PHYSICS

echo intensity, the animal can determine whether it is approaching
or receding from the object.
Example. If a bat detects an echo from an insect, it increases the
frequency of pulses to as high as 100 pulses per second. What is the batobject
distance?
Soultion. The distance (D) between the bat and insect is given by:
D = Vt/2 = (340 m/s)·(l/lOO s)/2 = 1.7 m.
The third mechanism is based on the frequency change of the
echo which is called the Doppler effect.
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8.3. THE DOPPLER EFFECT
There is a well known train-spotter's observation that the pitch
of a train's whistle changes as it passes the observer. As the train
approaches, the observer hears a note which is higher than the
true note and on passing, the pitch quickly falls to a lower note
than the true pitch. C. I. Doppler in 1842 was the first to give an
explanation for the phenomenon which has been entitled the
Doppler effect. In the example above, if the frequency of the
whistle is f o when the train is stationary, then the frequency (f)
as detected by an observer alongside the track, differs from f o in
relation to the speed (V) of the train. The fractional change in
the apparent frequency of the whistle (i.e. if - fo)/f o) is related to
the velocity of the train by the formula:
if - fo)lf o = ±VI V, (8.1)
Here V s is the speed of sound. A "+" sign indicates the train is
approaching the observer and a "-" sign indicates the train is
moving away from the trackside observer.
When either the source or the receiver of a propagating wave
moves, there is usually a change in frequency called the Doppler
shift. Such a shift can be used to determine the velocity of the
target along the line to it, which is to say its approach velocity. If
the transmitter generates a frequency of f o ' the velocity of the
sound is ~, and the approach velocity is a much smaller value
(V), the received frequency is approximated by:
1 = 10 (I + 2V a )
V s
(8.2)
The frequency shift is proportional to the approach velocity:
Af =1 - 10 to Va
s
(8.3)
Example. What is the Doppler frequency shift received by a bat, if the
insect is immobile with respect to the bat's motion with the velocity
equal to 5 m/s. The frequency of the bat's sound is 60 kHz.
Solution. We can insert the values into the Doppler shift equation (8.3):
fj.f = 2 fo Va 2·60 ·10 3 Hz 5 m/s = 1. 76 kHz
V, 340 m/s
The Doppler effect enables one to measure the translational,
rotational speed, and the frequency of flagellum beatings of microorganisms.
The Doppler shift of sound waves scattered by moving
erythrocytes (red blood cells) is used to measure the speed
of blood flow; also the Doppler shift of light waves scattered by
moving blood in the retina can be used to study blood flow there.
,r/
~~ . .If'.
1"'4 ~
"I love hearing that lonesome wail
ofthe train whistle as the magnitude
ofthe frequency ofthe wave changes
due to the Doppler effect. "
(From R.A. Serway, 1992)
Chapter 9. ACOUSTOBIOLOGY
Acoustobiology is the branch of biophysics which studies of
how living organisms hear sounds, and how sounds affect them
physically and behaviorally.
9.1. ACOUSTORECEPTION
Mammals. The ear is one of the most remarkable devices
known to science. This section considers several of the properties
and mechanisms of the ear. The ear is divided into three parts
designated simply as outer, middle and inner ear (fig. 9.1).
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