A police car is approaching you,traveling eastward at a speed of 31.0 m/s sounds his siren (frequency of 1050 Hz).What is your velocity if you hear a frequency of 1090 Hz.The speed of sound is 344 m/s.

Question

Quizplus · Accepted Answer

When a siren emitting a certain frequency approaches a stationary observer, the frequency heard by the observer is higher than the emitted frequency. When the siren moves away from the observer, the frequency heard is lower than the emitted frequency. The difference between the emitted frequency (f) and the observed frequency (f') is given by the formula:
Δf/f = (v_o ± v_s) /v_s
where vo is the velocity of the observer, vs is the velocity of the sound, and the ± sign depends on the direction of the motion (approaching or receding). 
In this case, we have:
f' = 1090 Hz, f = 1050 Hz, vs = 344 m/s, and vs = 31.0 m/s.
Plugging in the numbers and solving for the observer's velocity, we get:
vo = -19 m/s (negative sign means the observer is moving to the west).
Therefore, the correct answer is B: 19 m/s west.

A Police Car Is Approaching You,traveling Eastward at a Speed