Does the Doppler Effect Affect Wave Velocity in Moving Observers?

[Mr Davis 97]

Imagine that there is a stationary source that is propagating waves (such as sound waves). Let's say that the wave speed in the medium is 343 m/s. If I am an observer, and I begin to move towards the waves, will the wave speed increase due to the idea of relative velocities, or will only the frequency and wavelength change, in which case wave velocity remains unchanged? How does this idea relate to electromagnetic waves, where the wave speed is a constant?

 

[andrewkirk]

The wave speed and frequency measured by the observer will change, with both increasing by the same proportion. The wavelength will remain the same. It has to, in order for the equation $v=f\lambda$ to hold.

With electromagnetic waves, the frequency and wavelength both change, and the wave speed remains constant at $c$. The special theory of relativity is used to explain the difference between this treatment and that for sound waves.

 

[Mr Davis 97]

The wave speed and frequency measured by the observer will change, with both increasing by the same proportion. The wavelength will remain the same. It has to, in order for the equation $v=f\lambda$ to hold.

With electromagnetic waves, the frequency and wavelength both change, and the wave speed remains constant at $c$. The special theory of relativity is used to explain the difference between this treatment and that for sound waves.

I guess that makes sense. Could you enumerate the cases where the source approaches the observer and where both the source and the observer approach each other at the same time? I already see that in the case where the observer approaches the source the the velocity and the frequency change in proportion such that the wavelength remains the same. However, in the case where the source is moving towards the observer, the wavelength is smaller; so would frequency change so that velocity remains the same? I am a bit confused and it would be nice if you could list all of the different cases and explain which variables change as a result of the Doppler effect.

 

[andrewkirk]

However, in the case where the source is moving towards the observer, the wavelength is smaller; so would frequency change so that velocity remains the same?

That is correct.

 

[CrazyNinja]

Okay, now you confused me. When the source moves towards the observer, the observed frequency is more. The observed velocity is more too because of relative motion. Why did the wavelength become smaller?

 

[A.T.]

When the source moves towards the observer, the observed frequency is more. The observed velocity is more too because of relative motion.

For sound waves, the observed propagation velocity isn't more, if the observer is at rest relative to the medium, and only the source moves. For EM-wave there is no medium, and the observed propagation velocity is always the same.

 

[andrewkirk]

The observed velocity is more too because of relative motion.

No it isn't. The wave propagation velocity is determined by the motion of the medium (the air, in the case of sound), not the motion of the emitter. So the velocity is the same.
EDIT: Ah, I see A.T. has already answered this. As you were.

 

[nasu]

The wave speed and frequency measured by the observer will change, with both increasing by the same proportion. The wavelength will remain the same. It has to, in order for the equation $v=f\lambda$ to hold.

The speed in that equation is the speed of the wave relative to the medium. This does not change in Doppler effect.
Both wavelength and frequency change. You can see that the equations for Doppler effect can be written either in terms of frequency or wavelength.

 

[CrazyNinja]

Okay I figured it out. @Mr Davis 97 .. here is the list you need. All the quantities are as seen by the observer: (correct me if I am wrong)

1. Observer moving, source at rest : v changes, ƒ changes, λ does not change
2. Observer at rest, source moving: v does not change, ƒ changes, λ changes.

 

[nasu]

Wavelength changes in both cases.

 

[CrazyNinja]

So in case (1), v and ƒ don't change proportionately? God, I have to look this up again.

 

[A.T.]

Wavelength changes in both cases.

I think he means a sound source at rest to the medium.

 

[CrazyNinja]

I think he means a sound source at rest to the medium.

Yeah I meant that.