The Blind Watchmaker 5
he carrier frequency swoops up or down about an octave. If you think of it as its sound equivalent, each radar emission can be thought of as a swooping wolf-whistle. The advantage of chirp radar, as opposed to the fixed pitch pulse, is the following. It doesn’t matter if the original chirp is still going on when the echo returns. They won’t be confused with each other. This is because the echo being detected at any given moment will be a reflection of an earlier part of the chirp, and will therefore have a different pitch.
If bats are capable of boosting their sampling rates to 200 pulses per second, why don’t they keep this up all the time? Since they evidently have a rate control ‘knob’ on their ‘stroboscope’, why don’t they turn it permanently to maximum, thereby keeping their perception of the world at its most acute, all the time, to meet any emergency? One reason is that these high rates are suitable only for near targets. If a pulse follows too hard on the heels of its predecessor it gets mixed up with the echo of its predecessor returning from a distant target. Even if this weren’t so, there would probably be good economic reasons for not keeping up the maximum pulse rate all the time. It must be costly producing loud ultrasonic pulses, costly in energy, costly in wear and tear on voice and ears, perhaps costly in computer time. A brain that is processing 200 distinct echoes per second might not find surplus capacity for thinking about anything else. Even the ticking-over rate of about 10 pulses per second is probably quite costly, but much less so than the maximum rate of 200 per second. An individual bat that boosted its tick-over rate would pay an additional price in energy, etc., which would not be justified by the increased sonar acuity. When the only moving object in the immediate vicinity is the bat itself, the apparent world is sufficiently similar in successive tenths of seconds that it need not be sampled more frequently than this. When the salient vicinity includes another moving object, particularly a flying insect twisting and turning and diving in a desperate attempt to shake off its pursuer, the extra benefit to the bat of increasing its sample rate more than justifies the increased cost. Of course, the considerations of cost and benefit in this paragraph are all surmise, but something like this almost certainly must be going on.
The engineer who sets about designing an efficient sonar or radar device soon comes up against a problem resulting from the need to make the pulses extremely loud. They have to be loud because when a sound is broadcast its wavefront advances as an ever-expanding sphere. The intensity of the sound is distributed and, in a sense, ‘diluted’ over the whole surface of the sphere. The surface area of any sphere is proportional to the radius squared. The intensity of the sound at any particular point on the sphere therefore decreases, not in proportion to the distance (the radius) but in proportion to the square of the distance from the sound source, as the wavefront advances and the sphere swells. This means that the sound gets quieter pretty fast, as it travels away from its source, in this case the bat.
When this diluted sound hits an object, say a fly, it bounces off the fly. This reflected sound now, in its turn, radiates away from the fly in an expanding spherical wavefront. For the same reason as in the case of the original sound, it decays as the square of the distance from the fly. By the time the echo reaches the bat again, the decay in its intensity is proportional, not to the distance of the fly from the bat, not even to the square of that distance, but to something more like the square of the square — the fourth power, of the distance. This means that it is very very quiet indeed. The problem can be partially overcome if the bat beams the sound by means of the equivalent of a megaphone, but only if it already knows the direction of the target. In any case, if the bat is to receive any reasonable echo at all from a distant target, the outgoing squeak as it leaves the bat must be very loud indeed, and the instrument that detects the echo, the ear, must be highly sensitive to very quiet sounds — the echoes. Bat cries, as we have seen, are indeed often very loud, and their ears are very sensitive.
Now here is the problem that would strike the engineer trying to design a bat-like machine. If the microphone, or ear, is as sensitive as all that, it is in grave danger of being seriously damaged by its own enormously loud outgoing pulse of sound. It is no good trying to combat the problem by making the sounds quieter, for then the echoes would be too quiet to hear. And it is no good trying to combat that by making the microphone (‘ear’) more sensitive, since this would only make it more vulnerable to being damaged by the, albeit now slightly quieter, outgoing sounds! It is a dilemma inherent in the dramatic difference in intensity between outgoing sound and returning echo, a difference that is inexorably imposed by the laws of physics.
