# Doppler effect and amplitude

• omtri
In summary, the amplitude of a wave does change when the source is moving, even if it is slightly below the speed of the wave. This is due to the energy of the wave dissipating as a sphere with the square of the distance, causing the amplitude to decrease with the square of the distance traveled. However, if the speed of the source matches the speed of the wave, the amplitude can be N times larger than the original amplitude due to multiple wavefronts being emitted. In the case of the speed of the source exceeding the speed of sound, a shock wave occurs which causes a sudden change in pressure. The amplitude of a wave does not increase as the source moves faster than the speed of sound, but rather changes in a different way

#### omtri

Does the amplitude of a wave changes when the source is moving? I am mainly interested in waves in a medium (e.g. sound, water...)

No text about Doppler effect I have found mentions anything about the amplitude so I guess it does not change.

However in the case if the speed of the source is equal to the wave, I think, if there where N wavefronts emitted the amplitude should be N-times larger than that of one amplitude (see http://upload.wikimedia.org/wikipedia/commons/2/25/Mach_cone.svg" [Broken] (the case Ma=1)).

If the speed of the source is slightly below the wave speed, the amplitude should be slightly lower than N-times and so on...

So I get the feeling that the amplitude does indeed change.

What's correct, what's wrong? Why? It would be great if someone has a detailed explanation!

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I like Serena said:
To be clear, as long as the sound barrier is not breached, the amplitude or speed is not affected.
But when the sound barrier is breached, another type of effect plays a role: the shock wave.

Thanks for the answer. However I don't see why the amplitude is not affected in the case when the source moves slower than sound speed?

omtri said:
Thanks for the answer. However I don't see why the amplitude is not affected in the case when the source moves slower than sound speed?

Well, I may not have a foolproof explanation, but here is what I can offer.

Sound is a harmonic wave, just like a mass on a spring that oscillates, or a pendulum.
It has a certain energy that does not change when it is in motion.

A sound wave has a certain energy that dissipates as a sphere (in air) with the square of the distance.
The energy is independent of the frequency, but is linearly related to the square of the amplitude.
In particular this means that the amplitude decreases with the square of the distance traveled (in air).

This does mean of course that the amplitudes will be higher in the direction in which the sound source travels, but only as related to the distance the sound has traveled from its origin.

omtri said:
Does the amplitude of a wave changes when the source is moving? I am mainly interested in waves in a medium (e.g. sound, water...)

No text about Doppler effect I have found mentions anything about the amplitude so I guess it does not change.

However in the case if the speed of the source is equal to the wave, I think, if there where N wavefronts emitted the amplitude should be N-times larger than that of one amplitude (see This picture from Wikipedia (the case Ma=1)).

If the speed of the source is slightly below the wave speed, the amplitude should be slightly lower than N-times and so on...

So I get the feeling that the amplitude does indeed change.

What's correct, what's wrong? Why? It would be great if someone has a detailed explanation!

great question!
i have been doing thought experiments on this for years, and i find every few months i decide the opposite way. It seems intuition alone won't solve this, and i have been pondering about many experiments to setup to find out one way or another but i have not done it.

i have always thought that amplitude must be effected by dopler, exactly as you describe it, if you match the speed of transmission then you must be continually dumping more energy into that point in space-time (although moving, following the energy), to dump more in, and so on.

which leads me to also ponder what is the maximum energy you could pump into a particular moving pocket of energy in a transmission.

which makes me think this is something of a way of thinking which makes it obvious that a sonic boom would occur when exceeding the speed of sound, and so what is an electromagnetic boom ?

fascinating question, if you ever do/did find an answer id love to know!

i search 'dopler amplitude' and related terms often, and never find anything close to an answer, but finally at least i found your question which has been the most on-topic i have ever found on this subject!

so without anwering you, i registered just to say that, thanks! :)

If you take a snapshot of the waveform in the case where the speed is a bit below the speed of sound you'll see the N waves close together but each with its initial amplitude. You seem to feel that since each peak has 'caught up' the preceding one a bit it somehow makes it grow, but you're overlooking that the intervening trough has caught it up just as much, proportionally.
At the speed of sound, the snapshot does not show one wave with N times the magnitude. It shows no bow wave at all! It now only exists as a variation in pressure over time right at the source. So in your gut feel view you're not comparing waves that exist in the same sense.

well considering that we can't reach speed of EM waves it is safe to say that there are no chance of EM boom but what i think is what happens in case of transverse wave when its source moves faster than the speed of wave? .eg in case of wave on a string (i can't even imagine)

As far as the sources velocity is less than that of sound i see no reason that its amplitude should not change in the same way if it was stationary.

This is a good question, I think you are in general almost right. Remember that for an EM wave the frequency increases, an increase in frequency will result in an increase in energy. So although the amplitude does not increase the rate of energy deposition will.

I don't know about sound waves - I don't know how change in frequency affects wave energy. The physics of sound waves approaching the speed of sound is called 'weak shocks' if anyone want to read more.

Finally, sk9, there is such thing as an 'EM sonic boom', things can travel faster that light in a medium- look up Cherenkov Radiation.

i am sorry for my ignorance. i actually once wondered about speed of light in high refractive index but had never related it to Cherenkov Radiation. so thanks.

## 1. What is the Doppler effect?

The Doppler effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. This effect is commonly observed in sound waves, where the pitch of a sound will appear higher as the source moves closer and lower as it moves away.

## 2. How does the Doppler effect affect sound waves?

The Doppler effect causes a shift in the frequency of sound waves, resulting in a change in the perceived pitch of the sound. As the source of the sound moves closer, the waves are compressed and the frequency increases, making the sound appear higher. Conversely, as the source moves further away, the waves are stretched and the frequency decreases, making the sound appear lower.

## 3. What is the difference between the Doppler effect and amplitude?

The Doppler effect refers to the change in frequency of a wave, while amplitude refers to the height or strength of the wave. The Doppler effect is caused by the relative motion of the wave source and observer, while amplitude can be affected by factors such as distance and energy of the source.

## 4. How is the Doppler effect used in real life?

The Doppler effect has many practical applications in fields such as astronomy, meteorology, and medicine. In astronomy, it is used to measure the speed and direction of stars and galaxies. In meteorology, it is used to track the movement of weather systems. In medicine, it is used in ultrasound imaging to measure the velocity of blood flow.

## 5. Can the Doppler effect be observed with light waves?

Yes, the Doppler effect can also affect light waves. This phenomenon is known as the Doppler shift and is commonly observed in astronomy. As a light source moves closer, its waves are compressed and the frequency increases, causing the light to appear more blue. As the source moves further away, the waves are stretched and the frequency decreases, causing the light to appear more red. This is known as redshift and blueshift, respectively.