Obtain the equation for the speed of a sound wave in air and identify the error in this equation.

(N/A) The general equation for the speed of a sound wave in a gas is given by $v = \sqrt{\frac{B}{\rho}}$,where $B$ is the bulk modulus and $\rho$ is the density of the gas.
Newton assumed that the propagation of sound in air is an isothermal process.
For an isothermal process,$PV = \text{constant}$.
Differentiating both sides,we get $V \Delta P + P \Delta V = 0$,which implies $P = -\frac{\Delta P}{\Delta V / V}$.
Since the bulk modulus $B = -\frac{\Delta P}{\Delta V / V}$,we get $B = P$.
Substituting this into the general equation,we get Newton's formula for the speed of sound: $v = \sqrt{\frac{P}{\rho}}$.
For air at $STP$,$P = 1.01 \times 10^5 \text{ Pa}$ and $\rho = 1.29 \text{ kg/m}^3$.
Calculating the value: $v = \sqrt{\frac{1.01 \times 10^5}{1.29}} \approx 280 \text{ m/s}$.
The experimental value of the speed of sound in air is approximately $331 \text{ m/s}$.
The error in Newton's formula is that it underestimates the speed by about $15\%$. This is because sound propagation is actually an adiabatic process,not an isothermal one.