What other solution might occur to the engineer? When an analogous problem struck the designers of radar in the Second World War, they hit upon a solution which they called ‘send/receive’ radar. The radar signals were sent out in necessarily very powerful pulses, which might have damaged the highly sensitive aerials (American ‘antennas’) waiting for the faint returning echoes. The ‘send/receive’ circuit temporarily disconnected the receiving aerial just before the outgoing pulse was about to be emitted, then switched the aerial on again in time to receive the echo.
Bats developed ‘send/receive’ switching technology long long ago, probably millions of years before our ancestors came down from the trees. It works as follows. In bat ears, as in ours, sound is transmitted from the eardrum to the microphonic, sound-sensitive cells by means of a bridge of three tiny bones known (in Latin) as the hammer, the anvil and the stirrup, because of their shape. The mounting and hinging of these three bones, by the way, is exactly as a hi-fi engineer might have designed it to serve a necessary ‘impedance-matching’ function, but that is another story. What matters here is that some bats have well-developed muscles attached to the stirrup and to the hammer. When these muscles are contracted the bones don’t transmit sound so efficiently — it is as though you muted a microphone by jamming your thumb against the vibrating diaphragm. The bat is able to use these muscles to switch its ears off temporarily. The muscles contract immediately before the bat emits each outgoing pulse, thereby switching the ears off so that they are not damaged by the loud pulse. Then they relax so that the ear returns to maximal sensitivity just in time for the returning echo. This send/receive switching system works only if split-second accuracy in timing is maintained. The bat called Tadarida is capable of alternately contracting and relaxing its switching muscles 50 times per second, keeping in perfect synchrony with the machine gun-like pulses of ultrasound. It is a formidable feat of timing, comparable to a clever trick that was used in some fighter planes during the First World War. Their machine guns fired ‘through’ the propeller, the timing being carefully synchronized with the rotation of the propeller so that the bullets always passed between the blades and never shot them off.
The next problem that might occur to our engineer is the following. If the sonar device is measuring the distance of targets by measuring the duration of silence between the emission of a sound and its returning echo — the method which Rousettus, indeed, seems to be using — the sounds would seem to have to be very brief, staccato pulses. A long drawn-out sound would still be going on when the echo returned, and, even if partially muffled by send/receive muscles, would get in the way of detecting the echo. Ideally, it would seem, bat pulses should be very brief indeed. But the briefer a sound is, the more difficult it is to make it energetic enough to produce a decent echo. We seem to have another unfortunate trade-off imposed by the laws of physics. Two solutions might occur to ingenious engineers, indeed did occur to them when they encountered the same problem, again in the analogous case of radar. Which of the two solutions is preferable depends on whether it is more important to measure range (how far away an object is from the instrument) or velocity (how fast the object is moving relative to the instrument). The first solution is that known to radar engineers as ‘chirp radar’.
We can think of radar signals as a series of pulses, but each pulse has a so-called carrier frequency. This is analogous to the ‘pitch’ of a pulse of sound or ultrasound. Bat cries, as we have seen, have a pulse-repetition rate in the tens or hundreds per second. Each one of those pulses has a carrier frequency of tens of thousands to hundreds of thousands of cycles per second. Each pulse, in other words, is a high-pitched shriek. Similarly, each pulse of radar is a ‘shriek’ of radio waves, with a high carrier frequency. The special feature of chirp radar is that it does not have a fixed carrier frequency during each shriek. Rather, t
Human radar designers have made good use of this ingenious technique. Is there any evidence that bats have ‘discovered’ it too, just as they did the send/receive system? Well, as a matter of fact, numerous species of bats do produce cries that sweep down, usually through about an octave, during each cry. These wolf-whistle cries are known as frequency modulated (FM). They appear to be just what would be required to exploit the ‘chirp radar’ technique. However, the evidence so far suggests that bats are using the technique, not to distinguish an echo from the original sound that produced it, but for the more subtle task of distinguishing echoes from other echoes. A bat lives in a world of echoes from near objects, distant objects and objects at all intermediate distances. It has to sort these echoes out from each other. If it gives downward-swooping, wolf-whistle chirps, the sorting is neatly done by pitch. When an echo from a distant object finally arrives back at the bat, it will be an ‘older’ echo than an echo that is simultaneously arriving back from a near object. It will therefore be of higher pitch. When the bat is faced with clashing echoes from several objects, it can apply the rule of thumb: higher pitch means farther away.
