# I Does a wave in a moving medium propagate ...

#### geordief

....at the same speed in all directions?

Suppose we are an observer floating "stationary" above a body of water moving in a straight line .

We drop a weight vertically into the water and cause a wave to propagate out from the point where it meets the water.

If we have two additional observers,one upstream and one downstream and equidistant from where the weight lands(all watches synchronized) will they measure the same length of time between when the weight hits the water and when the wave reaches them- or will the motion of the medium (the water) cause the downstream observer to receive the wave soon than the upstream observer?

A second related question is whether the trajectory of the weight when it meets the surface of the water is of any significance.(ie if it does not drop vertically but at an angle)

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#### LURCH

Could you give your prediction (hypothesis); what do you think the results would be, and why? Also, can you think of a way to test it (experiment and observation)?

#### geordief

Could you give your prediction (hypothesis); what do you think the results would be, and why? Also, can you think of a way to test it (experiment and observation)?
Well to address my first scenario ,the first step is to synchronize watches.

Then a target is chosen and a balloon with an observer is stationed directly above.

The second and third observers position themselves at the surface of the moving body of water and at the base of an equilateral triangle with the hovering balloon at the apex.

The weight is dropped and the time it hits the water is timed by all observers (they should all agree to a very close approximation)

The time of arrival of the wave caused by the weight is recorded by the two observers (one upstream and one downstream) and the times compared.

For the second scenario a separate weight is fired at the same spot at an angle to the water (with an upstream or a downstream trajectory) and the corresponding times recorded.

What do I imagine will be the result? I don't know. If the times recorded are identical it will be interesting but it may be the case that the motion of the medium will slow the passage of the wave in the upstream direction.

I plump for the former outcome but am uncertain.

#### LURCH

I was thinking more along the lines of an experiment you can actually do, yourself. As a suggestion; do you live near a river? If not, try filling your kitchen sink with water, then pull the plug. Once the water starts to move quickly circling the drain, try dropping something small (like grains of sugar or salt) into the moving water, and see what the ripples do. It is a lot more enlightening when you can see it happening with your own eyes. And please, come back and describe what you saw, so we can talk about it.

#### sophiecentaur

Gold Member
This is basically a question about the Doppler effect, which (at sub relativistic speeds) says the received frequency is affected only by the relative velocity of the source, the observer and the medium. In your case, all three have zero relative velocity so there will be no perceived frequency shift. That link has some diagrams that will help you to get a feel for what's going on.
A second related question is whether the trajectory of the weight when it meets the surface of the water is of any significance.(ie if it does not drop vertically but at an angle)
The shape of the wave immediately around the impact point will not be circular because the initial 'hole' made by the stone will not be circular but, by the time the wave has travelled by no more than a very few multiples of the size of the hole, the wave will have a circular form about a point somewhere near the centre of the impact.

If the stone is travelling with a horizontal velocity component that's higher than the natural speed of the surface wave, you will get a 'shockwave' (as with a supersonic aircraft) but this will settle down after a very short distance (when the stone has slowed down) and the wave will travel outwards at the same speed in all directions.

#### geordief

This is basically a question about the Doppler effect, which (at sub relativistic speeds) says the received frequency is affected only by the relative velocity of the source, the observer and the medium. In your case, all three have zero relative velocity so there will be no perceived frequency shift. That link has some diagrams that will help you to get a feel for what's going on.

The shape of the wave immediately around the impact point will not be circular because the initial 'hole' made by the stone will not be circular but, by the time the wave has travelled by no more than a very few multiples of the size of the hole, the wave will have a circular form about a point somewhere near the centre of the impact.

If the stone is travelling with a horizontal velocity component that's higher than the natural speed of the surface wave, you will get a 'shockwave' (as with a supersonic aircraft) but this will settle down after a very short distance (when the stone has slowed down) and the wave will travel outwards at the same speed in all directions.
I am not asking about the frequency. It is specifically about the recorded time elapsed of the arrival of the very first wave .Both observers at sea level are stationary wrt each other .It is simply that the first (seaborne) observer receives a wave that has reached him or her across the surface of a medium (water) moving towards him and the other has received the same first circular wave across the water that has moved away from him.

I realize that for an observer in the same frame of reference as the moving (ie stationary to him) as the medium that the wave will propagate at the same speed in all directions but that is not what I am asking

#### LURCH

Take a look at this.

#### sophiecentaur

Gold Member
but that is not what I am asking
It comes down to the same thing and the explanation comes early on in the basic Doppler description. If the wave travels across the surface of the water in circles (in the reference frame of the water) then observers on a circle, centred on the stone, also in that frame (i.e. just floating and all at the same speed in the Earth's frame) will receive the wave in their direction, all at the same time. What reason do you have that makes you think otherwise? Is it non-intuitive?

#### geordief

It comes down to the same thing and the explanation comes early on in the basic Doppler description. If the wave travels across the surface of the water in circles (in the reference frame of the water) then observers on a circle, centred on the stone, also in that frame (i.e. just floating and all at the same speed in the Earth's frame) will receive the wave in their direction, all at the same time. What reason do you have that makes you think otherwise? Is it non-intuitive?
I don't think one way or the other. I want to learn what happens experimentally and align my understanding with that.

So ,what you seem to me to be saying (equivalently) is that ,if a fast moving jet speeds noisily across the centre of London ,observers on the ground in a circle around that point will all hear the sound at the exact same time regardless of the speed or trajectory of the plane?

It is really a very narrow point that I want to nail down (not what I think might or should happen ,but what actually happens )

(I am not interested (at present) in the Doppler effect which will change the pitch of the received sound )

#### geordief

Take a look at this.

Seems to carry the expanding waves downstream from that. Someone upstream will not receive any wave at all. Did I see that right? Or does the wave still propagate upstream at the same speed but so faintly it is imperceptible for all practical purposes?

#### CWatters

Homework Helper
Gold Member
. . it may be the case that the motion of the medium will slow the passage of the wave in the upstream direction.
If that were true then you would expect waves on a stationary pond to travel at the same speed in all directions. I'm sure you agree that is what happens.

However ponds are not actually stationary. The surface of the earth (including the water in any pond) is moving fast due to the earths rotation.

So the fact that the water is moving does not effect the speed of waves through the water.

#### geordief

I think I have it now. If you move continuously in the water at a speed higher than that of the propagating wave ,the wave will never reach you.

#### anorlunda

Mentor
I think I have it now. If you move continuously in the water at a speed higher than that of the propagating wave ,the wave will never reach you.
Yes, like this

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#### sophiecentaur

Gold Member
,observers on the ground in a circle around that point will all hear the sound at the exact same time regardless of the speed or trajectory of the plane?
Absolutely. The wave has no Memory about where it was formed or what formed it. Speeds in all directions (in a isotropic medium) are the same. You can't hurry a wave on by shouting LOUDLY!!!! .

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#### CWatters

Homework Helper
Gold Member
Seems to carry the expanding waves downstream from that. Someone upstream will not receive any wave at all. Did I see that right? Or does the wave still propagate upstream at the same speed but so faintly it is imperceptible for all practical purposes?
Just to summarize..

The wave moves through the water at the same speed in all directions.

What someone on the bank of the river sees depends on how fast the wave moves through the water compared to how fast the water is moving...

If the speed of river < speed of wave the wave will travel upstream relative to the bank. It will eventually reach someone on a bridge upstream if it lasts long enough.

If the speed of the river is > speed of wave then the wave will not travel upstream relative to the bank and it will never reach someone on a bridge upstream.

It's exactly the same as swimming in a river.

"Does a wave in a moving medium propagate ..."

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