Maths problem

[Brian Peacock]

That's not what Doppler is. The frequency doesn't change with distance from source. It only changes in relation to being either in front or behind the source.

I can't have been clear. Doppler effects relate to the percieved frequency (pitch, tone) shifting of a moving wave in relation to (in this case) a stationary observer. The stationary observer alongside the track experiences the Doppler effect - change in frequency (pitch) over time depending on distance - the observer on the train doesn't - their ditance from the wave source remains the same.

[Brian Peacock]

... So there's no reason, if you are using sound clocks, why you shouldn't be experiencing length contraction in the same way.

If you're moving with the sound clock your time (the frequency) doesn't change - the distance the sound travels to you remains the same - but an observer at the front of the train will experience a slightly higher frequency (pings closer together) than an observer at the back of the train (pings further apart), even though the ping's round trip is the same fore and aft - that is, the distance from the clock to the front and back of the train is the same. Likewise the distance from the clock to a reflector at the rear to the clock again is the same as the distance from the reflector at the front to the clock and back to the reflector at the front again. What changes is the return time from each reflector - speed of sound plus the speed of the the train in front, and speed of sound minus the speed of the train behind. The frequency (as in timing) is the same at the front and back of the train, but the frequency (as in wavelength, pitch) for an observer is different - shorter wavelengths in front, longer wavelengths behind.


edit: for clarity

I might do another animation to illustrate.

[pErvinalia]

I still suggest that's wrong. The observer at the front of the train is moving away from the sound wave, therefore experiencing the frequency lower by the same ratio that a stationary observer experiences it faster (i.e. the Doppler Effect, i.e. the same ratio the wavelength contracts). And the inverse at the rear of the train.

[pErvinalia]

That's not what Doppler is. The frequency doesn't change with distance from source. It only changes in relation to being either in front or behind the source.

I can't have been clear. Doppler effects relate to the percieved frequency (pitch, tone) shifting of a moving wave in relation to (in this case) a stationary observer. The stationary observer alongside the track experiences the Doppler effect - change in frequency (pitch) over time depending on distance - the observer on the train doesn't - their ditance from the wave source remains the same.

No, that's still wrong. There is no change in pitch relative to distance from source. There are broadly three pitches: 1, higher in front of an approaching source; 2, the same perpendicular to a source; and 3, lower behind a receding source.

[pErvinalia]

Time dilation has nothing to do with clock type. I explained this already. Time dilation occurs between relatively moving inertial frames. At non-relativistic speeds the sound clock reads slower simply because of the greater distance the sound has to travel on a moving train.

You're talking about time as measured by the clocks that you are familiar with, that's all.
If your time is measured by sound clocks only, then your time will dilate with motion of the clock in the medium.

Nobody's claiming that your normal everyday time is affected by the clock type. That's a red herring.

But your claim that clock type has anything to do with time dilation is quite simply wrong. Time dilation occurs to ALL clocks the same amount. The only variable that matters is the ratio of relative velocity to the speed of light.

[pErvinalia]

Time dilation is the phenomenon whereby two people, each in separate inertial frames moving relatively to each other, each view time slowing (and length contracting by the same ratio) in the other inertial frame. It's got nothing to do with the type of clock measure the time. It's a physical phenomenon that affects all clocks (whether mechanical, atomic or biological) the same.

[Brian Peacock]

That's not what Doppler is. The frequency doesn't change with distance from source. It only changes in relation to being either in front or behind the source.

I can't have been clear. Doppler effects relate to the percieved frequency (pitch, tone) shifting of a moving wave in relation to (in this case) a stationary observer. The stationary observer alongside the track experiences the Doppler effect - change in frequency (pitch) over time depending on distance - the observer on the train doesn't - their ditance from the wave source remains the same.

No, that's still wrong. There is no change in pitch relative to distance from source.

There is for a stationary observer alongside the the the track - the wavelength changesb over timev relative to distance and angle to the sound source.

