A Question about Sound Waves Propagating Through a Large Metal Cube

[Kaneki123]

Okay, I have a very simple question that...Suppose we have a very wide cube(dense and hard)...We place two persons at each of its ends...One the persons strikes its surface at one end. Now this person A will hear the sound due to vibrations of that end's surface (which further vibrate the air molecules). Now, almost at the same time, the person B at the other end of the cube will hear the sound. Now my question is that, does this person B hears this sound by the vibrations of the surface of his end (i.e. the vibrations from end A traveled through the cube at a greater speed than in air. At the end B, some amplitude wave is reflected back into the cube and some into outside air) or sound from end A traveled to end B thorugh air...In simple words, does the person B hears the sound with end B as the source or end A as the source?...Any help is appreciated...

 

[Chestermiller]

Okay, I have a very simple question that...Suppose we have a very wide cube(dense and hard)...We place two persons at each of its ends...One the persons strikes its surface at one end. Now this person A will hear the sound due to vibrations of that end's surface (which further vibrate the air molecules). Now, almost at the same time, the person B at the other end of the cube will hear the sound. Now my question is that, does this person B hears this sound by the vibrations of the surface of his end (i.e. the vibrations from end A traveled through the cube at a greater speed than in air. At the end B, some amplitude wave is reflected back into the cube and some into outside air) or sound from end A traveled to end B thorugh air...In simple words, does the person B hears the sound with end B as the source or end A as the source?...Any help is appreciated...

Suppose the side of the cube is 2 km long. What would your answer be?

 

[Kaneki123]

Suppose the side of the cube is 2 km long. What would your answer be?

Well, if we are going to talk about "which sound reaches first", then the sound through the cube will reach first. But I actually wanted an answer about whether the sound propagating through the cube will have enough amplitude left when it reaches the end B, when some of its amplitude is decreased due to reflection ( into same medium cube) at end B, and if the transmitted wave is strong enough to produce any significant sensation ( of sound) in our ear?

 

[anorlunda]

Well, if we are going to talk about "which sound reaches first", then the sound through the cube will reach first. But I actually wanted an answer about whether the sound propagating through the cube will have enough amplitude left when it reaches the end B, when some of its amplitude is decreased due to reflection ( into same medium cube) at end B, and if the transmitted wave is strong enough to produce any significant sensation ( of sound) in our ear?

As a youth, I pressed my ear to the railroad track. I could hear the wheels of trains many miles away.

Or are you hung up by the cube shape rather than rail shape? How does the shape of the atmosphere influence what you hear? Think of a stethoscope.

 

[Kaneki123]

As a youth, I pressed my ear to the railroad track. I could hear the wheels of trains many miles away.

Or are you hung up by the cube shape rather than rail shape? How does the shape of the atmosphere influence what you hear? Think of a stethoscope.

Well I don't think so that my question indicated that I was hung up on the shape. In your case, You had to press your ear against the track in order to hear. But what if you were standing at some distance from the tracks. Now, you could not hear the wheels. Now, the only way which I can think of is that, the sound did travel through the track to the point, near to which you were standing.The sound was both reflected and transmitted at the boundary, with the former with more amplitude. That's why you could not "hear" the sound at some distance.Now, back to the question, is there any thing which I got wrong in my above explanation?

 

[sophiecentaur]

Now, back to the question, is there any thing which I got wrong in my above explanation?

