Question

If the pressure amplitude of sound wave in a medium is tripled and the wavelength is doubled then the amplitude of displacement of the particles in the medium becomes $x$ times the initial value. The value of $x$ is

• A. $5$
• B. $3$
• C. $2$
• D. $6$

Answer 1

The correct option is D $6$

The relation between the maximum value of pressure in a medium and displacement of the particles in the medium is given by,

$P_o=B{A}_{o}k$

where, $P_o$ is maximum pressure in the medium, $B$ is the bulk modulus of the medium, $A_o$ is maximum displacement of particles in the medium and $k$ is the wave number of sound wave.

As $k=\frac{2\pi }{\lambda }$

$\Rightarrow P_o=\frac{2\pi B{A}_o}{\lambda }$

$\Rightarrow A_o=\frac{P_o\lambda }{2\pi B}....\left(1\right)$

If pressure amplitude is tripled and wavelength is doubled then,

$\Rightarrow A_o^{{}^{\prime }}=\frac{3P_o\times 2\lambda }{2\pi B}$

$\Rightarrow A_o^{{}^{\prime }}=\frac{6P_o\lambda }{2\pi B}=6A_o$ [from $\left(1\right)$]