# Mechanical waves compressions and rarefactions

#### rishch

Are all mechanical waves composed of compressions and rarefactions ? Apart from sound waves what other mechanical waves are there ?

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#### sophiecentaur

Gold Member
Some mechanical waves are 'shear' waves (in solids only), with side to side forces (e.g. strings, S-type seismic waves). But ALL real waves have, in some form, a displacement (potential energy) component and a motion (Kinetic energy) component. You can make up a mathematical wave, of course, that has no relationship to the Physics World -e.g. a Mexican Wave.

#### rishch

Sorry, but I couldn't understand your answer.Also,here are a few more questions I have -

1)My textbook says that- "the magnitude of the maximum disturbance in the medium on either side of the mean value is called the amplitude of the wave.For sound its unit will be that of density or pressure." How ? If amplitude is displacement shouldn't its unit SI unit be meter.But why is it of density of displacement ? Is it because in a sound wave amplitude is proportional to maximum density ?

2)If in transverse waves the particles moves up and down ( if the direction of the wave is horizontal ), then how is this up and down motion transferred from one particle to another ?

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#### Studiot

Are all mechanical waves composed of compressions and rarefactions ? Apart from sound waves what other mechanical waves are there ?
Is this classwork?

Of course there are other forms of (mechanical) wave.

If you have ever been to the seaside you will be familiar with water waves.
These are not compression waves
Water is a (nearly) incompressible fluid so compression waves do not travel well in it.

There are two sorts of waves viz travelling waves and standing (stationary) waves. Travelling waves are associated with carrying energy from one location to another - it is one of the characteristic properties of waves.

go well

#### rishch

Thanks ! Could you answer my other questions too ? And by the way, this is not classwork, these are questions that I had.

#### Studiot

Could you answer my other questions too ?

1)
'Displacement' is a general term for the quantity that varies in the wave as time goes on. It could be distance but need not be.

If you understand graphs, we plot time (and sometimes space) along the x axis. This is the primary or independant variable.

The Displacement is the quantity plotted on the y axis and is also known as the dependent variable, because its variation depends upon its x (time) coordinate. The mean value is the value it has undisturbed (=without the wave).

So a plot of pressure variation above and below mean atmospheric pressure gives a sound wave.

A plot of voltage with time gives an electric wave such as the AC mains.

The maximum 'displacement' (= the maximum or minimum value the plotted quantity reaches) is called the amplitude.

2)
Take a guitar string plucked and vibnrating in transverse mode. Every element of the string is still part of the string and therfore still mechanically coupled to its neighbour. So any motion it makes has an effect on its neighbour. The transfer of (some of) its motion to its neighbour and from neighbour to neighbour is what makes the wave.

Every transverse wave has such a mechanism.

Does this help?

#### rishch

1)
'Displacement' is a general term for the quantity that varies in the wave as time goes on. It could be distance but need not be.

If you understand graphs, we plot time (and sometimes space) along the x axis. This is the primary or independant variable.

The Displacement is the quantity plotted on the y axis and is also known as the dependent variable, because its variation depends upon its x (time) coordinate. The mean value is the value it has undisturbed (=without the wave).

So a plot of pressure variation above and below mean atmospheric pressure gives a sound wave.

A plot of voltage with time gives an electric wave such as the AC mains.

The maximum 'displacement' (= the maximum or minimum value the plotted quantity reaches) is called the amplitude.

2)
Take a guitar string plucked and vibnrating in transverse mode. Every element of the string is still part of the string and therfore still mechanically coupled to its neighbour. So any motion it makes has an effect on its neighbour. The transfer of (some of) its motion to its neighbour and from neighbour to neighbour is what makes the wave.

Every transverse wave has such a mechanism.

Does this help?
1)I understood what amplitude is but my question was why so they say that the unit for amplitude is that of density or pressure instead of meters ?

2)What about in water molecules where each molecule is not connected to the other ?

