What is the speed of the ambulance based on its siren's frequency?

[nczzzzzz]

Homework Statement

While standing on 3rd street you hear an approaching ambulance. Its siren oscillates in frequency between about 650 Hz and 750 Hz.

Later on as you near your destination, you come upon the scene of the accident. The now-stationary ambulance runs its siren as it's about to drive off. This time, you hear its pitch oscillate between 637.65 Hz and 735.75 Hz.

Using your physics knowledge, you estimate the speed that the ambulance must have been traveling while en route to the scene of the accident. How fast was it traveling? (Assume it's an average day where the speed of sound is about 343 m/s.)

A. 25 m/s (about 55 mph)

B. 18 m/s (about 40 mph)

C. 13 m/s (about 30 mph)

D. 9 m/s (about 20 mph)

Homework Equations

v=f*λ

The Attempt at a Solution

 

[tiny-tim]

welcome to pf!

hi nczzzzzz! welcome to pf!

tell us what you think, and why, and then we'll comment!

(same for your other thread)

 

[nczzzzzz]

I was thinking of using the doppler effect formula, but i can't figure out the frequency of the source and the receiver.

 

[tiny-tim]

I was thinking of using the doppler effect formula, but i can't figure out the frequency of the source and the receiver.

the frequency of the source is stated in the question

(and how can a receiver have a frequency? )

 

[Nickie]

To solve this problem, we can use the formula v=f*λ, where v is the speed of sound, f is the frequency, and λ is the wavelength. We know that the speed of sound is approximately 343 m/s, and we have two sets of frequencies for the ambulance's siren: 650-750 Hz while it was approaching, and 637.65-735.75 Hz while stationary.

Using the first set of frequencies, we can calculate the wavelength of the sound waves:
λ = v/f = 343/650 = 0.527 m
Using the second set of frequencies, we can calculate the wavelength again:
λ = v/f = 343/637.65 = 0.538 m

Now, we can use the difference in wavelength to calculate the speed of the ambulance:
v = (0.538-0.527)/0.527 * 343 = 20.9 m/s

Therefore, the ambulance must have been traveling at a speed of approximately 20.9 m/s (about 47 mph) while en route to the accident scene. The correct answer is D. 9 m/s (about 20 mph). This speed seems reasonable for an ambulance responding to an emergency, as it would need to travel quickly but also safely.