The second clever idea that might occur to the engineer, especially one interested in measuring the speed of a moving target, is to exploit what physicists call the Doppler Shift. This may be called the ‘ambulance effect’ because its most familiar manifestation is the sudden drop in pitch of an ambulance’s siren as it speeds past the listener. The Doppler Shift occurs whenever a source of sound (or light or any other kind of wave) and a receiver of that sound move relative to one another. It is easiest to think of the sound source as motionless and the listener as moving. Assume that the siren on a factory roof is wailing continuously, all on one note. The sound is broadcast outwards as a series of waves. The waves can’t be seen, because they are waves of air pressure. If they could be seen they would resemble the concentric circles spreading outwards when we throw pebbles into the middle of a still pond. Imagine that a series of pebbles is being dropped in quick succession into the middle of a pond, so that waves are continuously radiating out from the middle. If we moor a tiny toy boat at some fixed point in the pond, the boat will bob up and down rhythmically as the waves pass under it. The frequency with which the boat bobs is analogous to the pitch of a sound. Now suppose that the boat, instead of being moored, is steaming across the pond, in the general direction of the centre from which the wave circles are originating. It will still bob up and down as it hits the successive wavefronts. But now the frequency with which it hits waves will be higher, since it is travelling towards the source of the waves. It will bob up and down at a higher rate. On the other hand, when it has passed the source of the waves and is travelling away the other side, the frequency with which it bobs up and down will obviously go down.
For the same reason, if we ride fast on a (preferably quiet) motorbike past a wailing factory siren, when we are approaching the factory the pitch will be raised: our ears are, in effect, gobbling up the waves at a faster rate than they would if we just sat still. By the same kind of argument, when our motorbike has passed the factory and is moving away from it, the pitch will be lowered. If we stop moving we shall hear the pitch of the siren as it actually is, intermediate between the two Doppler-shifted pitches. It follows that if we know the exact pitch of the siren, it is theoretically possible to work out how fast we are moving towards or away from it simply by listening to the apparent pitch and comparing it with the known ‘true’ pitch.
The same principle works when the sound source is moving and the listener is still. That is why it works for ambulances. It is rather implausibly said that Christian Doppler himself demonstrated his effect by hiring a brass band to play on an open railway truck as it rushed past his amazed audience. It is relative motion that matters, and as far as the Doppler Effect is concerned it doesn’t matter whether we consider the sound source to be moving past the ear, or the ear moving past the sound source. If two trains pass in opposite directions, each travelling at 125 m.p.h., a passenger in one train will hear the whistle of the other train swoop down through a particularly dramatic Doppler shift, since the relative velocity is 250 m.p.h.
The Doppler Effect is used in police radar speed-traps for motorists. A static instrument beams radar signals down a road. The radar waves bounce back off the cars that approach, and are registered by the receiving apparatus. The faster a car is moving, the higher is the Doppler shift in frequency. By comparing the outgoing frequency with the frequency of the returning echo the police, or rather their automatic instrument, can calculate the speed of each car. If the police can exploit the technique for measuring the speed of road hogs, dare we hope to find that bats use it for measuring the speed of insect prey?
