What is the highest-frequency sound that can exist in Earth's atmosphere?

Radium

Hi:

What is the highest-frequency sound that can exist in Earth's
atmosphere?

AFAIK, there is no limit, but I would like some clarification.

Is it possible for a pure-sine-wave tone of 140 dB, 10^10,000 Hz [i.e.
10-to-the-power 10,000
Hz; or 10 followed by 10,000 zeros] to exist on Earth's atmosphere?

What determines the upper limit of high-frequency in the air?

Thanks,

Radium

René Meyer

There is a natural cutoff set by the average distance between two air
molecules, I guess. Everything with wavelengths shorter than that will
not propagate any more.

Radium schrieb:

> Hi:
>
> What is the highest-frequency sound that can exist in Earth's
> atmosphere?
>
> AFAIK, there is no limit, but I would like some clarification.
>
> Is it possible for a pure-sine-wave tone of 140 dB, 10^10,000 Hz [i.e.
> 10-to-the-power 10,000
> Hz; or 10 followed by 10,000 zeros] to exist on Earth's atmosphere?
>
> What determines the upper limit of high-frequency in the air?
>
> Thanks,
>
> Radium

Igor Khavkine

Radium wrote:
> Hi:
>
> What is the highest-frequency sound that can exist in Earth's
> atmosphere?
>
> AFAIK, there is no limit, but I would like some clarification.

Of course there is a limit.

> What determines the upper limit of high-frequency in the air?

Sound is associated with (relativly low amplitude) pressure waves in
air. However, such vibrations are only possible under conditions where
air can be approximated as a continuous fluid. This approximation
breaks down when the wavelength of the wave becomes comparable with the
mean free path of the molecules that make up the atmosphere. The mean
free path is roughly the average distance between collisions of
atmospheric molecules. It is collisions between molecules that keep air
in local equilibrium, which allows the continuum approximation. Below
the mean free path scale, hydrodynamic equations (which also describe
propagation of sound waves) are no longer sufficient and we must resort
to a molecular description. Consequently, coherent pressure waves are
impossible if the wave is supposed to make several oscillations before
the front of the wave has even collied with a sufficient number of
molecules to make the surrounding air move.

The mean free path in air at sea level is about 0.1 micron[1]. Let's
take the speed of sound to be roughly 300 m/s. Then the upper limit on
sustainable sound frequencies is

f_max = (300 m/s) / (10^-7 m) = 3*10^9 Hz = 3 GHz.

Incidentally, there should be a limit on the maximum amplitude of sound
in the athmosphere as well. The first obstacle would be non-linearities
of the hydrodynamic equations that become important when the wave
amplitude deviates strongly from equilibrium. Non-linear effects
usually mix different harmonics. But coherent waves may still be
possible. The larger the amplitude of sound wave the larger the
pressure differences that build up between the crests of the wave. At
sufficiently high pressures, air can change phase, while at
sufficiently low pressures, it can become so rarified that the
continuum fluid approximation fails as well. Both of these properties
destroy the hydrodynamic approximation. I'll leave someone more
knowledgeable in gas dynamics to estimate this upper bound.

Hope this helps.

Igor

ianparker2@gmail.com

Radium wrote:
> Hi:
>
> What is the highest-frequency sound that can exist in Earth's
> atmosphere?
>
> AFAIK, there is no limit, but I would like some clarification.
>
> Is it possible for a pure-sine-wave tone of 140 dB, 10^10,000 Hz [i.e.
> 10-to-the-power 10,000
> Hz; or 10 followed by 10,000 zeros] to exist on Earth's atmosphere?
>
> What determines the upper limit of high-frequency in the air?
>
> Thanks,
>
> Radium

No. The highest (effective) frequency that can exist is linked to the
mean free path. This at sea level is about 10^-7m. Hence the highest
frequency (even loosly defined as sound) is 340e7 Hz. Even that is
stretching a point.

http://www.kayelaby.npl.co.uk/genera...2_4/2_4_1.html

gives a general account of attenuation. At 100kHz we have about
1800dB/km in fairly dry air. Attenuation on a simple model goes up as
f^2. Range of 1000kHz therefore bein of the order of 10m (1.8dB/m). At
1MHz we have 10cm. At 10MHz 100 microns. In my book 100MHz+ can't
really exist in air.

