wave_mechanics critical_thinking Question 12
Question: A sound wave of frequency n travels horizontally to the right. It is reflected from a large vertical plane surface moving to the left with a speed v. The speed of sound in the medium is c, then
[IIT 1995; BCECE 2005]
Options:
A) The frequency of the reflected wave is $ \frac{\nu (c+v)}{c-v} $
B) The wavelength of the reflected wave is $ \frac{c(c-v)}{\nu (c+v)} $
C) The number of waves striking the surface per second is $ \frac{\nu (c+v)}{c} $
D) The number of beats heard by a stationary listener to the left of the reflecting surface is $ \frac{\nu \ v}{c-v} $
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Answer:
Correct Answer: B
Solution:
Number of waves striking the surface per second (or the frequency of the waves reaching surface of the moving target )$ n’=\frac{(c+v)}{\lambda } $
$ =\frac{\nu (c+v)}{c} $ Now these waves are reflected by the moving target (Which now act as a source).
Therefore apparent frequency of reflected second $ n’’=( \frac{c}{c-v} )n’ $
$ =\nu ( \frac{c+v}{c-v} ) $ The wavelength of reflected wave $ =\frac{c}{n’’}=\frac{c(c-v)}{\nu (c+v)} $ The number of beats heard by stationary listener $ =n’’-\nu =\nu ( \frac{c+v}{c-v} )-\nu =\frac{2\nu v}{(c-v)} $
BETA
