Question

A source of sound $S$ emitting waves of frequency $100Hz$ and an observor $O$ are located at some distance from each other. The source is moving with a speed of $19.4m{s}^{-1}$ 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. 103 Hz
• B. 106 Hz
• C. 97 Hz
• D. 100 Hz

Answer 1

Answer: (A)

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