Question

On a quiet day, when a whistle crosses you then its pitch decrease in the ratio 4/5. If a temperature on that day is ${20}^{\circ }C$, then the speed of whistle will be (given the velocity of sound at $0^{\circ }=332m{s}^{-1}$)

• A. 48.2 m$s^{-1}$
• B. 68.2 m$s^{-1}$
• C. 83 m$s^{-1}$
• D. 108.2 m$s^{-1}$

Answer 1

The correct option is C 83 m$s^{-1}$

Velocity of source (whistle) $v_{source}=vm/s$

Velocity of sound in air $v_{sound}=332m/s$

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

frequency heard by the stationary observer when the source moves away

from it.

Doppler effect when source moves away from stationary observer:

$f^{\prime }=f[\frac{v_{sound}}{v_{sound}+v_{source}}]$ $=f[\frac{332}{332+v}]$

Now it is given that $\frac{f^{\prime }}{f}=\frac{4}{5}$

Thus $0.8f=f[\frac{332}{332+v}]$

$⟹v=83m/s$