#### Studiot

'Displacement' is a general term for the quantity that varies in the wave as time goes on. It could be distance but need not be..........................
Try reading this post again a bit more slowly

#### pbuk

Edit:
I have removed the content of this post which was a duplication of #4 which somehow I missed.

#### rishch

OK, so what they meant by displacement is the distance between the point of maximum density/pressure or the point of minimum density/pressure ( on the graph ) from the horizontal line that represents the mean value of density ? If I say that by displacement they were not referring to the actual motion of the particles, they were referring to the density/pressure, is that correct?

And you missed my question on transverse waves in water molecules.

Here are another batch of questions - ( sorry I keep adding questions in each post, its because as I read the chapter more and more doubts keep coming )

1)How is sound 'energy'

2)How can you measure the amount of sound energy ?

3)In my book they initially say that if a sound wave has greater amplitude then it will be louder i.e more amplitude=louder sound and then later on in the chapter they say that sometimes we use the terms 'loudness' and 'intensity' interchangeably but this is wrong because loudness is actually a measure of response of the ear to the sound. This means that 2 identical sound waves having same amplitude need not have same loudness (because we may here one wave better) which contradicts what they said earlier.

#### Studiot

If I say that by displacement they were not referring to the actual motion of the particles, they were referring to the density/pressure, is that correct?
Yes that is correct.

And you missed my question on transverse waves in water molecules.
Nope I just thought is best to clear one point at a time.

Molecules are too small to individually be part of the wave. We talk of elements or particles of the fluid (or other vibrating medium) which are small enough to be considered as points in terms of our analysis. That ususally means that their dimensions are small compared with the wavelength say 1/1000 wavelength. Still much, much bigger than a molecule in the case of water waves.

When we study water waves closely we find that the trajectory of the elements is not straight up and down, but actually small circles or ellipses. So each element bumps into its neighbour as it goes round and round its circle.

How is sound 'energy'
Sound is not energy. It takes energy to generate and propagate a sound wave. I said earlier that a (travelling) wave is one way that energy is transported through a medium from on location to another. Sound is a wave phenomenon that does just this.

How can you measure the amount of sound energy ?
You would measure sound energy in air with a calibrated microphone.

In my book they initially say that if a sound wave has greater amplitude then it will be louder i.e more amplitude=louder sound and then later on in the chapter they say that sometimes we use the terms 'loudness' and 'intensity' interchangeably but this is wrong because loudness is actually a measure of response of the ear to the sound. This means that 2 identical sound waves having same amplitude need not have same loudness (because we may here one wave better) which contradicts what they said earlier.
Yes your book is correct we sometimes mix up terms a bit.
The energy of a wave is proportional to its frequency and the square of its amplitude. The amplitude is what is meant by intensity. Intensity depends only upon the wave itself and is not a subjective term.
Loudness is subjective - two people will identify the same sounds as at different 'loudness'. It does indeed depend upon the listener.
But things are more complicated because the same person will identify two sounds (of the same intensity) of different frequencies as being of different loudness. this is becuse the ear does not respond equally to all frequencies.

#### rishch

1)My textbook says sound is a form of energy which causes a sensation of hearing.I'm guessing that that's wrong then ?

2)If a sound wave transports energy then what type of energy does it transport ?

3)You said that sound is not a form of energy but then you said you can measure sound energy with a calibrated microphone.Did you mean that you can measure the amount of energy the sound is transporting with a calibrated microphone ?

4)What's a subjective term ? ( sorry if this is a silly question )

5)You said that "amplitude is what is meant by intensity." Does that mean amplitude and intensity are the same thing ? My book says intensity is the amount if sound energy passing each second through a unit area. Also,in my book when they said that loudness is proportional to amplitude did they mean intensity instead of loudness ?