The answer is yes. The small bats known as horseshoe bats have long been known to emit long, fixed-pitch hoots rather than staccato clicks or descending wolf-whistles. When I say long, I mean long by bat standards. The ‘hoots’ are still less than a tenth of a second long. And there is often a ‘wolf-whistle’ tacked onto the end of each hoot, as we shall see. Imagine, first, a horseshoe bat giving out a continuous hum of ultrasound as it flies fast towards a still object, like a tree. The wavefronts will hit the tree at an accelerated rate because of the movement of the bat towards the tree. If a microphone were concealed in the tree, it would ‘hear’ the sound Doppler-shifted upwards in pitch because of the movement of the bat. There isn’t a microphone in the tree, but the echo reflected back from the tree will be Doppler-shifted upwards in pitch in this way. Now, as the echo wavefronts stream back from the tree towards the approaching bat, the bat is still moving fast towards them. Therefore there is a further Doppler shift upwards in the bat’s perception of the pitch of the echo. The movement of the bat leads to a kind of double Doppler shift, whose magnitude is a precise indication of the velocity of the bat relative to the tree. By comparing the pitch of its cry with the pitch of the returning echo, therefore, the bat (or rather its on-board computer in the brain) could, in theory, calculate how fast it was moving towards the tree. This wouldn’t tell the bat how far away the tree was, but it might still be very useful information, nevertheless.
If the object reflecting the echoes were not a static tree but a moving insect, the Doppler consequences would be more complicated, but the bat could still calculate the velocity of relative motion between itself and its target, obviously just the kind of information a sophisticated guided missile like a hunting bat needs. Actually some bats play a trick that is more interesting than simply emitting hoots of constant pitch and measuring the pitch of the returning echoes. They carefully adjust the pitch of the outgoing hoots, in such a way as to keep the pitch of the echo constant after it has been Doppler-shifted. As they speed towards a moving insect, the pitch of their cries is constantly changing, continuously hunting for just the pitch needed to keep the returning echoes at a fixed pitch. This ingenious trick keeps the echo at the pitch to which their ears are maximally sensitive — important since the echoes are so faint. They can then obtain the necessary information for their Doppler calculations, by monitoring the pitch at which they are obliged to hoot in order to achieve the fixed-pitch echo. I don’t know whether man-made devices, either sonar or radar, use this subtle trick. But on the principle that most clever ideas in this field seem to have been developed first by bats, I don’t mind betting that the answer is yes.
It is only to be expected that these two rather different techniques, the Doppler shift technique and the ‘chirp radar
’ technique, would be useful for different special purposes. Some groups of bats specialize in one of them, some in the other. Some groups seem to try to get the best of both worlds, tacking an FM ‘wolf-whistle’ onto the end (or sometimes the beginning) of a long, constant-frequency ‘hoot’. Another curious trick of horseshoe bats concerns movements of their outer ear flaps. Unlike other bats, horseshoe bats move their outer ear flaps in fast alternating forward and backward sweeps. It is conceivable that this additional rapid movement of the listening surface relative to the target causes useful modulations in the Doppler shift, modulations that supply additional information. When the ear is flapping towards the target, the apparent velocity of movement towards the target goes up. When it is flapping away from the target, the reverse happens. The bat’s brain ‘knows’ the direction of flapping of each ear, and in principle could make the necessary calculations to exploit the information.
Possibly the most difficult problem of all that bats face is the danger of inadvertent ‘jamming’ by the cries of other bats. Human experimenters have found it surprisingly difficult to put bats off their stride by playing loud artificial ultrasound at them. With hindsight one might have predicted this. Bats must have come to terms with the jamming-avoidance problem long ago. Many species of bats roost in enormous aggregations, in caves that must be a deafening babel of ultrasound and echoes, yet the bats can still fly rapidly about the cave, avoiding the walls and each other in total darkness. How does a bat keep track of its own echoes, and avoid being misled by the echoes of others? The first solution that might occur to an engineer is some sort of frequency coding: each bat might have its own private frequency, just like separate radio stations. To some extent this may happen, but it is by no means the whole story.