I think your problem concerns the acoustic impedances of air and steel. Your ears were designed to pick up vibrations in Air (a low impedance medium, with large displacements and small pressure changes) Your ear is in a liquid medium and the ear drum - ossicles - oval window, transform the sound signal to a high impedance of the inner ear (small displacements and high pressure changes). You will not hear the noise of distant the train on the track unless your head is in contact with the rail. (The displacement of the steel surface is very small and doesn't couple sound into the air very well) Then, the high impedance of the steel allows direct transfer of the vibrations to the liquid and solid of your head / inner ear.
The issue of speed in different media is a separate one but the high modulus of the steel produces a high wave speed.
I suggest you Google "Speed of sound in different substances" and "acoustic Impedance"

 

[Khashishi]

Hmm, I'm trying to connect this to the closest real-world example I can recall, which is a giant bell.
If you hit a giant bell softly with a metal hammer, you will probably just hear an initial tink sound, which is probably mostly transferred through the air. But if you hit the bell hard with a soft mallet, you cause the whole bell to resonate and produce a long low pitch. The resonance is due to the fact that most of the sound waves in the metal reflect many times within the metal before escaping to the air.
A solid cube would be a lot stiffer than a bell, so it would have a much higher resonance. Depending on how you hit it, I guess that you would get a combination of a "tink" from the initial hit and a "diingg" from a short resonance period. The diingg would be from waves that travel through the metal and come out.

 

[sophiecentaur]

The vibrations in a bell are mainly Transverse, where the thin material flexes like a very rigid diaphragm. You or the clapper hit a bell against the side and that's how the transverse waves are set up. The speed of these waves is much slower than the longitudinal waves that you get with a cube when you hit it. There are longitudinal waves in the bell too but I don't think they support the audible frequencies of the transverse standing waves.
The relatively big area of the sides of the bell and the enclosed mass of air, give a better match for launching sound waves into the air. So it's shape and wave type that make the difference between a cube and a bell (which was specifically designed to sound loud).

 

[Kaneki123]

I think your problem concerns the acoustic impedances of air and steel. Your ears were designed to pick up vibrations in Air (a low impedance medium, with large displacements and small pressure changes) Your ear is in a liquid medium and the ear drum - ossicles - oval window, transform the sound signal to a high impedance of the inner ear (small displacements and high pressure changes). You will not hear the noise of distant the train on the track unless your head is in contact with the rail. (The displacement of the steel surface is very small and doesn't couple sound into the air very well) Then, the high impedance of the steel allows direct transfer of the vibrations to the liquid and solid of your head / inner ear.
The issue of speed in different media is a separate one but the high modulus of the steel produces a high wave speed.
I suggest you Google "Speed of sound in different substances" and "acoustic Impedance"

Well, most of my confusion has been resolved. But I do have one last question. As you said "The displacement of the steel surface is very small and doesn't couple sound into the air very well". The sound can be heard if one is right next to the "distant train". The reason is that the wheels of train vibrates the steel surface of the track, the displacement of steel surface vibrates the air, which in form of sound waves travels to our ears. But if a person standing far away from the train, he cannot hear the sound as "The displacement of the steel surface is very small and doesn't couple sound into the air very well". Now my question is that, at one point the displacement of steel surface is enough to produce perceivable sound and at one point it is not, is this because of the loss of energy along the way, loss of amplitude of transmitted wave due to reflection of wave at the boundary (of the point far from train) or both?

 

[anorlunda]

Church Bell sounds are easy to hear from far away. I think you are overdoing it trying to reason it out using logic without numbers.

 

[sophiecentaur]

Now my question is that, at one point the displacement of steel surface is enough to produce perceivable sound and at one point it is not

I don't think you have actually experienced this. You are making an assumption. Sound doesn't radiate any better from any particular part of the steel rail. The energy loss is pretty low from a rail because it is not 'spreading out' as sound does in air so it can propagate many km (particularly with continuous welded rail). It is 'contained' better and there is no 'inverse square law' at work. You will be able to hear the small amount of radiated sound easier at a quite remote site than anywhere near the train itself. As I remarked earlier, putting your head right against the rail is the way to couple much more sound into your head (not ears).
There is some loss (radiated sound and internal dissipation) at each section of the track and there is no mechanism that I can think of to change that. There will be transverse and longitudinal waves on the rail (as with the bell). I imagine it's the transverse wave that you hear, more than the longitudinal wave.