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In the Laplace corrrection for velocity of sound, the bulk modulus is replaced by gamma×Pressure. $(\gamma=c_p/c_v)$ In its derivation

$$PV^{\gamma} =\text{CONSTANT} $$ is used.

And the reason given is that since the process is very fast, there is no time for heat transfer hence it is adiabatic. My question is that if the process is fast then it is not quasi-static hence it is not reversible ,Then how can we use $$PV^{\gamma} =\text{CONSTANT} $$ As this equation is valid only for reversible adiabatic process.

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Laplace's model assumes infinitesimally small changes in pressure, and the non-adiabatic effects are negligible.

Later physicists including Rayleigh included extra terms in the model caused by the change in temperature during each cycle of the sound wave and the resulting thermal conduction through the medium (and also thermal conduction into and out of the boundary, e.g. for a sound wave inside a metal pipe), but for the amplitudes which normally occur in acoustics these effects are insignificant (IIRC they change Laplace's model by the order of $1$ part in $10^4$).

For large amplitudes (e.g. shock waves from explosions) everything is nonlinear, so Laplace's results are not applicable.

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