Question

A source of sound is moving along a circular orbit of radius 3m with an angular velocity of 10 rad/sec. A sound detector located far away from the source is executing S.H.M. along the line with an amplitude 1m. The freuency of oscillation of the detector is 5 per sec. The source is at the point A when the detector is at the point B. If the source emits a continuous sound wave of frequency 340 Hz, the minimum and maximum frequency recorded by the detector (velocity of sound in air = 330 m/s)

• A. 282 Hz, 410 Hz
• B. 245 Hz, 275 Hz
• C. 375 Hz, 495 Hz
• D. 175 Hz, 300 Hz

Answer 1

The correct option is A 282 Hz, 410 Hz

Velocity of source $v_{source}=r\omega =3\times 10=30m/s=v_s$

The detector frequency of oscillation: $f=5/s$

Velocity of detector: $v_d=2\pi fa=2\pi \times 5\times 1=10\pi$ since $a=1$ as given
Minimum frequency recorded by the detector: $f_{min}=\frac{v-v_d}{v+v_s}=340\times \frac{330-10\pi }{330+30}=340\times \frac{330-10\times \frac{22}{7}}{360}=282Hz$
Maximum frequency recorded by the detector: $f_{max}=\frac{v+v_d}{v-v_s}=340\times \frac{330+10\pi }{330-30}=340\times \frac{330+10\times \frac{22}{7}}{300}=410Hz$