# Can a propagating sound wave change the temperature of the medium?

When air molecules are given energy they compress the layer of air molecules next to them and so on which causes a high pressure wave to move forward so does this make any change in the average kinetic energy per molecule/atom of air and change its state like increasing temperature or internal energy and enthalpy

• The assumption most often made to reach the linearised wave equation is that the process is adiabatic, which holds to a good degree of approximation. In practice, there is some heat exchange but for practical reasons it suffices. I am not familiar with non-linear acoustics but this falls into this category. If there is any specific application (or example) you have in mind it could be beneficial to state it here ‘cause this will allow people here to base their explanation/solution/answer on your example to build intuition. Sep 21 at 18:21

The amount of pressure rise caused by the passage of a sound wave is very small compared to ambient, which by the gas law means the temperature rise will be correspondingly small. Note also that the duration of the pressure rise is extremely brief, and air is a poor conductor of heat, which means any temperature rise has nowhere to go and no time in which to do it. All these things mean that 1) the passage of a sound wave leaves the state of the air through which it moves unchanged and 2) the differential equation describing the motion of the wave can be simplified without loss of accuracy by setting any heat transfer terms to zero.

The situation is completely different for the movement of a supersonic shock wave through air. See Serber's book The Los Alamos Primer for more explanation.

For sound travelling in a gas the changes which occur can be assumed to be approximately adiabatic.
You might have noticed that the speed of sound $$c = \sqrt{\frac{\gamma P}{\rho}}$$ where $$P$$ is the ambient pressure, $$\rho$$ the density of the gas and $$\gamma$$ is the adiabatic constant , $$PV^\gamma= \rm constant$$.
Thus, there is no heat transfer between successive volume elements of the air as the sound wave progresses, ie no change in entropy, and after the sound wave has passes the temperature of the air is unchanged.
A fuller explanation is given in the answer to the question Why are sound waves adiabatic? where it is also explained that the adiabatic behaviour ceases at frequencies above $$10^9\,\rm Hz$$

Although the processes are adiabatic to a very good approximation there is some heat transfer and the temperature of the gas does increase a little as a sound wave passes through.
Some of the "ordered" movement of the gas molecules due to the passage of a sound wave become disordered, the gas is "heated", and this can be due to "irregularities" in the gas, eg dust particles, encountered by the sound wave.
The increase in temperature due to this effect is insignificant.

As stated in earlier answers, sound that is within the range of human hearing and not too loud for human hearing will propagate with hardly any dissipation of the sound energy.

There is some dissipation, the louder the sound the more dissipation, and higher frequencies have a higher rate of dissipation.

Example:
A crack of thunder generates a very wide range of frequencies of sound. When you hear a nearby crack you experience a high pitched sound. When a crack of thunder reaches you from a distance of tens of kilometers the higher frequencies have dissipated, and only low frequencies remain, so what you hear is a rumbling sound.

There have ben attempts to transmit energy using ultrasonic sound. You can have an ultrasonic emitter crank out a lot of sound energy; if it is far enough above the highest frequencies a human can hear then that ultrasound is not perceptible to humans. A special receiver can then convert that sound energy back to electric energy (the conversion has a low yield).

The thing that kills the endeavour is the rate of dissipation. The sound energy drops off very rapidly as you move away from the emitter. In a large room the sound energy doesn't even make it to the walls, within several meters of distance all of the sound energy dissipates to heat.