# The lowest possible frequency of sound wave

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?

• May 21 at 14:08
• 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] May 21 at 17:32

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).