Newton's Formula For The Velocity Of Sound In Gas MCQ - Practice Questions with Answers

Speed of sound wave in gas: Newton's formula

The main assumption before deriving the equation is when the sound propagates through a gas, temperature variation in compression and refraction is negligible. So, Newton assumed that in the exchange of heat with the surroundings, the temperature of the layer would remain the same. Hence this process is isothermal. Thus by using the formula that we have studied in the last concept, we can write that - 

$$
v=\sqrt{\frac{B_i}{\rho}} \ldots \ldots(i)
$$

Where $B_i=$ Isothermal Bulk modulus
Now, in the isothermal process, $\mathrm{PV}=$ Constant
Differentiating both sides, we get -

$$
\begin{gathered}
P d v=V(-d P) \\
P=\frac{d P}{\frac{d V}{V}} \quad(\text { Neglect the negative sign })
\end{gathered}
$$

$\left(A s, \quad B_i=\frac{d P}{\frac{d V}{V}}\right)$
So from the definition of Bulk modulus, we can say that the $\mathbf{P}=\mathbf{B}_{\mathbf{i}}$
So from equation (i), We can write that -

$$
v=\sqrt{\frac{P}{\rho}}
$$

This formula is given by Newton, So it is called Newton's formula.