# Pressure Waves. What's Going On?

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### #1 Mattzy

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Posted 05 July 2019 - 05:07 PM

We can make a slow moving wave in a water filled wave tank by moving a plate with a hydraulic ram. If we tap the plate with a hammer we will produce a sound wave that moves through the water at the sonic speed for that mediums' temperature and pressure. What is the difference between these two waves? At what point in dynamics does the movement of the plate start making sound? I guess that if the movement of the plate is greater than the speed of sound then the maximum speed of the emitted wave is reached - limited by Brownian motion (temperature and pressure).

Gases don't seem to behave in the same way. If we move a plate in our atmosphere we can produce sound in the same way that we do in a liquid but we can't send slow moving waves over the long distances that we see in liquids. Why is this?

Edited by Mattzy, 06 July 2019 - 02:11 AM.

### #2 exchemist

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Posted 06 July 2019 - 02:06 AM

We can make a slow moving wave in a water filled wave tank by moving a plate with a hydraulic ram. If we tap the plate with a hammer we will produce a sound wave that moves through the water at the sonic speed for that mediums' temperature and pressure. What is the difference between these two waves? At what point in dynamics does the movement of the plate start making sound? I guess that if the movement of the plate is greater than the speed of sound then the maximum speed of the emitted wave is reached - limited by Brownian motion (temperature and pressure).
Gases don't seem to behave in the same way. If we move a plate in our atmosphere we can produce sound in the same way that we do in a liquid but we can't send slow moving waves over the long distances that we see in liquids. Why is this?
Note: It is also interesting to note that a vessel making sound - say, a torpedo giving out pings - will make a sound wave that has constant speed in all directions irrespective of it's own. I wonder if the relativity crew has done any underwater experiments? Don't worry, I'm not suggesting a cosmic aether.

Unlike gases, liquids do not occupy the whole of the space available to them. They have a surface which is pulled flat by gravity. So you can have surface transverse waves, in which gravity provides the restoring force. Sound is a compression wave, in which the restoring force comes from the compressibility of the material. This gives a stronger response for a given degree of displacement of the medium, so the wave speed is higher.

Edited by exchemist, 06 July 2019 - 02:21 AM.

### #3 Mattzy

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Posted 06 July 2019 - 03:15 AM

After posting I realised that it would be useless to compare light behaviour to sound - so I deleted that thought from the original question. I should have engaged brain before opening mouth!

So waves in a wave tank are only present near the surface. That makes sense. But surface waves only seem to travel up to a low speed limit. We don't seem to be able to make waves move at (say) 50 kts (neither can the wind). If we move the plate at 5 M/s (over a few centimeters) I don't think the wave will travel at that speed. Does the energy go to the height of the wave (amplitude?) We can make sound at fixed speed and surface waves up to what speed?  Why is there a surface speed limit?

### #4 exchemist

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Posted 06 July 2019 - 09:36 AM

After posting I realised that it would be useless to compare light behaviour to sound - so I deleted that thought from the original question. I should have engaged brain before opening mouth!
So waves in a wave tank are only present near the surface. That makes sense. But surface waves only seem to travel up to a low speed limit. We don't seem to be able to make waves move at (say) 50 kts (neither can the wind). If we move the plate at 5 M/s (over a few centimeters) I don't think the wave will travel at that speed. Does the energy go to the height of the wave (amplitude?) We can make sound at fixed speed and surface waves up to what speed?  Why is there a surface speed limit?

I've told you: the speed is governed by the restoring force for a given displacement. For transverse surface waves in water, gravity determines that - though depth of water also has some effect when it is shallow.

### #5 Mattzy

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Posted 07 July 2019 - 12:35 AM

I was surprised to find that sea waves can reach speeds more than 50 kmh !! - needing around 90kmh winds for extended periods. This is about the maximum recorded, but there does not seem to be a speed limit for them. I guess a nuclear bomb might make an even faster wave.

Thankyou exchemist for your pointer on restoring force. The stronger response within the medium from compressibility makes sense too. I have read a little more but can't say that I really understand what is happening. My problem is that I thought that wave speed is determined by the properties of medium - this is what I read about waves.

Seismic sea pressure waves can travel at 760 km/h, sound waves at 5,400 km/h and surface waves - seemingly no speed limit except available force. The gravitational restoring force returns the surface waves to equilibrium - as in a pendulum effect (now I see what you mean about those waves - I think you are saying that the upward movement is slowed by gravity and therefore limits transverse speed - although it will also work in reverse when going back down towards the equilibrium !) but the medium is still capable of transmitting waves at different speeds.

Gravity is working at 90 degrees in all cases. What is the difference between these waves that allows them different speeds through the same medium?

### #6 exchemist

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Posted 11 July 2019 - 03:48 PM

I was surprised to find that sea waves can reach speeds more than 50 kmh !! - needing around 90kmh winds for extended periods. This is about the maximum recorded, but there does not seem to be a speed limit for them. I guess a nuclear bomb might make an even faster wave.

