A police car siren emits a sound at 600 Hz. If observer A moves toward the source at 50 km/hr, and the police car is traveling toward observer A at 100 km/hr all speeds relative to the road), calculate the siren frequency heard by observer A assume the speed of sound in air = 343 m/s).

Question

Quizplus · Accepted Answer

First, we need to determine the speed of sound relative to observer A:
v_sound = 343 m/s (given)
v_observerA = (50 km/hr) / (3.6) = 13.89 m/s
v_soundA = v_sound + v_observerA = 343 + 13.89 = 356.89 m/s

Next, we need to determine the velocity of the siren relative to observer A:
v_siren = (100 km/hr) / (3.6) = 27.78 m/s

Using the Doppler equation:
f_A = f_siren * (v_soundA / (v_soundA - v_siren))
f_A = 600 * (356.89 / (356.89 - 27.78))
f_A = 678.8 Hz, rounded to 679 Hz

Therefore, the answer is C, 679 Hz.

A Police Car Siren Emits a Sound at 600 Hz