Question

Choose the correct options for longitudinal wave

• A. maximum pressure variation is BAK
• B. maximum density variation is $\rho AK$
• C. pressure equation and density equation are in phase
• D. pressure equation and displacement equation are out of phase

Answer 1

Answer: (A), (B), (C)

The correct options are
A maximum pressure variation is BAK
B maximum density variation is $\rho AK$
C pressure equation and density equation are in phase

There are three equations associated with any longitudinal wave .

$y(x,t),\Delta P(x,t),and$ $\Delta \rho (x,t)$

y represents displacement of medium particles from their mean position parallel to direction of wave velocity .

From $y(x,t)$ equation we can make $\Delta$P(x,t) and $\Delta$$\rho$ (x,t) equation by using fundamental relations between them ,

$\Delta P=-B\frac{dy}{dx}$ and $\Delta \rho$ = - $\rho$ $\frac{dy}{dx}$

Pressure amplitude = BAK and density amplitude = ρAK

Therefore A and B are correct options.

$\Delta P(x,t)$ and $\Delta \rho (x,t)$ are in same phase . But $y(x,t)$has a phase difference of $\pi$/2 with rest two equations .

Therefore C is correct and D is wrong option