Solution:

Sonic Velocity for Isothermal Process:

For isothermal process : $\frac{p}{\rho}=$ constant

Differentiating both sides, we get,

$$ \frac{\rho \cdot d p-p \cdot d \rho}{\rho^{2}}=0 \quad \text { or } \quad \frac{d p}{\rho}-\frac{p \cdot d \rho}{\rho^{2}}=0 \\ $$

$$or,$$

$$ \frac{d p}{\rho}=\frac{p \cdot d \rho}{\rho^{2}} \quad \text { or } …