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What is the lowest possible frequency of sound waves. I imagine that if a plate vibrates slower and slower it stops producing sound and starts to just 'move' the air around. What is this minimum frequency and why is there a minimum frequency.

My guess is that the lower the frequency the faster the waves dissipate and turn into heat. Is this a valid explanation?

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    $\begingroup$ this might interest you background.uchicago.edu/~whu/SciAm/sym2.html people.virginia.edu/~dmw8f/BBA_web/unit05/unit5.html $\endgroup$
    – anna v
    May 21 at 14:08
  • $\begingroup$ All the dictionaries I've checked define sound as something that can be heard, but Wikipedia says: Sound is defined as "(a) Oscillation in pressure, stress, particle displacement, particle velocity, etc., propagated in a medium with internal forces (e.g., elastic or viscous), or the superposition of such propagated oscillation. (b) Auditory sensation evoked by the oscillation described in (a)."[ANSI/ASA S1.1-2013] $\endgroup$ May 21 at 17:32
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First of all, it depends on the size and shape of the plate. As a rule of thumb, the wave length cannot be longer than two times the extent of the object, which gives us the rough estmate of frequency as $$f=\frac{v_{sound}}{\lambda}$$ A more precise answer requires finding the eigenmodes of the plate (i.e., solving the sound wave equation with the boundary conditions imposed by the shape of the object).

If we assume that the plate is very big, then we have to account for other processes that may affect the wave existence/propagation. E.g., in the case of a very long wavelength (very small frequency) the random displacements of atoms in respect to each other may be more significant than those corresponding to the wave. There are also many damping mechanisms that play more important role at low frequencies, and can make a wave non-propagating.

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Sound in air is a periodic variation in pressure that propagates with a characteristic speed. When the frequency and amplitude of the variation is sufficient to vibrate the mechanism within your ear, you will hear it.

There is no hard minimum frequency for periodic variations in air pressure, although as the frequency becomes very low (much less than 1Hz) in open air, then the effects are more likely to get scrambled with the non-periodic random changes in air pressure that occur naturally. There is an upper bound to the frequency , however- as the frequency increases, the wavelength decreases to the point at which it is small compared with the mean spacing of air molecules, beyond which it can no longer propagate.

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