A stationary observer receives a sound from a sound of frequency v0 moving with a constant velocity vs=30m/s. The apparent frequency varies with time as shown in figure. Velocity of sound v = 300 m/s. Then which of the following is incorrect?
A
The minimum value of apparent frequency is 889 Hz.
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B
The natural frequency of source is 1000 Hz.
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C
The frequency-time curve corresponds to a source moving at an angle to the stationary observer.
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D
The maximum value of apparent frequency is 1111 Hz.
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Solution
The correct option is AThe minimum value of apparent frequency is 889 Hz. This frequency–time curve corresponds to a source moving at an angle to a stationary observer. In the region SN, the source is moving towards the observer, i.e., the apparent frequency n′=n0(vv−vscosθ) n′=n0(300300−30cosθ) Whenθ=π2. i.e., at N, n′=n0=1000Hz,i.e., natural frequency of source. In the region NS’ the source is moving away from the observer, i.e., apparent frequency n′=n0(300300−30cosθ) Whenθ=0,i.e.,cosθ=1, nmax=n0vv−vs=(1000Hz)(300m/s)(300m/s−30m/s) =109×1000Hz=1111Hz nmin=n0vv+vs=1000×300330=909Hz