acoustics - how do compression and expansion of air transfer energy(sound) and why it is adiabatic not isothermal?

Suppose a vibrating fork exerts force to the air particles to compress which leads to the increase of internal energy (heat).This heat or energy given by the fork is given to the next layer of air and in this way, this energy makes sound. But if it was so, it will be isothermal. And Laplace told it was adiabatic. How can it be? I am confused. The heat energy infact is the energy given by the fork. If it is adiabatic, how can the air pass this energy ?

Answer

This heat or energy given by the fork is given to the next layer of air and in this way,this energy makes sound.

This is the crux of the misunderstanding; sound energy is not transmitted by heat, but rather by the concerted kinetic energy of the gas movement.

It is adiabatic because the heat has nowhere to go other than the gas itself. It is not isothermal because during compression, the temperature increases, and vice versa.

Response to comment:

From which energy is heat energy evolved during compression of gas?Acc. to you, the kinetic energy of the molecules that makes the sound comes from the fork.Where does the heat energy go during expansion?I think the heat energy comes from the work of the fork on the gas during compression.But the energy goes as kinetic energy of the molecule.confused

Yes, heat is evolved during the compression. During expansion, the heat energy is converted into potential energy of the expanded gas. Energy cycles between heat and potential energy, similar to this slow motion video of a shotgun primer firing underwater. During the compression stages, the bubble heats up, and during the expansion stages, the bubble cools down. The energy is still there in both the expanded and contracted bubbles, just in different forms. However, in this case, the adiabatic assumption is slightly incorrect, and the bubble slowly loses energy after each oscillation, causing the bubble oscillations to be damped after about 5 oscillations.

Here is a simple derivation of the speed of sound; the key fact is to note that the speed is determined by $dp/d\rho$, which in some sense represents the "stiffness" of a gas. They use the adiabaticity of the process to show $c=\sqrt{\gamma RT}$, but don't totally explain why adiabaticity is used. Once you understand that page, read this one, which is a more complicated version which explains why the adiabaticity is used. In particular, Newton assumed Boyle's Law held in his derivation of wave propagation in gases, but this is actually false, as explained in the paragraph which starts with "The flaw in this reasoning is the assumption that changes in pressure of an acoustic disturbance are exactly proportional to the changes in density". But basically, the idea is that heat has nowhere to go except to heat up the gas.