

At the Rabenstrasse ramp the bell was sounded under the water surface. The part of the sound that was audible above the surface was transmitted by a cellphone. At the Schwanenwikbrücke on the other side, the sound of the bell underwater was recorded by the hydrophone on the left channel of the DAT recorder, and the sound from the receiving cellphone was simultaneously recorded by a regular microphone on the right channel of the DAT recorder. The delay between the two signals could then, theoretically, be measured later, once the recording had been transferred to a computer with sound processing software.(14)

Of course, the delay of the cellphone connection had to be taken into account. This was measured as follows: A metronome was recorded on one track of the DAT recorder directly with a microphone and on the second track simultaneously with a second microphone in an adjacent room over a cellphone connection. The recording was then transferred to the audio processing software and was measured on the timeline. The delay was a fairly constant 196 milliseconds.

It turned out to be impossible to recognise the bell signal across the Alster directly. The Alster is not exactly a silent water. Moreover, there was considerable surface noise, in spite of the measuring depth of about 1,5 meter. The sound of the bell simply was not strong enough to be detected directly, concealed as it was in the considerable background noise. Some bandpass filtering helped out: Two main resonance frequencies of the bell are: 400 and 700 Hz as can be seen from the following sonogram, which has been taken from a 'dry' recording of the bell underwater in a bathtub fully padded with thick (old) curtains to avoid reflections.


[Fig 8: 'Dry' recording of the 'Titanic' bell used in the Alster]

Indeed do these frequencies show up in the Alster recording after intensive bandpass filtering, but not quite as regularly as expected. There are a few factors that leave this experiment inconclusive: The delay of the cellphone connection was not measured at the same place and time of the Alster recording. It may have been quite different, and inconstant at the time of the actual experiment. Also, using the same device for measuring and communication at the same time proved to be highly inconvenient, both for the scientist and the assistant. The assistant was not clear when to exactly hit the bell. As the results were highly inconclusive, I decided to repeat the experiment in a quieter water, with a stronger bell and a transmitting device with a smaller and constant delay time, independent from the necessary communication over the cell phones.

As the preferred location I chose the Schaalsee near Zarrentin in Mecklenburg Vorpommern. This is a very beautiful natural environment, a so-called 'Biospärenreservat' which used to lie right in the former Deutsche Demokratische Republik border zone, where 'Zwangsruhe' was enforced for forty years.(15) It is a very quiet area, still, where the water is very silent, apart from the surface noise.

Apart from being quiet, and ideal for relaxation in nature, the Schaalsee happens to be the deepest lake of northern Europe: 72 meter. Unfortunately, the area with the greatest depth is not accessible from the shores.


[Fig 9 – Illustration credit: www.foerderverein-biosphaere-schaalsee.de]

The experiment was conducted from the Seeuferweg on the western shore of the lake a little bit north of the Zarrentin church to Schaliss on the eastern shore. On both sides there are convenient ramps that enable access to deeper water. The maximum depth between those two shores is 58,5 meter. The distance between the sound source and the recording was 1100 meter.

The bell was struck and recorded 1 meter under the water surface. Since the walkie talkie was not able to pick up and transmit the sound of the bell above the water surface, the assistant gave a vocal impulse simultaneously with the bell stroke. It could have worked as an approximation, if the bell had been strong enough to send its sound through a kilometer of water. It wasn't.

Included on the enclosed CD there is the sound of the bell recorded at at distance of 80 meters. The recording shows an interesting echo/reverberation.(16)

Further experiments included the use of an underwater loudspeaker.


[Fig 10: 'Dry' recording of the bell used in the Schaalsee]


6. Convolution – The Emagic Space Designer

The purpose of recording underwater reverb spaces would be to be able to synthesise these spaces in the computer and use them as reverb effects in music production. Artificial (electromechanical) reverb devices have been in use since the mid-thirties, when the first spring reverberation device was designed by Bell Labs. [www.accutronicsreverb.com/history.htm] Digital reverb machines in the nineteen-eighties made room (reverb space) simulation possible. The hardware was mysterious and expensive, and the algorithms behind it were mostly kept secret. The development of the personal computer enabled the creation and application of algorithms independent from expensive hardware. Generations of software plugins emerged, making algorithmic reverb available in an upgradable form at an affordable price.


6.1 Algorithmic Reverb

The reverb effects are created through a complex system of digital delays, filters and sound-altering parameters. [Ziebarth] Because there are so many parameters involved, one seems to have control over a sheer limitless amount of details. This can be very appealing. There has been, and I expect there will be, a big development in this area.


