Bats fly in the dark.  Dolphins and whales swim in water, which absorbs light much faster than air does.  So these animals need a way of finding food or finding their way, which doesn’t involve light.  Sound is the answer.  The sounds they emit seem very strange to us, and have presumably evolved to suit their needs.  This page does not describe any particular species: it only discusses general physical principles.

A basic problem with sound is that there is generally no source of illumination corresponding to the sun and the moon for light.  In some special cases there is a regular source of sound, such as a waterfall or a babbling stream in a mountain valley, but these are hardly ubiquitous enough to be useful..  And of course prey animals, like submariners, do not to emit unnecessary sounds which might help their predators.  Quite the reverse – in the long evolutionary interaction between species, the prey have evolved means of silencing their movements, while the predators have improved their hearing.  The prey have of course improved their ability to hear predators, who in turn have reduced their emissions as much as possible, so that an owl is to us completely silent.  

In general, animals have to provide their own sources of sound.  This presents a problem.  The intensity of the emitted sound falls away rapidly with distance – in fact the intensity is inversely proportional to the square of the distance.  At ten times the distance, the intensity is down by a factor of a hundred.  Worse still, most of the sound that is reflected from objects does not come back to the emitter – it goes in all directions.  And what does come back is also attenuated by the inverse square law – ten times the distance gives one ten-thousandth of the intensity.  No doubt the prey reflects as little sound as possible. 

One answer to this is a logarithmic response, so that minute sounds are audible without the ear being deafened by loud ones . In human terms this means that the change from a 1 watt amplifier to a 10 watt amplifier sounds much the same as going from 10 watts to 100 watts.  It also makes the production of many kinds of music much more possible.  If a 100-piece orchestra sounded 100 times louder than one violin then a violin concerto would hardly be feasible.  In fact things could have been  even worse, because many musical instruments can produce far more power than a violin.  But by careful orchestration, and the fact of the logarithmic response, all is well for lovers of the violin.  And of course we can also hear the different instruments of the orchestra quite clearly in many cases.

Emission of sound requires energy.  For a flying animal like a bat the direct power consumption and the power needed to carry the equipment is a burden.  The evolved system is a compromise between the need for greater sound power and the need  to reduce energy consumption.

What kind of sound is best for making and detecting echoes?  The simplest sound is perhaps a very short click, with a rectangular waveform.  This simple statement conceals a question – Is it the displacement or the velocity which is rectangular?  In the examples below the displacement has a rectangular waveform.  In reality, no signal can actually be rectangular, because the sharp step would require infinite Bandwidth, and these examples have a sloping front and rear edge.  The shorter the click, the more accurately we can time it and distinguish multiple echoes.  

The pictures below show oscilloscope traces of clicks and their echoes.  Please click on a picture to hear the sound.  A bat which is three metres from an insect will hear an echo after the time it takes the sound to travel six metres, about eighteen milliseconds.  The sounds in this web page are slower by a large factor, of the order of a hundred, compared with bat sounds, in order to make them easily audible.  The size of the echoes has also been greatly exaggerated to make them easy to hear.  The horizontal divisions in these pictures represent 0.1 second, so each picture represents 0.8 seconds.  The second, third and fourth pictures gives some idea of the ability of human hearing to resolve simple clicks.

Click on these pictures to hear the sounds.  Then choose  ‘Open file from its current location’.

We can even work out how short the clicks need to be.  Suppose a bat needs to locate a moth to an accuracy of 1 cm.  The speed of sound being about 330 m/second, we can find 2 X 0.01m/330 m/s = 0.00006 seconds = 0.06 milliseconds, or 60 microseconds.   The factor of two comes in because the sound has to make every part of the journey twice – there and back.

There is a disadvantage, though.  Thousands of bats clicking their way out of a cave would have to distinguish their own clicks from the clicks of other bats.  The languages of people have occasionally used clicks, but never as the only components.  Other sounds are used as well.  Most languages comprise a rich collection of sounds, probably far more than the necessary  minimum, but the redundancy helps to achieve clarity in noisy surroundings.  There are far more letters in alphabets than are strictly necessary.  Digital transmission systems usually use only two values, 1 and 0, which are used in many different combinations.  These systems often use extra bits of information to guard against error.  The cost of the extra bits in bandwidth and power is more than offset by the gain in fidelity of transmission.  

It pays to be different, even if you are not listening for echoes.  The singer who doesn’t sound like any other, the composer who is recognisable from a few bars of music, the actor with a distinctive voice – all may have a big advantage.  Birds and animals too, trying to establish and hold a territory or impress a female, need to be better than any competitors within reach.  A click is not necessarily the thing to use, any more than a diet of drum solos is varied enough for most musical tastes.

