# Sound waves in solids

1. Dec 14, 2004

### DeathKnight

I have three questions about sound waves. I could have asked my physics teacher but he fails to answer almost all the question out of our syllabus.

1- We have read that the speed of sound in solids doesnt depend on their desities. If thats the case then they depend on what thing?
2- There is a room made of pure aluminium. Outside this room a system is giving out sound waves. Will a person inside that room hear anything? What will be the difference on the outcome of the experiment its aluminium is replaced by wood?
3- Energy in sound waves travels as mechanical energy, right? If we are repeatedly hitting a steel bell with a striker, will the temperature of the steel bell increase since we are providing extra kinetic energy to the particles in sttel bell.

Abdullah

2. Dec 14, 2004

### pervect

Staff Emeritus
http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe2.html

gives the formula as sqrt(bulk modulus/ density) It'll define bulk modulus for you too, if you click on the link (assuming you are not familiar with it).

So to my way of thinking, the speed of sound does depend on the density, it's just not the only thing that controls the speed.

3. Dec 14, 2004

### DeathKnight

Thanks for the link pervect but what are your thoughts on my other two questions?
I'll be much pleased if someone can help me out with them.

4. Dec 14, 2004

### Clausius2

For question two, maybe you hear something. But that's more probable with Aluminium (I think?). Sure it has a greater Young Modulus and then a lower sound impedance.

For question three: all mediums are dissipative. So the atomic movement who is the transmisor of sound, has a finite kinetic energy. That energy will be dissipated into heat as the wave travels through the solid. At t--->infinite the wave doesn't exist yet and the solid has dissipated wave energy into heat in an irreversible way.

5. Dec 14, 2004

### DaveC426913

1- speed of sound in solids doesnt depend on their densities

I don't see how this can be true. Sounds waves travel through a material as dense as steel 5X faster than they travel through a material as dense as air.

2- Will a person inside that room hear anything?

Metals are an excellent conductor of vibrations because the atoms are so well packed and uniform. Wood is lousy because it's full of air pockets and differing materials.

3- will the temperature of the steel bell increase?

Most definitely. Try grabbing a nail after hammering it part way into wood. You won't make that mistake more than once.

6. Dec 14, 2004

### DeathKnight

The following table given in my book shows it doesnt:

Substance________Speed of sound(m/s)___________Density(kg/m3)
Air___________________330_____________________1.29
Oxygen_______________320_____________________1.43
Aluminium_____________5100____________________2710
Iron__________________5000____________________7870
(Doesnt look bad, does it? :tongue2: )
You can see that oxygen has greater density but still the speed of sound in it is less than its speed in Air. Same is the in the case of Al and Pb.

I believe in that case such a large difference in temperature is due to the friction between the nail and the hammer and the friction between the nail and the wood(I can be wrong though). In my question I wanted to ask will the propagation of sound waves lead to any temperature difference other than the change in T caused by friction. Thanks for trying to help me.

7. Dec 14, 2004

### Clausius2

Do not mix together both things: solid and fluids.

For fluids, the sound wave speed is:

$$a= \sqrt{\frac{\gamma R T}{W_{molecular}}}=\sqrt{\gamma\frac{P}{\rho}}$$

where W is the molecular weight.

For solids, the speed of an elastic wave is given by:

$$a=\sqrt{\frac{E}{\rho}}$$ where E=elasticity (Young) modulus. The contruibution is double. It is not only the density which has influence, also the proper rigidity of the material. Rigid materials (such as steel, titanium) have larger wave speeds. Note also that density has the inverse effect.

Last edited: Dec 14, 2004
8. Dec 14, 2004

### Dymium

I think it depends on the wave that is being produced. Maybe all waves have sound but not all waves can be heard or comprehended by our ears? If you were standing in a room made of pure Aluminum and waves were being produced outside you might be able to hear some sound ? waves could be penetrating this Aluminum structure but your ears may not hear it. Now if a wave was being produced which happened to be the same as the Atomic number cubed to Aluminum you will hear more than just sound, you may hear , see, taste, touch, feel a change in the structure of this building. A wave of 809.4462 , I mean can sound break things like an opera singer breaks glass?

If you wana go even bigger, lets say your in this Aluminum structure and outside nearby a scientific lab has machinery that is producing Scalarwaves. What effect will that have ? Earthquakes are waves also and so large that they can penetrate even our planet. Sincerly Dymium

9. Dec 15, 2004

### pervect

Staff Emeritus
Given that density *decreases* the speed of sound, that's what I'd expect. Gasses should have the same bulk modulus, roughly- so the lighter the gas, the faster the speed of sound, with hydrogen being the fastest (and helium being a close second). The high speed of sound of helium leads to the "squeaky voice" effect you may have heard from people breathing helium. The high speed of sound in hydrogen is what makes "hot hydrogen" the preferred gas for high performance "light gas guns". See for instance the webpage on the Livermore SHARP gun.

http://www.astronautix.com/lvs/sharp.htm

The other factor in the speed of sound is bulk modulus. Mass slows the propagation of sound down, but "stifness" (bulk modulus) speeds it up. Gasses compress very easily, so they do not have a high bulk modulus. Solids and liquids have a much higher bulk modulus, which accounts for the fact that the speed of sound through them tends to be higher than that of gasses, even though they have higher densities.

10. Dec 15, 2004

### pervect

Staff Emeritus
I'm still not positive what you're asking.

Sound waves carry energy (not very much energy), but that energy will not heat up the material it travels through unless the sound waves dissipate. This should be obvious from the conservation of energy - if the energy stays in the sound wave, it can't heat the material up "permanently".

There is one exception I can think of, which might be related to what you are asking.

If you set up a very strong "standing wave", you might notice an insignificant amount of heating in the high pressure nodes due to adiabatic compression. (Sorry if the terminology sounds scary, but I want to be precise since I'm not sure exactly what point you are trying to make).

However, the effect is very small, and it's usually explicitly assumed that sound waves are not intense enough to cause significant amount of this sort of heating.

11. Dec 15, 2004

### Chronos

Part of the impact energy transfered to a stuck object is converted directly to heat.