6.2 Convolved Reverb

In the nineteen-nineties there emerged another method of creating digital sound effects. The method of convolution (= folding) does not require detailed knowledge about the acoustic parameters of the room (or sound effect) to be simulated. It is enough to take a sample of the room by recording an impulse together with the room response. This 'response' is the way the room makes the impulse sound through for instance reflections, scattering, absorption and interference. The next step is to simply remove the original impulse from the response, so you are left with the pure response information. This information can be applied (convolved, or folded) to any other audio signal, which will then sound as if it was made in that particular room.

6.3 Impulse or Sweep?

The easiest way to measure the impulse response of a room (17) is through using an extremely short impulse, like a click, a handclap, a blank shot from a pistol, or a bursting balloon. Once the impulse is gone, you are left with the pure room response, which can directly be used. However, the total energy of an impulse together with its response is low in comparison to its peak level. [Emagic, Deconvolution – Background] To get a more energetic response, more energy needs to be put in the room. One of the ways to do that is to use a longer impulse with a high RMS, like a sinesweep. Because the response will be happening while the stimulus is still 'going', the two are mixed together. The stimulus will need to be removed from the response. The method designed for this is called 'deconvolution'.

Emagic has supplied a 'dry' sweep file with their tutorial. Sweeps need a powerful and linear speaker system (18) that can render the sound undistorted.

Emagic states that for instance in the case of reverb devices with modulated reverb (reverb + chorus) it is necessary to use impulses rather than sweeps, because the deconvolution process will "not produce the expected results".


6.4 Linearity and Time-invariance

The room conditions need to be invariable (=stay the same) over the entire duration of the stimulus. If the room modulates its size or shape for instance, this will have a modulating effect on the reverb. This effect is is non-linear: it adds frequencies to the whole that are not present in the original stimulus. Then the stimulus cannot be deconvolved (folded out of) the response anymore. The response is then 'polluted' with frequencies that have the effect of unwanted noise.

It would be so great to be able to sample deep dea reverberation using deconvolution. However, the deep sea environment, apart from being practically inaccessible for civilians, is not a time-invariant environment. It is 'wild', full of 'random functionality'. Waves are moving, currents are moving, and uncharted marine life of no commercial value is moving about in unexpected places. Modulations of all kinds are happening all the time.

Here lies a great challenge for a dedicated programmer. Maurer envisions in his article that "…some simplification may be made in combination with random functionality that might still mimic the dynamic complexity involved with frequency smearing of a broadband sound source underwater."


6.5 The Sound Source

One of the major issues I encountered in pursuing the subject of underwater acoustics was to find suitable and affordable sound sources.

Underwater loudspeakers of any sort of quality are expensive, and I postponed investing in this till the last.

Since the Navy is so well equipped, I searched the Internet in 'Government Auctions' for surplus naval equipment, and found that the Israelian Navy was offering an old batch of submarines, fully equipped, for sale. Slightly above my budget…

I asked both Atlas Elektronik in Bremen and the International Transducer Corp in Santa Barbara California to possibly lend me equipment or point me in a useful direction. Atlas never bothered to answer, while ITC politely informed me that they are not inclined to help me out.

For a while I considered using explosives, but then abandoned the idea, since deploying explosives in the Ausenalster (not far from the US Embassy) might be interpreted as terrorist activity. More importantly, the sound of explosives cannot be exactly repeated. How would I be able to create a 'dry' recording of an underwater explosion?

Then I came to clickfrogs: wonderful little toys, that can make quite some noise, but far too weak to be useful in bigger water spaces.

Then I considered using a bell, just like Colladon and Sturm did. Finally, I acquired two ship's bells through eBay. I used a padded bathtub to create 'dry' recordings of the bells as test and reference signals.

Finally, to be able to sound a sinesweep underwater, I decided to put together a small, portable sound system out of a portable MD player, a car hifi amplifier and an underwater loudspeaker. The frequency range of the 60 Watt speaker is confined to 40-16.000 Hz. The whole is powered by a 12 Volt car battery and can be transported more or less easily to the water front.


7. Sampling Underwater Spaces

7.1 The Bathtub

First I sampled the bathtub, using the ship's bell as a sound source and the 'dry' recording for deconvolution.

