Wave Motion 4 Question 27
25. A band playing music at a frequency $f$ is moving towards a wall at a speed $v _b$. A motorist is following the band with a speed $v _m$. If $v$ is the speed of sound. Obtain an expression for the beat frequency heard by the motorist.
(1997, 5M)
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Answer:
Correct Answer: 25. $\frac{2 v _b\left(v+v _m\right)}{v^{2}-v _b^{2}}$
Solution:
- Frequency received in case 1 .
$$ f _1=f\left(\frac{v+v _m}{v+v _b}\right) $$
and in case 2, $f _2=f\left(\frac{v+v _m}{v-v _b}\right)$
Obviously, $f _2>f _1$
$\therefore$ Beat frequency,
$$ \begin{aligned} f _b=f _2-f _1 & =f\left(\frac{v+v _m}{v-v _b}\right)-f\left(\frac{v+v _m}{v+v _b}\right) \\ \text { or } \quad f _b & =\frac{2 v _b\left(v+v _m\right)}{v^{2}-v _b^{2}} \end{aligned} $$
