Stupid Audio Question

Air pressure doesn't affect sound velocity, but temperature does. I'd imagine that a change of temperature would detune wind instruments to some extent, certainly with more effect than, say, using Monster cables or tube DACs or picosecond jitter reducers.

Music sellers should be required to note ambient recording temperature for every track. That would give the audiophools something new to argue over.

John

Eh, John? Are you sure about that? Maybe, as atmospherics are concerned, but how about 200PSI versus 20PSI ??

...Jim Thompson

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|  James E.Thompson, P.E.                           |    mens     |
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I love to cook with wine.      Sometimes I even put it in the food.

Wikipedia never lies!

John

It got it right this time, anyway. Look up some more controversial topics, and you'll get a very different picture of its accuracy.

Within the range where ideal gas behaviour applies, i.e. mean free path between molecule-molecule collisions is much greater than the molecular diameter but much smaller than a breadbox, the speed of sound depends only on temperature.

This is because sound is transmitted by those collisions, and it can't go faster than the mean velocity of the molecules (there's a factor of, iirc, 1/sqrt(3) because the collisions randomize the particle directions).

Shock waves are what you get when the sound is strong enough to significantly change the mean molecular velocity, and they can go much faster than the speed of sound.

Cheers,

Phil Hobbs

Wikipedia has cleaned up its speed of sound info since the last time I looked, but it is still only a presentation of the infinitesimal ("small signal") equations (provided with the vague caveat "This equation applies only when the sound wave is a small perturbation on the ambient condition") without any derivations. For derivations or the finite amplitude sound equations you still need a book. IMO the best is Blackstock, Fundamentals of Physical Acoustics (presumes comprehension of partial differential equations). The introduction chapter defines wave propogation, presents some simple examples (electrical transmission line and plucked string) and derives the lossless one dimensional wave equations for sound in ideal gasses from conservation of mass and momentum on an infintessimal control volume. When the pesky nonlinear terms are dropped (valid only for infintessimal amplitude sound) you get the Wikipedia version of sound. When they are not dropped you have the finite amplitude sound equations, in which the speed of sound is not a constant - the higher pressure parts of the wave travel faster because they are hotter (adiabatic compression required by the lossless assumption). Shock waves do not really go faster than the speed of sound (how can sound go faster than sound?), they only go faster than the infintessimal amplitude speed of sound.

BTW, the speed of infinitesimal amplitude sound varies with the mean molecular weight of the air, which changes with humidity (~.4% increase dry to wet at STP). And the characteristic impedance of air varies directly as infinitesimal amplitude speed * density, a function of pressure, temperature and humidity.

And don't forget the effect of the increasing concentration of CO2 in the atmosphere :-).

If all you mean by "speed of sound" is "how fast this particular disturbance travelled from A to B", then you're right, but that isn't the usual (or useful) definition, because it only applies to the one case. The usual definition of a shock wave is one where the entropy density is significantly increased by its passage.

Yes, all of which are very very constant on the time scales of sound waves (see subject line).

Back on your heads.

Cheers,

Phil Hobbs

If you ever heard the effect of helium on changing the voice by breathing a little of it due to the decrease in air density, the same thing would happen to all the wind instruments but to a lesser extent. The string instruments would not change due to the difference in air density. How much the freq. would change is up to you to find out.

John

Ah, the best answer yet. Air density is the key.

Al

If the composition doesn't change, density does not change sound velocity. Temperature does.

John

Right, a change in density due to a change in pressure with constant temperature and composition has absolutely no effect whatsoever on the (small-signal) speed of sound in air. A change in temperature or to a lesser extent humidity (which changes the composition of the air) will require retuning of instruments, a change in pressure will not.

What does change with pressure is the impedance of air, which is directly proportional to air density. Impedance can be thought of as the ratio of "push" to "flow". In a DC electrical circuit the impedance (resistance) is push (volts) / flow (amps); R = E/I. In an acoustic "circuit", impedance is push (sound pressure) / flow (particle displacement). So as air pressure decreases from NYC (14.7 PSIA) to Denver (12.1 PSIA), the sound pressure produced by the same instrument surface vibration amplitude will be reduced by a factor of

12.1/14.7, or about 82% of the sound pressure level produced by the same amplitude surface vibration at sea level.

Glen

I'd have guessed that lower pressure air, which is lower density, would raise the resonant freq. of an instrument, kinda like helium makes your sinuses resonate higher.

Or am I just blowing smoke up my own headbone?

Thanks, Rich

I was merely complaining that Wikipedia presents the small-signal approximation of the speed of sound (and the rest of the small signal sound properties) without properly explaining what the approximation is and what its limits of validity are. Not to mention a complete lack of explanation as to why the speed of sound is what it is.

A drawback of the standard convention of referring to the small-signal speed of sound as the speed of sound is that there is a tendency to apply it (and the other small-signal sound properties) to all sound with the possible exception of shock waves or sound loud enough to clip at zero absolute pressure. This is like assuming that the small signal response of an amplifier applies right up to clipping at the power supply rails - it just isn't so.

Real finite amplitude sound has losses. The primary losses, or "increase in entropy density" if you prefer, are due to the conduction of heat from the higher pressure, hotter part of the wave (peaks) to the lower pressure, cooler part of the wave (troughs), converting mechanical energy into heat. These losses are insignificant over short distances within the frequencies of human hearing and at comfortable listening levels, but they become significant at high frequencies because the peaks and troughs get close, putting an upper limit on the frequency of ultrasound which will propogate a significant distance in air. At high enough frequencies a transducer will simply heat the air in front of it, increasing entropy density. Over long distances this effect selectively attenuates higher frequencies even within the range of hearing, again increasing entropy density. Likewise where the sound pressure approaches atmospheric pressure the temperature differences between peaks and troughs increase, losses increase significantly - and the speed of sound becomes significantly non-constant.

So your "usual" definition of a shock wave applies to non-shock finite amplitude sound also, and is probably why no source I consider to be authoritative on the subject uses it (e.g. Shapiro - The Dynamics and Thermodynamics of Compressible Fluid flow, Thompson - Compressible Fluid Dynamics, Blackstock - Fundamentals of Physical Acoustics). All of these sources use what I regard as the usual definition, essentially a "large" change in state variables (pressure, temperature, density ..) in a very "thin" layer (or "short" time depending on frame of reference). Entropy density also increases, not because that is a defining characteristic of shock waves but for the exact same reasons other finite amplitude waves increase entropy density - primarily due to the conduction of heat.

The thickness of the shock layer is not independent of the magnitude of pressure change across it; as a shock wave weakens with propogation (and usually expansion) its thickness increases until it is no longer a shock wave but rather an oridinary finite amplitude sound wave, with no clear dividing line between the two, and no sudden change in the significance of the entropy density increase.

But not constant between NYC and Denver (see original question and my response re: air impedance, the significant change with altitude.)

On a slightly longer time scale, the atmospheric CO2 increase has decreased the small-signal speed of sound at STP from 1126.91 Feet/Sec in 1976 to 1126.89 Feet/Sec in 2003. Retune those instruments :-).

With, maybe, a corresponding increase in Q.

John