Answer
$$\boxed{\frac{(\frac{dV}{dp})_s}{(\frac{dV}{dp})_i}=9.018}$$
Work Step by Step
The speed $v$ of a sound wave in a medium having bulk modulus $B$ and density $\rho$ is
$v=\sqrt {\frac{B}{\rho}}$
or, $f\lambda=\sqrt {\frac{B}{\rho}}$
or, $f=\frac{1}{\lambda}\sqrt {\frac{B}{\rho}}$
Now,
$\frac{f_s}{f_i}=\frac{\frac{1}{\lambda}\sqrt {\frac{B_s}{\rho}}}{\frac{1}{\lambda}\sqrt {\frac{B_i}{\rho}}}$
or, $\frac{f_s}{f_i}= \sqrt {\frac{B_s}{B_i}}$
or, $\frac{f^2_s}{f^2_i}= \frac{B_s}{B_i}$
or, $\frac{f^2_s}{f^2_i}=\frac{-\frac{1}{V}(\frac{dp}{dV})_s}{-\frac{1}{V}(\frac{dp}{dV})_i}$
or, $\frac{(\frac{dV}{dp})_s}{(\frac{dV}{dp})_i}=\frac{f^2_i}{f^2_s}$
or, $\frac{(\frac{dV}{dp})_s}{(\frac{dV}{dp})_i}=\frac{1}{0.333^2}$
or, $\boxed{\frac{(\frac{dV}{dp})_s}{(\frac{dV}{dp})_i}=9.018}$
