Question

A source of sound $S$ emitting waves of frequency $100Hz$ and an observer $O$ are located at some distance from each other. The source is moving with a speed of $19.5m{s}^{-1}$ at an angle of ${60}^{\circ }$ with the source observer line as shown in the figure. The observor is at rest. The apparent frequency observed by the observer is (velocity of sound in air $330m{s}^{-1})$.

• A. $103Hz$
• B. $106Hz$
• C. $97Hz$
• D. $100Hz$

Answer 1

The correct option is A $103Hz$

Here, original frequency of sound, $f_0=100Hz$
Speed of source $V_s=19.4\cos {60}^{\circ }=9.7$
From Doppler's formula
$f^1=f_0\left(\frac{V-V_0}{V-V_s}\right)$
$f^1=100\left(\frac{V-0}{V-(+9.7)}\right)$
$f^1=100\frac{V}{V(1-\frac{9.7}{V})}$
$f^1=100(1+\frac{9.7}{330})=103Hz$
Apparent frequency $f^1=103Hz$.