# Is the speed of all waves constant?

1. Dec 21, 2015

### mrsmitten

the equation for wave velocity is velocity = wavelength * frequency. now by using the Doppler equation for change in frequency and the Doppler equation for change in wavelength. if you multiply those two equations together you get. frequency' *wavelength' = original frequency * original wavelength.

2. Dec 21, 2015

### Staff: Mentor

Welcome to the PF. Is there a question you would like to ask?

3. Dec 21, 2015

### mrsmitten

based on the derived equation does it mean that all waves have a constant velocity for all reference frames.

4. Dec 21, 2015

### Staff: Mentor

In the relativistic Doppler effect for light (and other electromagnetic radiation) in a vacuum, what you wrote in the first post is true. For other kinds of waves (mechanical waves, sound waves,...) it is not true. In fact, for light traveling through a medium it is not true. This was measured experimentally by Fizeau as far back as 1851:

https://en.wikipedia.org/wiki/Fizeau_experiment

5. Dec 22, 2015

### mrsmitten

so I should be able to take any sound and measure its frequency and wavelength to determine if the source is moving toward or away from me. I also have no previous knowledge of the sources original frequency. because if the source is moving the wave velocity will be different then if it was stationary.

6. Dec 22, 2015

### alw34

no, the frequency will be different.

If you ran toward a sound source, would that change it's velocity through air?

An electromagnetic wave always travels at 'c' in a vacuum. A sound wave always travels about 1126 ft per second in dry air regardless of the source speed. [says Wikipedia] The frequency varies. See the following.

Electromagnetic wave:
"A Doppler radar is a specialized radar that uses the Doppler effect to produce velocity data about objects at a distance. It does this by bouncing a microwave signal off a desired target and analyzing how the object's motion has altered the frequency of the returned signal.

Sound wave:
"The Doppler effect (or Doppler shift), named after Austrian physicist Christian Doppler who proposed it in 1842, is the difference between the observed frequency and the emitted frequency of a wave for an observer moving relative to the source of the waves. It is commonly heard when a vehicle sounding a siren approaches, passes and recedes from an observer. The received frequency is higher (compared to the emitted frequency) during the approach.."

7. Dec 22, 2015

### Staff: Mentor

There is one really important difference between these two statements. The speed of sound in dry air is relative to the speed of the air, so if the receiver is moving relative to the air, the sound wave will not be moving at 1126 fps relative to them. However, the speed of light in a vacuum is c for all observers regardless of their motion (it kind of has to be because there's no such thing as a speed relative to vacuum - there's nothing in the vacuum to be relative to).

8. Dec 22, 2015

### Ibix

Mechanical waves move at a constant speed with respect to the medium in which they propagate (all things being equal). So sound travels at 330m/s (give or take - it depends on temperature, among other things) relative to the air. If you run through the air, the speed of sound relative to you can change. If you are doing 10m/s relative to the air, the speed of a sound wave relative to you could be anywhere between 320m/s and 340m/s. You can even go supersonic - travel faster through the medium than the wave can propagate.

Light is different. It has no medium, and it travels at 3x108m/s regardless of your state of motion. If you are moving towards the source, light passes you at 3x108m/s. If you are moving away from the source, light passes you at 3x108m/s.

Edit: Beaten to it by Nugatory, appropriately enough.

9. Dec 22, 2015

### mrsmitten

The thing is that the velocity of waves is measured with the equation $\nu=f*\lambda$. It is not measured with $v= \nu \pm v_{o}$. Correct me if i am wrong the Doppler equations are
$f'=f \frac{\nu \pm v_{o}}{\nu \pm v_{s}}$
and
$\lambda '=\lambda \frac{\nu \pm v_{s}}{\nu \pm v_{o}}$
To find the wave velocity you would use the equation
$v'=f'*\lambda'$
Which if you multiply $f'*\lambda'$ it goes to.
$f'* \lambda' = f* \lambda$

Let’s say that you here a frequency sound in the distance. Which equation would you use to determine the wave velocity? Could you be able to tell if the source was moving?

10. Dec 23, 2015

### Ibix

Not without extra information. Your velocity with respect to the medium and the original frequency, off the top of my head.