Thankyou exchemist for your pointer on restoring force. The stronger response within the medium from compressibility makes sense too. I have read a little more but can't say that I really understand what is happening. My problem is that I thought that wave speed is determined by the properties of medium - this is what I read about waves.

Seismic sea pressure waves can travel at 760 km/h, sound waves at 5,400 km/h and surface waves - seemingly no speed limit except available force. The gravitational restoring force returns the surface waves to equilibrium - as in a pendulum effect (now I see what you mean about those waves - I think you are saying that the upward movement is slowed by gravity and therefore limits transverse speed - although it will also work in reverse when going back down towards the equilibrium !) but the medium is still capable of transmitting waves at different speeds.

Gravity is working at 90 degrees in all cases. What is the difference between these waves that allows them different speeds through the same medium?

If you cannot see that compressing water is a lot more difficult than lifting it, then this discussion is not going to get much further.

A transverse water wave simply requires you to displace a bit of water upwards. It then tends to fall back under gravity and as it does so it causes the next bit of water to be pushed up in turn, etc. Whereas a sound wave involves physically compressing the water, like compressing a spring. Gravity does not come into it. The restoring force is a lot higher and the wave travels a lot faster.

For surface waves in water there are two relations determining the speed:-

For shallow water c=√(gd) where d is depth of the water and g is the acceleration due to gravity.

For deep water however, it depends on wavelength, λ,  as well as g, but not on depth: c= √(gλ/2π). When the speed depends on wavelength the medium is said to be dispersive. (This is true of light waves in glass for instance and is why refraction of blue light is more marked than for red light).

For sound waves, c = √(K/ρ), where K is the bulk modulus .i.e. the stiffness or resistance to compression and ρ is density.

Edited by exchemist, 11 July 2019 - 03:50 PM.

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### #7 GAHD

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Posted 12 July 2019 - 01:16 PM

It might help you to think of the different SOS between the hammer, plate, and the water. If the plate you strike on the water has a lower SOS than the water(EG a sponge) you're just going to get surface displacement instead of a sonic shock. It comes down to the surface wave along the metal plate exceeding the value of the SOS in the water (or air).

You totally do get surface waves slower than sound in atmos BTW. and what exactly do you think the waves you get from hand fans, or the "sloshing" that can be found in the upper atmos are if not slow wave propagation? As for long distance slow waves: If you got an air filled tube you can send a wave along it just fine up till the equalization of the pressure along it's span. The difference is more in the elasticity of the medium and the size of the "tank" I'd think.

Edited by GAHD, 12 July 2019 - 01:41 PM.
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### #8 Mattzy

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Posted 15 July 2019 - 12:59 AM

If you cannot see that compressing water is a lot more difficult than lifting it, then this discussion is not going to get much further.

A transverse water wave simply requires you to displace a bit of water upwards. It then tends to fall back under gravity and as it does so it causes the next bit of water to be pushed up in turn, etc. Whereas a sound wave involves physically compressing the water, like compressing a spring. Gravity does not come into it. The restoring force is a lot higher and the wave travels a lot faster.

For surface waves in water there are two relations determining the speed:-

For shallow water c=√(gd) where d is depth of the water and g is the acceleration due to gravity.

For deep water however, it depends on wavelength, λ,  as well as g, but not on depth: c= √(gλ/2π). When the speed depends on wavelength the medium is said to be dispersive. (This is true of light waves in glass for instance and is why refraction of blue light is more marked than for red light).

For sound waves, c = √(K/ρ), where K is the bulk modulus .i.e. the stiffness or resistance to compression and ρ is density.

OK, now I'm seeing it. Clearly I had not really understood surface waves. The orbital nature of the medium and it's restriction at shallow depths (to about 1 wavelength - so I read) were new to me. Your first answer was a bit deep to fathom - ha-ha!

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### #9 Mattzy

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Posted 15 July 2019 - 01:50 AM

It might help you to think of the different SOS between the hammer, plate, and the water. If the plate you strike on the water has a lower SOS than the water(EG a sponge) you're just going to get surface displacement instead of a sonic shock. It comes down to the surface wave along the metal plate exceeding the value of the SOS in the water (or air).

You totally do get surface waves slower than sound in atmos BTW. and what exactly do you think the waves you get from hand fans, or the "sloshing" that can be found in the upper atmos are if not slow wave propagation? As for long distance slow waves: If you got an air filled tube you can send a wave along it just fine up till the equalization of the pressure along it's span. The difference is more in the elasticity of the medium and the size of the "tank" I'd think.

Yes, I'm getting it now. Thanks for the explanations. I had never heard of sloshing in the upper atmosphere! What causes it? I wonder if there is an atmospheric tidal wave in the atmosphere caused by the moon. It seems reasonable to assume so.

I'm not sure about waves from hand fans though. There is a local increase in pressure but I think it is absorbed by compressibility as exchemist says - and answers my question! I think we sense a local turbulence / eddy currents etc. I don't think we can send waves through the atmosphere like that - only sound - but I stand to be corrected. An aircraft propeller makes sound that can be heard over kilometers but the local efflux (like the hand fan) is not in wave form (I argue).

I have read a little about shock waves from explosions too. They can be supersonic! Which was also new to me.