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, the expression for the beat frequency he

Question

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, the expression for the beat frequency heard by the motorist is

TestHub · Accepted Answer

The motorist receives two sound waves, direct one from the band and that reflected from the wall, figure. For direct sound waves, apparent frequency

$f^{'} = \frac{(v + v_{m}) f}{v + v_{b}}$

For reflected sound waves.

Frequency of sound wave reflected from the wall

$f^{''} = \frac{v \times f}{v - v_{b}}$

Frequency of reflected waves as received by the moving motorist,

$f^{'} = \frac{(v + v_{m}) f^{''}}{v} = \frac{(v + v_{m}) f}{v - v_{b}}$

$∴$ Beat frequency $= f^{''} - f^{'}$

$= \frac{(v + v_{m}) f}{v - v_{b}} - \frac{(v + v_{m}) f}{v + v_{b}} = \frac{2 v_{b} (v + v_{m}) f}{v^{2} - v_{b}^{2}}$

Physics - Sound Wave Question with Solution | TestHub

Options:

Doubts & Discussion