But, can a ship's bell actually be used as sound source for deconvolution? According to the ISO 3382:1997 Standard(14) , the impulse source "should not be reverberant in itself". I realised a ship's bell is reverberant in itself. The result (19) is a kind of metallic side-effect, which surely does not represent just the bathtub. The bell in the bathtub is a reverberant space within a reverberant space, so maybe we could call the resulting reverb preset 'Bell in the Tub'.

Moreover, I did not consider the need for sample-precise synchronisation of the test signal and the response recording in the deconvolution process. This will be discussed in the next section.

The sinesweep played in the bathtub made the whole tub resonate in a way that sampling a clean reverb space was not possible.


7.2 Bigger and More Challenging Waters

I decided to reserve the sinesweep for a bigger and more challenging waters: the Schaalsee, where I also attempted once again to measure the speed of sound. The Schaalsee was definitely too big for the ship's bell. The sinesweep did a lot better.

The loudspeaker was suspended from a ramp, at a depth of 3 meters, positioned in such a way that the 180o radiation angle was directed at the body of the lake. Then I assumed three recording positions.

Recording Position One: The first recording was performed in the immediate proximity of the loudspeaker. The hydrophone was suspended at a depth of 3 meters, about 3 meters away from the loudspeaker. There was a lot of resonance from the ramp that I was not able to avoid. (20)

Recording Position Two: The second recording was performed at a distance of 80 meters, with the hydrophone suspended at a depth of 3 meters. (21)

Recording Position Three: The third recording was done at a distance of 1100 meters, with the hydrophone suspended at a depth of 1,5 meters. The reason fo this depth change was simply the fact that the water at the Chaliss ramp was a mere 2 meters deep. (22)

The second recording seemed to be interesting enough to be subjected to a try-out deconvolution. The result was a blobby, sausage-like waveform with something that looks like a modulated DC offset, with faint echoes of the original sinesweep in it.

It is clear from the above that in order to sample underwater spaces other than bathtubs or swimming pools, another equipment and set-up is needed.


7.3 Problems Encountered


The first major problem was the timing. For a successful deconvolution, the 'dry' signal needs to be anchored with the 'wet' signal. Synchronizing the sinesweeps to the level of sample precision by ear proved not possible. If I had used a multitrack recorder that could play and record the signal simultaneously, that problem would have been solved. A simple laptop with multitrack recording software and a proper audio interface would have done it, but then only in Recording Position One, in the immediate proximity of the loudspeaker. Recording at other distances would have been limited to the length of the cables (23) and the availability of ramps. The next ramp on the scene was the one at 80 meters distance.

There must be ways of synchronizing tape recorders remotely and wirelessly. I have not (yet) inquired into this possibility.

Then, once the synchronizing has been solved, there are other factors to be looked at.

Surface conditions

In all the underwater recordings that I did, I have seen, or rather heard, that 'surface conditions' indicates whether the surface is more or less at rest, or in commotion, deploying ripples, wavelets and waves. As became apparent in my experiments, surface commotion inevitably means surface noise, lessening the signal to noise ratio. A big amount of surface commotion makes the signal to noise ratio so small that there seems to be only noise, or, in other words, the desired signals simply disappear in the noise carpet.

To get workable results, sound generation and recording should happen at a much greater depth than three meters. In my next experiments I will have to use boats and longer cables to access deeper water.


7.4 About Sampling

What are we actually sampling when we sample a reverb space? This is an interesting question, and the answer is simple and complex at the same time. In sampling a reverb space, be it a room, a church, a lake, or an underwater cave, one samples EVERYTHING that alters the original dry signal. The 'impulse response' is the total result of playing the signal over a sound system consisting of a player (MD, CD, tape or hard disk), an amplifier and a loudspeaker. Any non-linearities in any component of the sound source system, including the cables and plugs, are as a sum total present in the sample. Any non-linearities in the recording system, from the microphone to the recorder to the recording medium including the cables and plugs, are as a sum total present in the sample, resulting in a poorer signal to noise ratio.

Then there is the ambient noise, which is present everywhere, all the time. I recorded the ambient noise at the Schaalsee, simultaneously above and under the water. (24)

Ambient noise can seriously lessen the signal to noise ration to unworkably low levels.

So when we sample a reverb space, we sample the totality of sound source, room response and recording equipment. Naturally, the better the equipment, the cleaner the result will be.


7.5 The ISO 3382:1997 Standard

The International Standard for Measurement of the reverberation time of rooms with reference to other acoustical parameters says a.o. the following about equipment:

"The sound source should be as close to omni-directional as possible. It shall produce a sound pressure level sufficient to provide decay curves with the required minimum dynamic range without contamination by background noise. Commercial domestic loudspeakers are not acceptable as an omni-directional source."

