the siren of a stationary police car emits sound waves of wavelength 0.55m with its siren on the police car bow approaches a stationary listerner at constant velocity on a straight road assume that the speed of sound in the au=ir is 345m.s^-1.
1} calculate the frequency of the sound wave observed by the listerner if the car approaches him at a speed of 120 km/h^T-1
First, we need to convert the speed of the police car from km/h to m/s:
120 km/h = 120,000 m/3600 s = 33.33 m/s
Now we can calculate the frequency observed by the listener using the Doppler effect equation:
f' = f (v + v_s) / (v + v_o)
Where:
f' = observed frequency
f = emitted frequency
v = speed of sound in air = 345 m/s
v_s = speed of the police car = 33.33 m/s
v_o = speed of the listener = 0 m/s (since the listener is stationary)
Plugging in the values:
f' = f (345 + 33.33) / (345 + 0)
f' = f * 378.33 / 345
f' = f * 1.097
We know that the wavelength, λ = 0.55 m
The speed of sound, v = f * λ
345 = f * 0.55
f = 345 / 0.55
f = 627.27 Hz
Now, we can substitute this back into the equation:
f' = 627.27 * 1.097
f' = 687.27 Hz
Therefore, the frequency of the sound wave observed by the listener when the police car approaches him at a speed of 120 km/h is 687.27 Hz.