Wave superposition and Doppler effect.

[FerN61]

Homework Statement

A student is at some point between two sound reflecting walls. He's holding a tuning fork and runs towards one of the walls at 5m/s. The pulsating frequency he hears is 8Hz. ¿What's the sound frequency emitted by the tuning fork?
Answer: 137.17 Hz.

I know I'm supposed to use doppler effect but I guess I have to consider wave superposition since there are two walls, but I don't know how to unify both.

 

[Doc Al]

I know I'm supposed to use doppler effect but I guess I have to consider wave superposition since there are two walls, but I don't know how to unify both.

In addition to the Doppler effect, you need to understand beat frequency. (Look that up!)

 

[FerN61]

Beats

Ok so, it is a beat frequency so

f2-f1 = 8

f2= f1+8

using doppler's formula

f1+8=f1((Vsound+5)/Vsound)
Assuming Vsound= 343 m/2

f0=548.8

The answer is supposed to be 137.17... What am I doing wrong?

 

[Doc Al]

You're on the right track, but there's a bit more to it. The two sounds that are creating the beat frequency are the reflections off the two walls. So you have to find those frequencies. Hint: For each of those reflections you'll need to apply the Doppler formula twice.

 

[Nickie]

I would like to clarify that wave superposition and the Doppler effect are two separate concepts that can be applied in this scenario. Wave superposition refers to the phenomenon of two or more waves overlapping and creating a resultant wave. In this case, the sound waves emitted by the tuning fork will reflect off both walls and interfere with each other, resulting in a specific frequency being heard by the student.

On the other hand, the Doppler effect is the change in frequency of a wave due to the relative motion between the source of the wave and the observer. In this scenario, the student's motion towards the wall causes a decrease in the wavelength and an increase in the frequency of the sound waves reaching his ears.

To find the sound frequency emitted by the tuning fork, we can use the equation for the Doppler effect, which is given by f' = f(v ± u)/ (v ± vs), where f' is the observed frequency, f is the emitted frequency, v is the speed of sound, u is the relative velocity between the source and observer, and vs is the speed of the source.

Substituting the given values, we get f' = f(343 ± 5)/ (343 ± 0), where 343 m/s is the speed of sound and 5 m/s is the student's velocity towards the wall. Solving for f, we get f = f'/ (343 ± 5) = 8/ (343 ± 5) = 137.17 Hz.

In conclusion, we can use the concepts of wave superposition and the Doppler effect to determine the sound frequency emitted by the tuning fork in this scenario. By considering both of these concepts, we can better understand the behavior of sound waves and how they are affected by different factors.