There are broadly three pitches: 1, higher in front of an approaching source; 2, the same perpendicular to a source; and 3, lower behind a receding source.

I haven't said otherwise. I think some confusion is steming from 'frequency' being applied interchangeably to the timing component and the wavelength component of the discussion - the frequency of the clock cycle vs the frequency of the ping. I'll try and be more specific.

[pErvinalia]

That's not what Doppler is. The frequency doesn't change with distance from source. It only changes in relation to being either in front or behind the source.

I can't have been clear. Doppler effects relate to the percieved frequency (pitch, tone) shifting of a moving wave in relation to (in this case) a stationary observer. The stationary observer alongside the track experiences the Doppler effect - change in frequency (pitch) over time depending on distance - the observer on the train doesn't - their ditance from the wave source remains the same.

No, that's still wrong. There is no change in pitch relative to distance from source.

There is for a stationary observer alongside the the the track - the wavelength changesb over timev relative to distance and angle to the sound source.

There is no variable for distance in the Doppler equations. The only factors that matter are the speed of sound and the relative velocity between the source and observer:

https://en.wikipedia.org/wiki/Doppler_effect#General

There are broadly three pitches: 1, higher in front of an approaching source; 2, the same perpendicular to a source; and 3, lower behind a receding source.

I haven't said otherwise.

Yes you did. Multiple times. You just quoted yourself saying: "...Doppler effect - change in frequency (pitch) over time depending on distance...". The frequency absolutely has nothing to do with distance from the source. Velocities are the only relevant factors.

[Brian Peacock]

That's not what Doppler is. The frequency doesn't change with distance from source. It only changes in relation to being either in front or behind the source.

I can't have been clear. Doppler effects relate to the percieved frequency (pitch, tone) shifting of a moving wave in relation to (in this case) a stationary observer. The stationary observer alongside the track experiences the Doppler effect - change in frequency (pitch) over time depending on distance - the observer on the train doesn't - their ditance from the wave source remains the same.

No, that's still wrong. There is no change in pitch relative to distance from source.

There is for a stationary observer alongside the the the track - the wavelength changesb over timev relative to distance and angle to the sound source.

There is no variable for distance in the Doppler equations. The only factors that matter are the speed of sound and the relative velocity between the source and observer:

https://en.wikipedia.org/wiki/Doppler_effect#General

There are broadly three pitches: 1, higher in front of an approaching source; 2, the same perpendicular to a source; and 3, lower behind a receding source.

I haven't said otherwise.

Yes you did. Multiple times. You just quoted yourself saying: "...Doppler effect - change in frequency (pitch) over time depending on distance...". The frequency absolutely has nothing to do with distance from the source. Velocities are the only relevant factors.

I'm not sure why you're disagreeing with me in your agreement with what I'm saying. You're missing the 'over time' part I think. The Doppler effect is characterised by the foreshortening of wavelengths from an approaching source and the lengthening of wavelength from a receeding source. For the static sound observer the pitch appears to change over time as the sound source comes and goes.

[pErvinalia]

Because multiple times you have said that the distance from the source has something to do with the frequency. That is absolutely wrong.

[pErvinalia]

Brian, you need to stop editing comments using the moderator function. When the rest of us edit comments it shows that it has been edited. When you edit using the moderator settings it doesn't show that it has been edited. That often removes proceeding comments out of the proper context.

[Brian Peacock]

Sorry. I'm on the bus.

[pErvinalia]

Well when you get home, try and make it clear what you are trying to say. Because at least four times now (under the current content of your posts) you've claimed that the frequency changes as the observer gets closer to the source. It absolutely doesn't.

[mistermack]

But your claim that clock type has anything to do with time dilation is quite simply wrong. Time dilation occurs to ALL clocks the same amount. The only variable that matters is the ratio of relative velocity to the speed of light.

pErvin, I don't know how I can make it any clearer.
The time dilation I am talking about is the slowing of the sound clock, which you have already agreed exists.
I'm NOT saying that your watch will slow. Your watch works due to electromagnetic particles interacting and will only slow, as you are saying, with the speed relative to the speed of light.

