Wave Motion 4 Question 17
16. A sound wave of frequency $f$ travels horizontally to the right. It is reflected from a large vertical plane surface moving to left with a speed $v$. The speed of sound in medium is $c$
$(1995,2 M)$
(a) The number of waves striking the surface per second is $f \frac{(c+v)}{c}$
(b) The wavelength of reflected wave is $\frac{c(c-v)}{f(c+v)}$
(c) The frequency of the reflected wave is $f \frac{(c+v)}{(c-v)}$
(d) The number of beats heard by a stationary listener to the left of the reflecting surface is $\frac{v f}{c-v}$
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Answer:
Correct Answer: 16. (c)
Solution:
- Moving plane is like a moving observer. Therefore, number of waves encountered by moving plane,
$$ f _1=f\left(\frac{v+v _0}{v}\right)=f\left(\frac{c+v}{c}\right) $$
Frequency of reflected wave,
$$ f _2=f _1\left(\frac{v}{v-v _s}\right)=f\left(\frac{c+v}{c-v}\right) $$
Wavelength of reflected wave
$$ \lambda _2=\frac{v}{f _2}=\frac{c}{f _2}=\frac{c}{f}\left(\frac{c-v}{c+v}\right) $$