I definitely used a commercial domestic loudspeaker, and it definitely was not omnidirectional. However, played from the side of the lake at 180o radiation angle, and recorded at a big distance, it would not be possible to distinguish it from an omnidirectional loudspeaker.

"Omni-directional microphones shall be used to detect the sound pressure…"

My Dolphin Ear hydrophone is omnidirectional. In that sense it also comes the closest to the way humans hear underwater. (25)

"The microphone should be as small as possible, and preferably have a maximum diaphragm diameter of 13 mm"

Sound waves with a frequency of 20.000 Hz have a wavelength of 17 mm, and would therefore be able to diffract around an object of 13 mm without problem. Since wavelengths underwater are four times as big as in air, I would conclude that the maximum diaphragm diameter of the hydrophone can be 52 mm. However, my Dolphin Ear has a diameter of 60 mm…

"No microphone position shall be too close to any source position in order to avoid too strong influence from the direct sound. The minimum distance dmin in meters, can be calculated from:

dmin = 2.V/cT

where V is the volume in cubic meters and c the speed of sound, in meters per second and T an estimate of the expected reverberation time, in seconds."

The part of the Schaalsee where I recorded the sinesweeps, contains a very rough estimate of 2000 m x 3000 m x 58,5 m = 351.000.000 cubic meters of water. (26)

The minimum microphone distance for that whole part of the lake would have to be (for an estimated reverb time of 1 second)

dmin = 2.351.000.000/1450 = 2.242068 = 2 x 492 = 984 meter

So at least the Recording Position Three was a good one, although the impulse was clearly not strong enough to reverberate threehundredfifty-one million cubic meter of water!


8. Summary and Conclusion

The inspiration for this thesis was an article by John A. Maurer, who also pointed out some limitations in underwater acoustic research for artistic purposes. The effects described by Robert J. Urick (27) only occur in the bigger dimensions of the ocean, not in the bathtub, nor in the relatively quiet waters of the Alster and the Schaalsee.

Not many people are or have been concerned with underwater acoustics for artistic purposes. The French musician Michel Redolfi is one of them. His website at www.redolfi-music.com is devoted to underwater music.

I wanted to see how far I could come with the equipment that I could get together. Considering the high level of ambient noise underwater, I wonder if it is possible at all to sample underwater spaces using the techniques described in this thesis. There must be other and better ways. I shall not give up my quest.

One of the things I really would like to do is to visit a SOSUS station (28) and use the Deep Sound Channel to create a reverb with some magnitude.

Finally, I would like to thank the people who were crucial in the conduction of my outdoor experiments: Jan Herrmansen who assisted me at the Aussenalster, Uta van Steen who patiently kept striking the bell and running sinesweeps in the Schaalsee, and Chris Krogman, who encouraged me to go on on the point where I wanted to give up.

Hamburg, 20 April, 2004


9. Sources

1. O'Connor J.J. and Robertson E.F. Pythagoras of Samos. (www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Pythagoras.html)

2. Urick, Robert J. Principles of Underwater Sound. 3rd Edition (New York: McGraw-Hill, 1983)

3. Etter, Paul C. Underwater Acoustic Modelling. 2nd Edition (London: E&FN Spon, 1996)

4. Kaharl, Victoria. Sounding Out The Ocean's Secrets. Written with the assistance of Drs. David Bradley, Kenneth Brink, Christopher Clark, Christopher Fox, Peter Mikhalevsky, Walter Munk, Jeffrey Nystuen, and Gary Weir for Beyond Discovery(tm): The Path from Research to HumanBenefit, a project of the National Academy of Sciences. (www.beyonddiscovery.org/content/view.article.asp?a=219)

5. Pike, John. Sound Surveillance System (SOSUS). 2002 (www.globalsecurity.org/intell/systems/sosus.htm)

6. Fox, Chris, Dr. and Staff. Vents Acoustic Monitoring Program: Underwater Acoustics Tutorial. National Oceanic and Atmospheric Administration. 1998 (www.pmel.noaa.gov/vents/acoustics/tutorial/tutorial.html)

7. Maurer, John A. Research in Underwater Sound With Focus On Musical Applications and Computer Synthesis. 1998 Stanford University, California (ccrma-www.stanford.edu/~blackrse/h2o.html)

8. Fish, John P. Acoustics and Sonar Primer. 2002 The Institute for Marine Acoustics (www.marine-group.com/SonarPrimer/SideScanSonar.htm)

