Question

The pitch of a sound source appears to be 20% decreased to an observer. The velocity of source with respect to the observer will be

• A. 0.825 m$s^{-1}$
• B. 8.25 m$s^{-1}$
• C. 82.5 m$s^{-1}$
• D. 330 m$s^{-1}$

Answer 1

The correct option is C 82.5 m$s^{-1}$

Velocity of source w.r.t observer $v_{source}=vm/s$

Velocity of sound in air $v_{sound}=330m/s$

Let $f$ be the frequency of the source and $f^{\prime }$ be the apparent

frequency heard by the stationary observer when the source moves.

As the apparent frequency decreases, thus the source appears to move away from the observer.

Doppler effect when source moves away from stationary observer:

$f^{\prime }=f[\frac{v_{sound}}{v_{sound}+v_{source}}]$ $=f[\frac{330}{330+v}]$

Now it is given that $f^{\prime }=80$ % of $f⟹f^{\prime }=0.8f$

Thus $0.8f=f[\frac{330}{330+v}]$

$⟹v=82.5m/s$