Why doesn't (or does) the speed of sound slow down over distance?

I have a keen interest in physics from a layman’s point of view, and enjoy reading pop-science books devoted to the subject. I sometimes get frustrated with what I feel are inadequate explanations for admittedly tricky subjects, explanations that don’t really improve my understanding of what I am trying to learn about (a good example of this was this thread from a few weeks ago, started by another poster).

Many pop-science books talk about how sound travels through a medium (eg air), and a common analogy is like the one found on this site:

… except that can’t be quite how a sound wave works, because when a cue ball strikes a billiard ball, there’s a loss of speed when the energy transfers over to the billiard ball. In fact, the cue ball itself starts slowing down from the moment it gets struck.

So… why doesn’t a sound wave slow down? Or does it?

IIRC, it does slow down. When it slows down to below the speed of sound, it isn’t sound anymore. A better way to think about it is that the maximum speed your wave of billard balls can travel is dependent on the compressibility of the balls.

Think about it where does the momentum that’s lost by the billard balls as they slowdown go? Also, what happends when you line a load ofbillard balls up so they’re touching and strike the end one?

If it didn’t slow down (i.e., lose energy), wouldn’t sound travel forever?

While the speed of the wave doesn’t change over distance, the volume of the sound certainly does. Also, higher frequencies that make the particles bounce around a lot faster are even more absorbed over distance.

You’re not rembering correctly. Sound waves do not slow down. Atoms and molecules colliding behave like perfectly rigid billiard balls in a zero friction environment.

It doesn’t slow down, but the wave spreads and the energy gets spread out over a larger area. At some point the energy is indistinguishable from the random movements of molecules not at absolute zero.

As above, the molecules that make up the air behave as perfect elastic objects. When they bounce against one another they don’t absorb energy in a manner that takes energy out of the gas system. Biliiard balls are macroscopic objects, when they bounce off one another sound waves propagate around inside them, and some of that energy results in heating of the billiard ball, so energy is removed. But a gas molecule has nowhere for the energy to go - it is so fundamental that the kinetic energy remains as such and is available to be transferred to the next molecule it hits.

This is one of the brilliant results of statistical mechanics. Start with just a few basic assumptions, the nature of the molecules, the degrees of freedom they have to move, the magic sauce of equipartition of energy between these degrees of freedom, simple Newtonian mechanics, and out pops the gas laws. These same mechnanics give us the propagation of sound in the gas.

The sound energy propagates away from the source, and with no boundaries the sound level drops with an inverse square law. Eventually it drops below the noise inherent from the thermal agitation of the gas molecules (obeying those Newtonian mechanics.) At this point it gets pretty hard to detect the sound, and as the sound becomes ever more diffuse you get into the province of Shannon’s law, but in principle, at least from a classical point f view, the sound keeps on travelling, and does so at the speed of sound in that gas.

You do get weird things happening, especially noticeable if you have really high power levels of sound. Air is not a perfectly symmetric medium. Sound will compress the air enough that the leading edge of the sound causes the speed of sound to slightly increase in the compression phase, and drop on the rarefaction. This slowly distorts the wave. One would generally characterise this as a second order effect. In general you mostly worry about the simple propagation.

Why is there absolutely no drop in the speed of a sound wave? Is there a tiny drop? How can the movement be truly “frictionless”?

Just to reitterrate the point. Friction is a macroscopic thing. When we are looking at the physics of atom/molecules banging around - the only forces that exist are those that describe the fundamental forces. Conservation of momentum, energy. The rules of quantum electrodynamics which tell us how the electrons that form the outside boundary of the molecule will interact - and in this case repel one another.

Conservation of energy requires that the energy go somewhere. In the macroscopic world that usually means it finally ends up heating things up. But the heat in a gas ***is ***the energy of the molecules bouncing around. The energy isn’t going any place else. Sound is simply an organisation of that bouncing around. In order for the sound to go away you need to disorganise the organisation.

Look above. (I know, this was posted just as you were about to hit submit yourself, but it perfectly answers your question.)

I’m pretty skeptical that collisions of gas molecules are perfectly elastic. Presumably they have vibrational modes of freedom and angular momenta that can absorb energy upon collision.

The reason the speed of sound isn’t because the molecules don’t loose kinetic energy, but because the speed of sound isn’t dependant on the energy in the molecules. This is pretty obvious when you think about it, a loud sound doesn’t travel any faster then a quite one.

Wouldn’t it be with an inverse cube law? We are dealing with three dimensional space rather than a plane.

The sound is an expanding sphere, we measure the energy density on the surface of that sphere. Hence it is an area. If we stop emmiting the sound the inside of the sphere does not stay filled, rather it becomes a (still expanding) hollow shell. Same argument as for light. It is when we think of sound in normal life that we tend to think of it as a diffuse, non directional thing that will fill a volume. But without the sound bouncing off things it behaves much more neatly. Sound in an enclosed, reverberent space is a vastly nastier thing to describe.

Indeed they do (hence some of the wiggle room in what I wrote. But these modes are also lossless. Put some energy into them and it doesn’t get sucked away into any other sort of energy. It becomes into a vibrational mode of kinetic energy and a potential energy in the repulsion of the electron cloud of the distorted molecule. The exact nature of this is described by QED. But on the next interaction with another molecule this vibrational energy can be transferred back into the gas. They key point is that it hasn’t anywhere else to go. For a simple monatomic gas - Helium for instance - no such modes are available anyway.

This however isn’t true. As I wrote above, a loud sound does suffer from effects due to the way it changes the speed of sound. However it is more complex as the rarefaction has a lower speed of sound than the compression. The metric of energy in the gas molecules is otherwise known as the temperature, and for the same pressure the speed of sound does depend upon the temperature, the square root of the absolute temperature in fact.

Of course. It’s not like molecules compress or rub against anything.:smack:

Thanks everyone.