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The driver of a car travelling with speed 30 m/s towards a hill sounds a horn of frequency 600 Hz. If the velocity of sound in air is 330 m/s, the frequency of reflected sound as heard by driver is
A
500 Hz
B
550 Hz
C
555.5 Hz
D
720 Hz
Detailed Solution
Step 1: the hill is a stationary observer and the car is a source moving towards it. Frequency received (and reflected) by the hill: $f_1 = f\frac{v}{v - v_s} = 600\times\frac{330}{330 - 30}$
Step 2: the hill now acts as a stationary source of frequency $f_1$, and the driver is an observer moving towards it. Frequency heard by the driver: $f_2 = f_1\frac{v + v_o}{v} = f_1\times\frac{330 + 30}{330}$
Combining: $f_2 = f\frac{v + v_c}{v - v_c} = 600\times\frac{360}{300}$
$f_2 = 600\times1.2$
$f_2 = 720$ Hz
Step 2: the hill now acts as a stationary source of frequency $f_1$, and the driver is an observer moving towards it. Frequency heard by the driver: $f_2 = f_1\frac{v + v_o}{v} = f_1\times\frac{330 + 30}{330}$
Combining: $f_2 = f\frac{v + v_c}{v - v_c} = 600\times\frac{360}{300}$
$f_2 = 600\times1.2$
$f_2 = 720$ Hz