# What is sound in terms of acoustic sources?

Sound is nothing more than small amplitude, unsteady pressure perturbations that propagate as a longitudinal wave from a region in space which created it (called the source region) into a quiescent (still) region where it is observed by hearing.

It is at this point where I get slightly confused in that we may distinguish between two types of pressure perturbations: hydrodynamic pressure perturbations and acoustic pressure perturbations. The acoustic perturbations are what we term sound, as they are characterized by their ability to propagate into the hearing region. The hydrodynamic pressure perturbations could be a consequence of fluid flow simply changing in the source region, and this may not necessarily propagate and become what we term sound.

Perhaps evanescent waves can serve as some insight to what I am trying to explain: with reference to this link the pressure fluctations created by the subsonically pulled wavy plate decay exponentially in the upward direction and so do not constitute a sound.

Is my interpretation so far correct? If so are there any rigorous methods for determining if pressure fluctations will propagate (thus becoming sound), or is sound simply that which we can hear outside a source region? Are there other cases besides the linked example for which pressure fluctations are created, but do not propagate as sound?

Hydrodynamic perturbations = change in pressure due to a flow velocity (particles don't return to equilibrium positions).

Acoustic perturbations = change in pressure due to the fact the particles undergo an elastic restoring force (for a compressible fluid) which causes perturbations to travel at the speed of sound.

Any change in the pressure/velocity field will experience acoustic perturbations. The hydrodynamic fluctuating velocity therefore causes acoustic perturbations. Lighthill's analogy explains the equivalent source term in the wave equation, which is a weakly radiating quadrupole source for turbulence, depended on the magnitude of the fluctuating hydrodynamic velocity. The acoustic perturbations are of much smaller magnitude than the hydrodynamic perturbations.

If you define sound as the change in pressure at a receiver, then sound = hydrodynamic + acoustic perturbations. The hydrodynamic part only exists within the source region.

• Thanks for answering. Could you elaborate on this "elastic restoring force" - is this due to the compressibility of the fluid? Because we are dealing with fluids, I thought there was no restoring force (as there would have been for a solid in which molecules are held in a lattice). I'm also unsure of the causality in your definition of Hydrodynamic perturbations: I am used to thinking of flow velocity being caused by pressure gradients. – Dipole Mar 23 '14 at 13:29
• @Jack: Yes, if the fluid is compressible then sound waves will exist in it for this reason. The bulk modulus is an elasticity since it describes pressure per density strain. See the derivation of the sound wave equation for more details. – xyz Mar 24 '14 at 2:28

That's an interesting link, explaining how if fluid contacts a plate, and if there is a vibration pattern in the plate, what vibration pattern you get in the fluid.

As I read it, if the speed of sound in the plate is very high compared to the fluid, the fluid sees a plate that vibrates into and away from the fluid, creating a sound wave that propagates directly away from the plate.

If the speed of sound in the plate is very low compared to the fluid, then the fluid sees a very wavy surface, so up close to the surface the fluid moves with the surface, but at greater distance from the surface these waves cancel each other out.

At intermediate speeds of sound in the plate, interesting things happen. If the speed of sound in the plate is faster than in the fluid, but not much faster, the sound wave radiates at an angle approaching parallel to the surface (not perpendicular).

If the speed of sound in the plate is slower than in the fluid, then you get that cancellation effect at a distance.

Regardless, if waves hit your eardrum, you will hear it and call it sound. If your ear is a distance from the surface and the waves have cancelled at that distance, then of course there is nothing to hear.

Very interesting!

• Yes, indeed it is interesting! I like your interpretation. – Dipole Mar 23 '14 at 13:00

The answers so far have been very good, but I will attempt to answer my own question, building on what has already been said.

Lighthill and Ffowcs Williams make use of the term pseudo-sound to denote sound which can physically be observed by say a microphone, but which will not propagate into the homogeneous quiescent region. The example of a turbulent jet emanating from an orifice or nozzle will explain this. Considerding such a turbulent jet, if we place a microphone very close to the jet we will hear very loud noise due to the fluctuating pressure caused by the turbulent eddies. These eddies I think of as tubes of vorticity (rotational flow) that have a characteristic frequency. Thus they themselves will create "pseudo-sound" because unsteady pressure fluctations are created corresponding to maxima and minima of the pressure created by the eddie movements. However the eddies are not travelling at the speed of sound (they move slower) and so will not propagate. The pressure fluctuations fall off rapidly with distance. I wonder if this "pseudo-sound" is associated with the near field component of sound with a inverse square distance relation with pressure (compared to "real -sound" for which pressure falls off as inverse distance?)