Perhaps a better sound than a click is a short burst of oscillation.  The frequency can be unique to each individual.  There are two other advantages.  In a click, nothing much happens between the beginning and the end.  But with a tone-burst there is energy all the way through, and this can provide information if the hearing system is based on frequency rather than timing.  Most people can distinguish two tones better than they can estimate the time between two clicks.  See and hear the sounds depicted below.  The second advantage of a tone is that if there is relative movement the frequency of the echo may be shifted by the Döppler effect, which is familiar from the sound of a passing ambulance.

In the example above, the bat would need one cycle of oscillation to be less than 60 microseconds long.  This means a minimum frequency of more than 16 kHz.  Bat sounds  in fact go a lot higher than this, well into the region of ultrasound, because they need to detect very tiny insects..  To examine internal organs in a human body, or an unborn baby, or flaws in an industrial artefact, frequencies have to be a lot higher still, because much finer detail is needed, and because the speed of sound in solids (steel 6000 m/s) and liquids (water 1500 m/s) is much higher than it is in air, which means longer wavelengths for a given frequency.  Frequencies of up to 100 MHz, sometimes even more, have been used.

In the next two pictures a simple burst of 40 cycles at 1 kHz was emitted.  The first picture simulates a simple echo from a very small reflecting object, with the echo expanded.  The second picture simulates the example of a structured reflecting object that has sent back multiple echoes.  Can you hear the small difference in the two echoes?  The scale is again 0.1 second per division   Perhaps the complex echo could be analysed to find out something about the reflecting object.  One problem is the difficulty of distinguishing amplitude variations caused by actual parts of the object from those caused by Interference from reflections from different parts.

Click on these pictures to hear the sounds.  Then choose  ‘Open file from its current location’.

It may be possible to do even better than the simple tone-burst, by sending a tone-burst in which the frequency sweeps up or down during the burst.  This can be called  a chirp.  At any one frequency there is a lot less energy than before, but there is energy at many different frequencies, increasing the chance of getting the right information back.  The sounds of humpback whales illustrate this type of sound very well, though in a very complex way.

The next picture shows a chirp from 200 Hz to 4200 Hz.  Because the cycles are too close to see, the beginning and end have been expanded in the second and third traces.  You can see the difference in the periods of the first three cycles.  The chirp lasts about one second.  The fourth trace is a frequency spectrum of the chirp, on a logarithmic vertical scale.  The small wrinkles and the slopes at the ends are caused by the abrupt start and finish in the time domain.  The pages on Bandwidth and Interference give a little more explanation of this type of phenomenon.

Click on this picture to hear the sounds.  Then choose  ‘Open file from its current location’.

In the next picture we see the result of a chirp reflecting from two identical objects.  With enough processing power, we can obtain some information about the distance between the reflecting objects.  The beating effect that you see (and hear if you listen carefully) is caused because of the time delay, 5 milliseconds, between the two echoes.  At certain frequencies this time delay results in the signals adding constructively.  In between, they add destructively.  The frequency spectrum below the time trace shows the same result in a different way.  The deep plunging troughs reflect the logarithmic scale.  The number of bumps is the same in both graphs.  If the time delay were increased, the number of bumps per second would increase, and  might be impossible to hear. This is where the frequency domain comes into play.

Click on this picture to hear the sounds.  Then choose  ‘Open file from its current location’.

How do we measure the distance between the objects?  In fact we can only measure the distance in the line of sight.  The oscilloscope scale is 0.2 seconds/division for the top trace.  There are two bumps per division in the picture above.  So there is one bump per 0.1 seconds, or 10 bumps/second.   But unless we know something about the chirp we can go no further.  The spectrum is what gives us the answer.  Let’s start again.  From the previous picture we see that the frequency scale of the lowest trace is 0.5 kHz//division, or 500 Hz/div.  We can see that five bumps occupy four divisions, so there are 1.25 bumps/div.  This means 2.5 bumps per kHz, or one bump per 400 Hz   

We also know that the bumps are at frequencies where the two reflections are in phase.  This happens when one wave is an exact number of cycles out of step with the other.  So 400 Hz means one step in the number of cycles.  The reciprocal of 400 Hz is 2.5 milliseconds, which was the delay fed into the generator.  So the reflections differ by 2.5 ms.  Because the sound goes there and back, it takes 1.25 ms to cover the distance between the objects.  Knowing the speed of sound in air, 330 m/s, we could work out the distance between the objects as 0.00125 X 330 metres, about 40 cm.  Note that the signal is actually too long to resolve the objects directly, unlike the simple click method.  Whether any animal can do this is another matter.