- Ian Parker

Boo

Radium wrote:
> Hi:
>
> What is the highest-frequency sound that can exist in Earth's
> atmosphere?
>
> AFAIK, there is no limit, but I would like some clarification.
>
> Is it possible for a pure-sine-wave tone of 140 dB, 10^10,000 Hz [i.e.
> 10-to-the-power 10,000
> Hz; or 10 followed by 10,000 zeros] to exist on Earth's atmosphere?
>
> What determines the upper limit of high-frequency in the air?
>

Well, if the wavelength is shorter than the mean spacing between air molecules
there's an obvious problem, but I don't know if anything gets in the way before
that...

--
Boo

Igor Khavkine

Igor Khavkine wrote:

> The mean free path in air at sea level is about 0.1 micron[1].

Sorry, I forgot to give the reference.

[1]http://amsglossary.allenpress.com/glossary/search?id=mean-free-path1

Igor

Radium

René Meyer wrote:
> There is a natural cutoff set by the average distance between two air
> molecules, I guess. Everything with wavelengths shorter than that will
> not propagate any more.

So the closer the distance between the two air molecules, the higher
the frequency that can propagate??

Richard Saam

Radium wrote:

> Hi:
>
> What is the highest-frequency sound that can exist in Earth's
> atmosphere?
>
> AFAIK, there is no limit, but I would like some clarification.
>
> Is it possible for a pure-sine-wave tone of 140 dB, 10^10,000 Hz [i.e.
> 10-to-the-power 10,000
> Hz; or 10 followed by 10,000 zeros] to exist on Earth's atmosphere?
>
> What determines the upper limit of high-frequency in the air?
>
> Thanks,
>
> Radium
>
In the context of the de Broglie Hypothesis:

http://en.wikipedia.org/wiki/De_Broglie_hypothesis

"The second de Broglie equation relates the frequency of a particle to the
kinetic energy"

So an individual air molecule frequency approaches infinity as its velocity
approaches the speed of light.

Richard

frankauteri@northernsystemssolutions.com

Boo wrote:
> Radium wrote:
> > Hi:
> >
> > What is the highest-frequency sound that can exist in Earth's
> > atmosphere?
> >
> > AFAIK, there is no limit, but I would like some clarification.
> >
> > Is it possible for a pure-sine-wave tone of 140 dB, 10^10,000 Hz [i.e.
> > 10-to-the-power 10,000
> > Hz; or 10 followed by 10,000 zeros] to exist on Earth's atmosphere?
> >
> > What determines the upper limit of high-frequency in the air?
> >
>
> Well, if the wavelength is shorter than the mean spacing between air molecules
> there's an obvious problem, but I don't know if anything gets in the way before
> that...
>
> --
> Boo

Not sure why I feel compelled to chip in ... but a supersonic pulse,
like from lightning and such ... could, and very likely would contain
higher frequencies than GHz as an FT of the pulse. Though not
technically "audible" by the human ear, it could still be characterized
by a group of mechanical wavefunctions. And while we are on the
subject, you could super heat the air, indefinitly, to the point of
first disociating the molecules, then geting up to stiping the
electrons from the nuclei and getting, well, plasma. That's where I'd
have to leave off as I don't know much about high energy physics.

Boo

>>> What determines the upper limit of high-frequency in the air?
>>>
>> Well, if the wavelength is shorter than the mean spacing between air molecules
>> there's an obvious problem, but I don't know if anything gets in the way before
>> that...
>
> Not sure why I feel compelled to chip in ... but a supersonic pulse,
> like from lightning and such ... could, and very likely would contain
> higher frequencies than GHz as an FT of the pulse.

But you can't put an arbitrary shaped pulse into a band limited transmission
medium, so the pulse shapes you can transport are determined by the high
frequency cutoff, not vice-versa.

--
Boo