# B What is the speed of sound from a fast-approaching train?

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1. Jul 28, 2016

### fizixfan

Someone once said, there are no stupid questions, just stupid people. All the questions I have read about sound coming from an approaching object only seem to deal with the frequency of sound, not its speed. So with that in mind, I have the following (hopefully non-stupid) question:

A train is approaching me at 60 mph, and blows its whistle. Sound travels at 768 mph (at 68° F, sea level), so will the sound of the whistle reach me at speed of train + speed of sound = 828 mph, or will it reach me at the speed of sound? I have a feeling that the sound of the whistle will reach me at 768 mph, but I don't know why. I you throw a rock at 20 mph from a train moving at 60 mph (in its direction of motion), the rock will travel at 80 mph. Why would it be any different with the speed of sound coming from an approaching train?

2. Jul 28, 2016

### Grinkle

The speed of sound is not absolute. If you are moving at MACH 1 away from a wavefront also moving at the same speed, the wavefront will never reach you until / unless you slow down relative to the speed of the wave front. If you could somehow observe the wave front behind you, you would measure its speed as zero relative to yourself.

3. Jul 28, 2016

### Grinkle

Thinking more about your question, I believe I missed your point. The train is not pushing the wave front. When the train excites the air to cause the wavefront, it does so by releasing steam from a vent. The energy transfer of the steam to the air that causes the wavefront probably is not much affected by the motion of the vent through the air.

If it were physically possible to make a device that could accelerate a wavefront, then it could do so - its just classical physics at work.

Edit -

A boat outruns its own wake. This situation imo is exactly analogous.

4. Jul 28, 2016

### Staff: Mentor

Sound is a traveling disturbance in a medium. (Unlike a thrown rock.) The speed of sound is determined by the properties of the medium and is with respect to that medium. So it doesn't matter how fast the train is moving, the speed of the sound with respect to the air is the same.

5. Jul 28, 2016

### Staff: Mentor

What he said.

It doesn't matter how fast the train is moving, but it does matter how fast the air is moving. If the wind is blowing from the train towards you at 10 miles per hour, the sound will approach you at 768+10=778 mph; if the wind is blowing from you towards the train the sound will approach you at 768-10=758 mph. 768 mph is the speed of sound in still air, or equivalently the speed of sound as measured by an observer who is riding along with the wind.

6. Jul 29, 2016

### davenn

The train is compressing the wavefront as it comes towards you. This shortens the wavelength and increases the frequency.
As Doc Al and Nugatory said have said, the speed of the sound in the medium ( the air) stays the same ( if the medium doesn't change)
but the freq and wavelength change ... hence the Doppler effect

http://www.animations.physics.unsw.edu.au/jw/doppler.htm

Dave

7. Jul 29, 2016

### Grinkle

Yes, this is what prompted me to post the second time. I had to think a while to separate the Doppler effect from what could cause the wavefront itself to move faster in my own mind, and after that I think I understood the OP's confusion. Once one pictures clearly the difference between wave propagation speed and wave frequency, the rest falls into place. For someone new to these concepts, its possible to get the two muddled at first.

8. Jul 29, 2016

### A.T.

Only if there is also 60 mph wind, parallel to the train movement. The medium (air) matters.

9. Jul 30, 2016

### fizixfan

The animation (The Doppler effect with a moving source) in the above link made it clear to me. Sound waves emanating from a moving object propagate at the speed of sound. That was the missing piece of the puzzle.

10. Jul 30, 2016

### fizixfan

I have one more question. If I am moving away from the train at 90% the speed of sound (691.2 mph), the sound will still reach me at 768 mph, right? How is this any different than the speed of light then, except for their velocities?

11. Jul 31, 2016

### Staff: Mentor

You have to be very specific about specifying your reference frames: are you saying you are moving at 90% of the speed of sound with respect to the air? In that case, you would measure the speed of the sound waves to be 1.9x the standard speed of sound.

12. Jul 31, 2016

### Staff: Mentor

Only if there happens to be a 691.2 mph wind blowing from the train towards you. If there is no wind, the sound will be travelling at 768 mph relative to the ground, so will be moving at $768-691.2=76.8$ mph relative to you.
The speed of light will be $c$ relative to you no matter how you and the source are moving relative to one another or the air around you. The speed of sound will be 768 mph relative to the air around you, so will be 768 mph relative to you only if the air is not moving relative to you.

13. Jul 31, 2016

### Grinkle

Picture two boats in the water moving in the same direction at different speeds, with sufficient speed and difference in speeds so that the faster boat will never be touched by the wake of the slower boat.

If the slower boat is the train, the faster boat is you, and the wake are sound waves, (I hope) you can use this analogy to picture the situation and intuitively understand that you need to slow down to less than the speed of the slower boats wake if you want that wake to catch you, and the more you slow down, the faster the wake will catch you.

14. Jul 31, 2016

### fizixfan

That's what I thought. So, assuming the air is still, the temperature is 68° F, and this takes place at sea level:

1. I am standing still. A train moving toward me at 90% the speed of sound (691.2 mph) blows its whistle. The sound from the whistle will still reach me at the speed of sound (768 mph).
2. The train is stationary. I am moving away from it at 691.2 mph. The sound of the whistle will reach me at 768−691.2 = 76.8 mph. Is this correct?

15. Jul 31, 2016

### TomHart

1. Correct.
2. Correct.

However, the whistle certainly won't sound the same in both cases.

So if one could accelerate and decelerate to a fairly high speed very quickly, you could actually talk to yourself. No extra charge for that thought. :)

16. Aug 1, 2016

### bahamagreen

Maybe it helps to recall that the speed of sound in air is based on the average mean free path speed of the molecules comprising the air, which is independent of the motions of the source and listener (relative to the air), but is dependent on airflow (relative to you), and temperature.

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