A complicated object would generate more complicated echoes, so these simple ideas must be regarded as only hints of the possibilities.  Just as the wings and bones of bats and birds  are in some ways more sophisticated in construction than the wings and spars of aircraft, evolution will have refined the transmission and receiving apparatus of bats.  And the costs of complex construction my be far less for an evolved animal than for manufacture, because the development costs have been paid by past generations.  Bats can adjust the sounds to suit the circumstances.  When a moth is far away, the minimum number of pulses should be sent, to try to avoid alerting the moth.  But as the moth is approached, and it takes avoiding action a greater rate of pulsing is needed to track it adequately.  The bat is doing a lot of data processing while it locates and closes on a moth.  

The brain of a flying animal is necessarily limited in weight and power consumption, and so we would expect to find larger brains in walking animals.  Those animals that swim and are buoyant have even less constraint on brain size, and  the brains of dolphins and whales can indeed by very large.  One peculiar phenomenon is the beaching of whales.  Perhaps a very shallow beach attenuates their sound waves, preventing the echoes from getting back, and they think that there is only open sea ahead.

In order to achieve directional accuracy the bat needs to transmit a narrow beam of sound and to receive in the same way.  This is explained in Diffraction and Side Lobes.  Like everything else in nature, this is a compromise, bigger nose-lobes and ear-lobes means bigger drag.  If the ear-lobes are much longer than their width, they will be more directional in one direction the other.  It would pay to have them sticking out of the head about about right angles to each other, though being up to 30 degrees off would not make much difference in practice.

Some Links to Bat Sites      Bat Links

Like bats and whales, people can use use sounds for location.  At sea, sonic beams can be used to locate submarines and underwater obstacles.  They may also be used to map the sea-bed and to search for lost ships or aircraft.  On land, ultrasonic beams are used in human diagnostics and for non-destructive testing for internal flaws in manufactured objects.  Inspecting the interior of a weld or a piece of metal or composite without taking apatr is a necessity in many industries.  Conversely, a powerful ultrasonic beam can clean dirty surfaces and break up kidney stones.

As in the case of bats, there is no general source of illumination such as light provides for sight, or the heat that pit vipers use to detect their prey.  It seems that where the illumination is provided, nature has evolved image making devices, but where the illumination has to be provided, only a beam can be made, and any image has to built up by scanning.

So it is with ultrasonics.   A beam of sound is made by sending a short pulse of electrical energy into a transducer.  A transducer is a device for converting one kind of energy into another, one kind usually being electrical energy.  Loudspeakers and microphones are transducers.  We don’t usually include electric lights because normally as transducer is used with some kind of signal.  The transducer is often a piece of piezo-electric crystal, which changes its size minutely when in an electric field.  Like many transducers, it works the other way round – if you squeeze a piezo-electric crystal it creates an electric field.  This is used in a type of gas-lighter.  Some bat detectors use a piezo-electric crystal.

The sonar of bats and submarines differs from industrial and medical imaging in that the the latter cases have control of the target.  So a scanning system can be constructed which enables a picture to be built up.  There are several basic systems.  The first simply measures the time from the transmitted pulse to the received pulse and deduces a distance.  The second scans along a line and gives a profile of distances, while the third scans many parallel lines in  succession, in the manner of a TV system, and constructs an image in two dimensions.  A fourth way is to use tomography by sending a beam in from many different directions in the same plane, and computing an image of that slice through the object, using the recorded signals.

To get some idea of the difficulty of finding something on the sea bed using sonar, imagine looking for a greenish brown frisbee on a dark night in a field full of cowpats and tussocks, using only a torch, and being so short-sighted that anything more than six feet away looks as fuzzy as the torch beam.

Here is a rough idea of the way the beam starts out from the transducer.  

For more explanation please click on Wave Beams.

When an electrical pulse reaches a piezo-electric crystal, the crystal is liable to ring like a bell, because it is an elastic solid.  The first diagram above shows a fairly well damped example.  This has a bad effect on the images, which are liable to be covered in waves of light and dark.  Damping the crystal can reduce the effect, but also absorbs energy and reduces the intensity of the beam.  The second diagram illustrates this.  The pulse is usually a compromise.  

A very ingenious technique to make a narrow pulse is to use a specially shaped electrical pulse that cancels the resonance once the crystal has emitted the main pulse.  The frequency spectrum of the pulse effectively has a gap at the resonant frequency of the crystal, and so cannot excite it.  This is quite a feat – imagine trying to strike a bell in such a way that it makes a loud noise that isn’t a ring.  Nevertheless, a transducer can indeed be excited in the correct way.

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