#### nasu

Does that mean amplitude and intensity are the same thing ? My book says intensity is the amount if sound energy passing each second through a unit area. Also,in my book when they said that loudness is proportional to amplitude did they mean intensity instead of loudness ?
No, they are not the same thing. The intensity is in general proportional to the amplitude squared. The proportionality constant depends on what kind of amplitude is used.
For example, for a plane wave in air, the intensity is given by
$$I=\frac{p_m^2}{2 \rho_0 c}$$
where p_m is the amplitude of the pressure, rho_0 is the equilibrium density and c is the speed of sound.
p designates the change in pressure relative to the equilibrium pressure (it is also called acoustic pressure) and p_m is the maximum change in pressure (amplitude of the acoustic pressure oscillation).

Particle displacement can be used as well to describe the wave and to calculate intensity even though for gases the pressure is more common.
The displacement (x) is related the acoustic pressure:
$$x= \frac{p}{Z \omega}$$
where Z is the acoustic impedance
$$Z=\sqrt{\rho_0 c}$$
and omega is the angular frequency.
For a gas this is not the displacement of individual particles but rather the average for a thin "slice" of gas.

#### nasu

Water is a (nearly) incompressible fluid so compression waves do not travel well in it.
To "travel well" is a little fuzzy.
However considering speed of sound and attenuation, it may appear that compression (longitudinal) waves travel better in water than in air. The speed of longitudinal sound in water is almost 5 times larger than in air. Attenuation is about 50-70 times lower in water than in air (at 1 kHz). The whales and dolphins know this very well, I suppose. As the submarine sonar operators.

As a more general observation, the effect of decreasing compressibility is to increase the speed of longitudinal waves.
The effect on attenuation is not so straightforward. The solids with their low compressibility (lower than for water) are pretty good at transmitting longitudinal waves (they can travel across the whole earth).

#### Studiot

The speed of longitudinal sound in water is almost 5 times larger than in air. Attenuation is about 50-70 times lower in water than in air (at 1 kHz).
Yes you are absolutely right, I looked it up in Kaye and Laby.
Thank you for that.

#### sophiecentaur

Gold Member
To "travel well" is a little fuzzy.
However considering speed of sound and attenuation, it may appear that compression (longitudinal) waves travel better in water than in air. The speed of longitudinal sound in water is almost 5 times larger than in air. Attenuation is about 50-70 times lower in water than in air (at 1 kHz). The whales and dolphins know this very well, I suppose. As the submarine sonar operators.

As a more general observation, the effect of decreasing compressibility is to increase the speed of longitudinal waves.
The effect on attenuation is not so straightforward. The solids with their low compressibility (lower than for water) are pretty good at transmitting longitudinal waves (they can travel across the whole earth).
And the modulus of the mantle is so high that the speed takes a P seismic wave to the antipodes in about 20 minutes!

#### nasu

And the modulus of the mantle is so high that the speed takes a P seismic wave to the antipodes in about 20 minutes!
Interesting. Now you made me curious about the value of the speed.
My estimate (based on the 20 min) is about 10,000 m/s.
Not bad. Diamond in normal conditions has around 12,000 m/s.
A search on Wiki shows that the speed actually varies between about 6000 to about 14,000. It depends on depth. At the interface between mantle and liquid core drops sharply (it enters a liquid region).

#### sophiecentaur

Gold Member
I used to have a brilliant animation showing a picture of the Earth with the actual plots at various Seismic Recording Stations around the globe and the concentric wave fronts propagating (racing) over the surface. The animation is 'actual time' and fits the recorded plots. I have not been able to find it again recently but it used to impress everyone I showed it to.

#### Bobbywhy

Gold Member
rishch, you are receiving a mixture of information from a variety of individuals that appears to be not too helpful for your learning process.

I suggest you visit this website and view each animation there. This may help guide you into physical acuoustics painlessly.

http://www.acs.psu.edu/drussell/demos.html

#### sophiecentaur

Gold Member
@rishch

A wave is how we describe the process in which a 'disturbance', of some kind, propagates (travels) from one place to another. The disturbance may be a change of position, pressure, temperature, electric field, tension is a string etc. etc etc. The Units of this disturbance will be whatever happens to be appropriate. One thing that they all have in common is that Energy is transferred. Energy is always in the same units and relates to the Square of the amount of disturbance (or 'displacement').