9. About Hydrophones. Globalspec: The world's largest database of technical products and services. 2004 (www.globalspec.com)

10. Goodson, Dave and Lepper, Paul. A cheap sensitive hydrophone for monitoring cetacean vocalisations. 1995 Loughborough University of Technology, UK (sonar-fs.lboro.ac.uk/uag/downloads/bender2.pdf)

11. Kuntsal, Ender and Bunker, William A. Guidelines for Specifying Underwater Electroacoustic Transducers. Revised version of a paper presented at UDT 1992 Conference, London, UK ITC International Transducer Corporation, Santa Barbara, California

12. ITC Product Catalogue 2003 ITC International Transducer Corporation, Santa Barbara, California

13. Griesinger, David. Impulse Response Measurements Using All-Pass Deconvolution. Lexicon, Inc. Waltham, Masachussets 02154, USA. 1992 (world.std.com/~griesngr/dgaes92b.pdf)

14. ISO 3382 1997 International Standard. Acoustics - Measurement of the reverberation time of rooms with reference to other acoustical parameters. (pcfarina.eng.unipr.it/Public/Papers/141-JSV00.PDF)

15. Smith, Stephen W. The Scientist and Engineer's Guide to Digital Signal Processing. 1997. Chapter 6. (www.analog.com/processors/ resources/ technicalLibrary/manuals/training/materials/pdf/dsp_book_Ch6.pdf)

16. Goerne, Thomas. Mikrofone in Theorie und Praxis. 5. Auflage 2001 (Elektor-Verlag, Aachen, 1994)

17. Dickreiter, Michael. Handbuch der Tonstudiotechnik. 6. verbesserte Auflage (Saur Verlag GmbH & Co. KG, Muenchen, 1997)

18. The Concise Oxford Dictionary of Current English, fifth edition. (Oxford University Press, 1964)

19. Ziebarth, Mark. Faltungshall – der Perfekte Raum. Keys Magazine, PPV Medien GmbH, Bergkirchen. (February 2004)

20. Henderson, Tom. The Physics Classroom. Glenbrook South High School Glenview, Illinois, USA. 1996-1997 (www.physicsclassroom.com)


10. Footnotes

[1] The Pythagorean Theorem: The square of the hypothenuse of a right triangle equals the sum of the squares of its right sides

[2] Both the date and the name Colladon are spelled differently in different articles; I go with the Urick version.

[3] Fessenden ‘oscillators’ have played a big role until recently for research purposes. [Urick(2) page 3]

[4] This intriguing phenomenon is explained in more detail in chapter 3.

[5] The abbreviations in Fig 1: SURTASS = Surveillance Towed Array Sensor System; NOPF/MEC = Naval Ocean Processing Facility and Meteorology Center; NAVFAC = Naval Facilities Engineering Command

[6] It should be noted that sound can exist, albeit for a relatively short period of time, after its source has ceased, in the form of echoes and reverberation.

[7] Without getting too philosophical and wondering about commonplaces such as the lonely falling tree in the forest, I would say that for a sound to be complete, there needs to be a source, a medium and a receiver.

[8] In a non-sexual sense...

[9] With ‘subjective’ I mean that there must be a human listener involved.

[10] Listen to track 1

[11] Of course I am not trying to suggest that it is only the US Navy that is doing research. All self-respecting Navies do. Especially in the case of underwater acoustics, military research always seems to precede ‘civilian’ research.

[12] So much for underwater stereo equipment in swimming pools!

[13] It was Winter/early Spring at the time of the Alster experiments: it was COLD!

[14] For a specification of the equipment and software used in the experiments, please refer to chapter 7.

[15] This, I would say, is definitely another one of the rare positive outcomes of the Cold War, just like SOSUS

[16] Listen to track 2

[17] I use the word ‘room’ in this context to denote a space, a seascape, or a system.

[18] This was something of a problem for my research, because it seemed not feasible to get a proper underwater loudspeaker. For a while I tried to find other solutions, that would fit better in my budget.

[19] Listen to track 3

[20] Listen to track 4

[21] Listen to track 5

[22] Listen to track 6

[23] Both the loudspeaker cable and the hydrophone cable were 10 meters long

[24] Listen to track 7

[25] See ‘Hearing Underwater’, page 19

[26] A friend of mine asked jokingly if I intended to create standing sound waves in the Schaalsee.

[27] See ‘Surface Scattering’, page 17

[28] Sound Surveillance System: see page 7