Q.What is the effect of pressure on velocity of sound?

[!TLDR] At constant temperature, a pressure change has no effect on the speed of sound in air, since Boyle's Law keeps PV (and hence …

By Laplace's formula, $v=\sqrt{\gamma P/\rho}$. Writing density as $\rho=M/V$ for a fixed mass M of air occupying volume V, this becomes $v=\sqrt{\gamma PV/M}$. At CONSTANT temperature, Boyle's Law states $PV=\text{constant}$ for a fixed mass of gas; since M and γ are also fixed for a given gas sample, the entire quantity under the square root does not change when P alone changes -- so v itself stays constant. The same conclusion follows from the ideal-gas form $v=\sqrt{nRT\gamma/M}$: with temperature T held fixed, v depends only on T, not on P directly. So a pressure change, BY ITSELF, with temperature unchanged, has no effect on t …

Substitute $\rho=M/V$ into Laplace's formula and apply Boyle's Law ($PV=\text{constant}$ at fixed temperatur …

Assuming higher pressure must mean faster sound (since pressure appears explicitly in the formula) without accounting for the accompanying change in density t …