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

  1. 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
     
  2. jcsd
  3. Re: What is the highest-frequency sound that can exist in Earth'satmosphere?

    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
     
  4. Re: What is the highest-frequency sound that can exist in Earth'satmosphere?

    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
     
  5. Re: What is the highest-frequency sound that can exist in Earth'satmosphere?

    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/general_physics/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
     
  6. Boo

    Boo 0

    Re: What is the highest-frequency sound that can exist in Earth's

    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
     
  7. 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
     
  8. 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??
     
  9. Re: What is the highest-frequency sound that can exist in Earth's

    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
     
  10. Re: What is the highest-frequency sound that can exist in Earth's

    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.
     
  11. Boo

    Boo 0

    Re: What is the highest-frequency sound that can exist in Earth's

    >>> 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
     
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