Where did you get your expressions for the Doppler effect (link, or your working)? They aren't trivially related to the expressions I derive, and they don't match (for example) https://en.wikipedia.org/wiki/Relat...#Systematic_derivation_for_inertial_observers. Also, they have the implausible property you describe, that the speed of sound is invariant in all frames. If that were the case, an aircraft travelling at Mach 1 would be paradoxical.

Last edited: Dec 23, 2015
11. Dec 23, 2015

### mrsmitten

Exactly there is no difference between a 440Hz sound with both observer and source stationary and a 440Hz sound that is produced by relative motion. According to what I have read hear you would not need any extra information because just from the sound you can measure the frequency and wavelength. If the wave velocity $v=f*\lambda$ is different from a source that is stationary then the source is moving. Don't take the last sentences out of the context of this paragraph.

In any fundamentals of physics book that derives the Doppler effect you can get the equations from there. the standard equations that is used to convert from frequency shift to wavelength shift is $f=\frac{\nu}{\lambda}$ and $f'=\frac{\nu}{\lambda'}$. That is how the wavelength equation is derived for the relativistic equation. here is a link that describes Doppler wavelength change http://hyperphysics.phy-astr.gsu.edu/hbase/sound/dopp.html#c2. Under the Doppler wavelength change section there are these two equations.
Source receding
$\lambda'=\frac{\nu +v_{s}}{\nu }*\lambda_{s}$
Source approaching
$\lambda'=\frac{\nu -v_{s}}{\nu }*\lambda_{s}$
Which can be combined to say if only the source is moving
$\lambda'=\frac{\nu \pm v_{s}}{\nu }*\lambda_{s}$
The equation is not complete because they did not address a moving observer.
The definition of wave speed is $\v=\lambda*f$ which applies to all waves.
so the equation for speed of wave with source approaching the observer is
$v=\lambda' * f' = \frac{\nu -v_{s}}{\nu }*\lambda_{s} *\frac{\nu}{\nu-v_{s}}*f_{s} = \lambda{s} * f_{s}$
Which means that the source would measure the same wave speed as the observer.
As for the derivation for inertial observers it proves my point to.
$f'=\gamma (1-\frac{v_o}{\nu })*f$
$\lambda'=\frac{1}{\gamma} (\frac{1}{1-\frac{v_o}{\nu }})*\lambda$
$f'*\lambda'=f*\lambda$
Waves do not have mass. Waves transport energy not mass.
Can i see the expressions that you derive. Why would an aircraft travelling at Mach 1 be paradoxical

Last edited: Dec 23, 2015
12. Dec 23, 2015

### Ibix

Sorry - I assumed you'd messed up the relativistic formula for Doppler, but you're using non-relativistic physics.

Everybody agrees on the wavelength, but they disagree on the frequency. This gets you a different wave speed for observers in relative motion. Think of the wave crests travelling along. If they're 1m apart, they're 1m apart. You or me moving doesn't change that. It does change how long it takes for each subsequent crest to overhaul us, which is where the frequency change comes in.

The expression for Doppler wavelength change is the change in the wavelength emitted by a particular source when it starts moving relative to the medium. The expression for Doppler frequency change is the change in the frequency received when the source and receiver are in relative motion. These are not quite the same thing. Simply dividing the one by the other is implicitly assuming that the receiver is at rest with respect to the medium.

The reason that I described an aircraft doing Mach 1 as paradoxical is that it is travelling at the same speed as sound. That is, the speed of sound is zero from this perspective. Yet according to your formula, it should measure the speed of sound to be 330m/s. That's a paradox - and that's one reason you can't travel at the speed of light, which genuinely is invariant.

13. Dec 25, 2015

### Staff: Mentor

Here is a good page that explains how to unify the Doppler shift for light and for sound.

http://mathpages.com/rr/s2-04/2-04.htm

You can use $v=f*\lambda$ if you like, but the corresponding expression for $\lambda$ is not very simple in any reference frame except for the rest frame of the medium. In other frames $\lambda$ depends on the velocity of the medium as well as the direction of propagation.