# Is there a limit to how loud a sound can be?

#### tee

Just wondering...
Is there a limit to how loud a sound can be?

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#### wimms

define loud and sound first.

seems to me there is one. Limited by speed of sound and mass contained in wavefront.

#### anilrapire

...or rather the density of the medium the sound's in.

#### Chi Meson

Homework Helper
I like this question, and I'm waiting to see what answers are developed.

Since "loudness" is actually a human auditory response to the pressure amplitude of a wave (let's assume a sound wave in air), I *think* loudness would be limited by the compressability of the air.
and also by the extent of rarefaction possible. Total vacuum is the limit of rarefaction, but I can't answer for the other end.

I would also think that at some point the air would "liquify" at some pressure-amplitude, or otherwise undergo a drastic change of properties. But that's as far as my input goes right now.

#### anilrapire

^ I think all of that stuff is more succinctly encapsulated in that person's speed of sound explination.

#### hypnagogue

Staff Emeritus
Gold Member
Well, we can put an upper bound on loudness as the maximal firing rate of auditory neurons in the ear. Since subjective loudness is a function of how rapidly the auditory neurons are firing, and there is a theoretical limit to how rapidly neurons can fire due to their biochemistry, there should be a corresponding "maximum loudness." Although I don't know offhand what this would be, I would imagine the human limits of perceiving loudness would fail long before we had to take into account the limits of the ability of the physical medium to carry energy in the form of pressure waves.

#### anilrapire

good point, but that could well be less than the maximum "loudness" as determined by the physical properties of the medium in question, in air at least.

#### Chi Meson

Homework Helper
Originally posted by anilrapire
^ I think all of that stuff is more succinctly encapsulated in that person's speed of sound explination.
Perhaps, and I'm not disagreeing, but I'm not satisfied with it. Since an increased pressure amplitude would increase the mass in the wave-front, what limits the mass in the wave-front?

And the intensity of the wave itself is also a function of the frequency of the sound which leads to a tangential question: is there a limit to the frequency that can be carried in a particular medium?

And I don't yet see how the speed of sound limits the intensity of a wave.

#### wimms

Thats why I thought definition of sound and loudness would be nice. For human ear, 120db is too much. More than that, and damage occurs. And 120db isn't very "loud" actually. Jets produce more every takeoff.

I'm not sure, but afaik sound is result of change in pressure, not pressure level itself, and typical medium has limit to its compressibility. Air when compressed too much becomes liquid. Thats different medium. So definition of sound is needed. Wind can be very low frequency sound, but we call it mechanical motion of molecules.

Suppose soundwave in air with max intensity, I thought it would be limited by compressibility of air at wavefront, and that depends on speed of medium reaction, or speed of sound. Sonic boom is example of energy imparted to air, and air pressure at front depends on inertia of air ahead of it, else pressure would dissipate. Speed of sound also depends on density of medium, or its pressure level perhaps.

Seems to me, speed of sound determines max slope of wavefront, and velocity also defines kinetic energy carried. You know that low frequency sound to carry same energy as high frequency sound needs more amplitude. Imo, its because slope of wavefront is what defines "loudness". Sure, meteorite entering atmosphere can impart huge amounts of energy to air, but sound wave leaving it cannot be sustained in the medium. Thus, although pressure level at collision point is immense, its not exactly sound.

What limits mass in wavefront? I guess normal mass density of medium together with speed of sound. Slope of wavefront is limited by this speed, and amount of mass moved depends on that slope and time. You can move huge masses with more time, or less mass faster - frequency-amplitude dependance.

But I'm not very sure here. Perhaps someone who knows better could help us out.

As to limits of frequency, I guess so too. Lower limit depends on where we make distinction between sound and mechanical motion, upper limit is somewhat foggier to me. But if assume limited slope of wavefront, then higher frequency periodic motion results in reduced amplitudes. Higher limit is then defined by minimum possible amplitude, that is still meaningful as being sound. I know several (or even hundreds) MHz sounds can easily travel in air. Afaik even TV-sets used acoustic delaylines using sound to decode color signals. I believe there is limit, and it also depends on speed of sound, but I don't know how to find it. Maybe limit is somewhere where we stop calling it sound and start calling it heat.

#### Chi Meson

Homework Helper
I guess we're talking about the maximum intensity of the wave, since the word "sound" falls apart way before the maximum. I agree that it must approach a limit and I think you're right that we would start calling it "heat" (thermal energy, properly). A meteor is heated, afterall, not by "friction" with the air but due to the adiabatic compression of the air in front of it.

As for is it "sound," well the immense pressure in front of the meteor is followed by a rarefied zone behind it, ergo "pressure amplitude." Voila: a sound so loud you blow up!

#### wimms

Originally posted by Chi Meson
As for is it "sound," well the immense pressure in front of the meteor is followed by a rarefied zone behind it, ergo "pressure amplitude." Voila: a sound so loud you blow up!
I'd only avoid to call that sound wave, because it is unable to travel in air separately, without continuous addition of energy from meteor. Immense pressure in front of meteor is unable to travel by itself. More like explosion rather than sound.

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