Question

A source of sound is moving along a circular orbit of radius 3 m with an angular velocity of 10 rad/*. A sound detector located far away from the source is executing simple harmonic motion along the line BD (Fig. 9.6) with an amplitude BC = CD = 6 m. The frequency of oscillation of the detector is 5/π per second. The source is at the point A when the detector is at the point B. If the source emits a continuous sound wave of the frequency 340 Hz find the maximum and the minimum frequencies recorded by the detector.

Answer 1

The speed of the source = vs = rω = 30 m *–1

Time ** of the source

The time periods for the circular motion and *.H.M are the same. Thus, when the source is at X, the detector is at C [they are moving away from each other] and the apparent frequency is minimum. When the source is at Y, the detector is at C [they are moving toward each other] and the apparent frequency is maximum. The velocity of the detector at C is

Minimum frequency recorded is