Question

A source is moving with constant speed $v_s=20m/s$ towards a stationary observer due east of the source. Wind is blowing at the speed of $20m/sat{60}^{\circ }$ north of east. The source has frequency 500 Hz. Speed of sound = 300 m/s. The frequency registered by the observer is approximately

• A. 541 Hz
• B. 552 Hz
• C. 534 Hz
• D. 517 Hz

Answer 1

The correct option is C 534 Hz

Velocity of wind in the direction of sound i.e towards East $v_w^{\prime }=v_{w}cos{60}^o=20\times 0.5=10m/s$

Let the apparent frequency heard by the stationary observer be $n^{\prime }.$

Using Doppler effect: $n^{\prime }=n[\frac{v_{sound}+v_w^{\prime }}{v_{sound}+v_w^{\prime }-v_{source}}]$

$n^{\prime }=500[\frac{300+10}{300+10-20}]$

$⟹n^{\prime }=534.4Hz$