I can tell you are not too confident about this and you are very concerned by the actual terms used - looking for inconsistencies ("is the book wrong?"). This is quite a common problem and not all books (certainly not all Web Pages!!!) can get things 100% right. That's life, I'm afraid. All I can suggest is that you look at as many sources as you can. Wikipedia is not 100% reliable for many things but its mainstream stuff like this is pretty reliable. As you have found, Forum posts tend to be conversational and other peoples' conversations can be totally useless when you are floundering. You need to respond continually if you want to keep things on the lines you need. A 'daft' question ceases to be daft once the question is resolved.

Animations are fine but they are only what they are. You can make anything happen in an animation and it can look convincing (Pixar are great at this). Look at the writing too and, as soon as you can, use some Maths to take it further. Words and Arm waving can only take you so far and can even lead to wrong conclusions.

#### Bobbywhy

Gold Member
The referenced website in post # 19 is not by Pixar.

"Acoustics and Vibration Animations

Dan Russell, Ph.D., Professor of Acoustics & Director of Distance Education

Graduate Program in Acoustics, The Pennsylvania State University

#### sophiecentaur

Gold Member
The referenced website in post # 19 is not by Pixar.

"Acoustics and Vibration Animations

Dan Russell, Ph.D., Professor of Acoustics & Director of Distance Education

Graduate Program in Acoustics, The Pennsylvania State University
Of course there are excellent animations around but, along with the ever-popular Simulations, they may or may not deliver the right message when used in isolation. They never constitute 'proof'. Just look at what Pixar would have you believe.

#### rishch

Thanks a lot guys ! All my questions were answered ( even though some of the answers are above my level ).The website is really helpful.

#### rishch

Sorry, but I couldn't understand your answer.Also,here are a few more questions I have -

1)My textbook says that- "the magnitude of the maximum disturbance in the medium on either side of the mean value is called the amplitude of the wave.For sound its unit will be that of density or pressure." How ? If amplitude is displacement shouldn't its unit SI unit be meter.But why is it of density of displacement ? Is it because in a sound wave amplitude is proportional to maximum density ?

2)If in transverse waves the particles moves up and down ( if the direction of the wave is horizontal ), then how is this up and down motion transferred from one particle to another ?
Sorry, but I just realized that when you answered Q1 you said that 'displacement' is any quantity that varies with time. But what I actually meant was the other displacement ( the initial point final point one ).So my question was the unit should be meters ( as the SI unit of displacement is meters ) not that of density or pressure.Also, I searched the net and some books and no where was it mentioned that 'displacement' ( NOT the initial point final point one ) is a general term for a quantity that varies with time.

#### Studiot

Hello rishch, you seem to be having trouble with this idea

If you understand graphs, we plot time (and sometimes space) along the x axis. This is the primary or independant variable.

The Displacement is the quantity plotted on the y axis and is also known as the dependent variable, because its variation depends upon its x (time) coordinate. The mean value is the value it has undisturbed (=without the wave).

So a plot of pressure variation above and below mean atmospheric pressure gives a sound wave.

A plot of voltage with time gives an electric wave such as the AC mains.

The maximum 'displacement' (= the maximum or minimum value the plotted quantity reaches) is called the amplitude
When you plot voltage or pressure or force or some other quantity on a piece of paper you obtain a graph of the variation of that quantity.
I'm sure you know that in a graph the quantity is represented by distance on the paper.

A posh term for the y value at any point would be 'the excursion from the mean'. You could use that if you like, many Victorians did. Other expressions you might come across would be 'the instantaneous voltage', the 'instantaneous pressure' , the deviatory pressure'.
I'd warrant that most people would understand and prefer a single term to cover all of these and I used displacement as logical since this is what you actually measure on paper.

Does this help?

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