An ambulance is generating a siren sound at a frequency of 2,400 Hz.The velocity of sound is 345.0 m/s.The observer is traveling at a velocity of 24.00 m/s toward the ambulance and the ambulance is traveling at a velocity of 20.00 m/s toward the observer.What is the frequency of the siren perceived by the observer?
A) 2,489 Hz
B) 2,560 Hz
C) 2,675 Hz
D) 2,725 Hz
E) 2,830 Hz

Question

Quizplus · Accepted Answer

First, we need to calculate the relative velocity between the observer and the ambulance:

Vrel = Vobs - Vamb
Vrel = 24.00 m/s - (-20.00 m/s)  (Note that we need to use a negative sign for the velocity of the ambulance since it's moving towards the observer)
Vrel = 44.00 m/s

Next, we need to use the formula for the Doppler effect:

fobs = fsource * (Vsound + Vobs) / (Vsound + Vsource)

where fsource is the frequency of the siren (2,400 Hz), Vsound is the velocity of sound (345.0 m/s), Vobs is the velocity of the observer (24.00 m/s), and Vsource is the velocity of the source (ambulance) (-20.00 m/s).

Plugging in the values, we get:

fobs = 2,400 Hz * (345.0 m/s + 24.00 m/s) / (345.0 m/s - 20.00 m/s)
fobs = 2,725 Hz

Therefore, the frequency of the siren perceived by the observer is 2,725 Hz. The correct answer is D.

An Ambulance Is Generating a Siren Sound at a Frequency