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Multiple Choice
A police siren emits a sound somewhere around 700 Hz. If you are waiting at a red light, and a police car approaches you from behind and passes you, moving at a constant 30 m/s, what is the frequency you hear from the siren as it approaches you from behind? What about once it's passed you? Assume the air temperature to be 20°C.
A
fD,towards=639 m/s, fD,away=761 m/s
B
fD,towards=644 m/s, fD,away=767 m/s
C
fD,towards=761 m/s, fD,away=638 m/s
D
fD,towards=767 m/s, fD,away=644 m/s
Verified step by step guidance
1
First, understand the Doppler Effect, which describes the change in frequency of a wave in relation to an observer moving relative to the source of the wave. In this case, the police car is the source, and you are the observer.
Calculate the speed of sound in air at 20°C using the formula: v = 331.4 + 0.6 * T, where T is the temperature in Celsius. Substitute T = 20°C to find the speed of sound.
Use the Doppler Effect formula for a source moving towards a stationary observer: f' = f * (v + v_o) / (v - v_s), where f' is the observed frequency, f is the source frequency (700 Hz), v is the speed of sound, v_o is the observer's speed (0 m/s since you are stationary), and v_s is the speed of the source (30 m/s).
Substitute the known values into the formula to calculate the frequency you hear as the police car approaches: f' = 700 * (v + 0) / (v - 30).
For the frequency you hear once the police car has passed, use the formula: f' = f * (v - v_o) / (v + v_s). Substitute the known values to find the frequency: f' = 700 * (v - 0) / (v + 30).