Question

A sound wave of wavelength $50\text{cm}$ travels in a gas medium. If the difference between the maximum and minimum pressures at a given point is $5\times {10}^{-3}{\text{N/m}}^2$ and the amplitude of vibration of the particles of the medium is $5\times {10}^{-10}\text{m}$, find bulk modulus of the medium.

• A. ${10}^5{\text{N/m}}^2$
• B. $2\times {10}^5{\text{N/m}}^2$
• C. $3\times {10}^5{\text{N/m}}^2$
• D. $4\times {10}^5{\text{N/m}}^2$

Answer 1

The correct option is D $4\times {10}^5{\text{N/m}}^2$

Given that,
Wavelength, $\lambda =50\text{cm}$
Displacement amplitude, $S_0=5\times {10}^{-10}\text{m}$
Pressure amplitude $P_0=Bk{S}_0$
where $B$ is bulk modulus of the medium and $k$ is wave number.
$P_0=\frac{P_{max}-P_{min}}{2}$
$=\frac{5\times {10}^{-3}}{2}$
$=2.5\times {10}^{-3}{\text{N/m}}^2$.
$k=\frac{2\pi }{\lambda }=\frac{2\pi }{0.5}=4\pi$

Hence, $B=\frac{P_0}{k{S}_0}$
$=\frac{2.5\times {10}^{-3}}{4\times 3.14\times 5\times {10}^{-10}}$
$=3.98\times {10}^5{\text{N/m}}^2$
$\approx 4\times {10}^5{\text{N/m}}^2$