IF your watch worked on the principle of sound in air, then your watch WOULD slow. That's all I'm saying. Yes, it's because the distance moved increases with the velocity through the air, as you pointed out. I'm not arguing against that. I'm agreeing with that. When I say "time dilation", I'm just referring to the slowing of a sound clock, due to it's motion through the air.

As far as length contraction goes, if your clock is experiencing time dilation, then the phenomenon will occur.
This is what wki says :

Another method is to use a clock indicating its proper time {\displaystyle T_{0}} T_{0}, which is traveling from one endpoint of the rod to the other in time {\displaystyle T} T as measured by clocks in the rod's rest frame. The length of the rod can be computed by multiplying its travel time by its velocity, thus {\displaystyle L_{0}=T\cdot v} L_{0}=T\cdot v in the rod's rest frame or {\displaystyle L=T_{0}\cdot v} L=T_{0}\cdot v in the clock's rest frame.[7]
In Newtonian mechanics, simultaneity and time duration are absolute and therefore both methods lead to the equality of {\displaystyle L} L and {\displaystyle L_{0}} L_{0}. Yet in relativity theory the constancy of light velocity in all inertial frames in connection with relativity of simultaneity and time dilation destroys this equality. In the first method an observer in one frame claims to have measured the object's endpoints simultaneously, but the observers in all other inertial frames will argue that the object's endpoints were not measured simultaneously. In the second method, times {\displaystyle T} T and {\displaystyle T_{0}} T_{0} are not equal due to time dilation, resulting in different lengths too.

Sorry but the formulae don't paste over in the original format.
https://en.wikipedia.org/wiki/Length_co ... e_dilation
scroll down to "BASIS IN RELATIVITY"

[pErvinalia]

But your claim that clock type has anything to do with time dilation is quite simply wrong. Time dilation occurs to ALL clocks the same amount. The only variable that matters is the ratio of relative velocity to the speed of light.

pErvin, I don't know how I can make it any clearer.
The time dilation I am talking about is the slowing of the sound clock, which you have already agreed exists.

Yes, but you're misusing a term. That's not time dilation. Time dilation is a relativistic effect.

As far as length contraction goes, if your clock is experiencing time dilation, then the phenomenon will occur.
This is what wki says :

Another method is to use a clock indicating its proper time {\displaystyle T_{0}} T_{0}, which is traveling from one endpoint of the rod to the other in time {\displaystyle T} T as measured by clocks in the rod's rest frame. The length of the rod can be computed by multiplying its travel time by its velocity, thus {\displaystyle L_{0}=T\cdot v} L_{0}=T\cdot v in the rod's rest frame or {\displaystyle L=T_{0}\cdot v} L=T_{0}\cdot v in the clock's rest frame.[7]
In Newtonian mechanics, simultaneity and time duration are absolute and therefore both methods lead to the equality of {\displaystyle L} L and {\displaystyle L_{0}} L_{0}. Yet in relativity theory the constancy of light velocity in all inertial frames in connection with relativity of simultaneity and time dilation destroys this equality. In the first method an observer in one frame claims to have measured the object's endpoints simultaneously, but the observers in all other inertial frames will argue that the object's endpoints were not measured simultaneously. In the second method, times {\displaystyle T} T and {\displaystyle T_{0}} T_{0} are not equal due to time dilation, resulting in different lengths too.

Sorry but the formulae don't paste over in the original format.
https://en.wikipedia.org/wiki/Length_co ... e_dilation
scroll down to "BASIS IN RELATIVITY"

Yeah, length contraction is the partner of time dilation. But again, this relates to Einstein's relativity. A sound clock running slow on a moving train at non-relativistic speeds has nothing to do with relativity. Therefore, length contraction won't apply.