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159. Problem 20.65 (RHK) A device that contains a transmitter and a receiver of
waves in a single instrument is used to measure the speed V of a target object
(idealised as a flat plate) that is moving directly toward the unit,
by analysing waves reflected from it. (a) We have to apply the Doppler
equations twice, first with the target as observer and with the target as a
source, and have to show that the frequency
where v is the speed of the waves. (b) In great
many practical applications,
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of
the reflected waves at the receiver is related to their source frequency
by 
in
this case, we have to show that the equation above becomes 
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Solution: Click For PDF Version (a) Let the speed of the target which is moving toward the instrument be V. Let the source frequency be
Frequency of the waves received by the target,
Now the moving target becomes a moving source. We will now calculate the
frequency
Let
Substituting for
(b) In great many practical situations
We thus find
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and
be the
wavelength of the waves emitted by the transmitter of the instrument.
,
by the Doppler effect will be
measured
by the stationary detector. 
be the
wavelength measured by the detector. As the source is moving toward the detector
with speed V and is emitting waves of frequency
the
wavelength
, we get
, then
