Q.State Newton's formula for velocity of sound.

[!TLDR] Newton's formula gives the speed of sound as the square root of the medium's elastic modulus divided by its density, specialised for air using the (isotherma …

Newton proposed that the speed of a sound wave through a medium is $v=\sqrt{\dfrac{E}{\rho}}$, where E is the medium's proper (elastic) modulus and ρ is its density -- since sound propagates via compressions and rarefactions, its speed should depend on how strongly the medium resists that compression (elasticity) and how much inertia it has (density). Newton assumed sound propagation in air happens at constant average temperature (an isothermal process), so the relevant modulus is the ISOTHERMAL bulk modulus, which for a gas equals simply the ambient pressure P -- giving, specifically for air, $v=\sqrt{\dfrac{P}{\rho}}$. Using NTP values ($P=hdg$ with h=0.76 m, d=13600 kg/m³, ρ=1.293 kg/m³, g=9.8 m/s²), th …

State Newton's general formula $v=\sqrt{E/\rho}$ and its air-specific isothermal form $v=\sqrt{P/\rho}$, tog …

Stating only the air-specific form $v=\sqrt{P/\rho}$ without mentioning it rests on the (later shown to be wrong) isothermal assumption -- which matter …