Question

For the pressure variation in a longitudinal wave represented as $P=P_o\cos (\omega t-kx)$, the density $\left(\rho \right)$ equation for the given medium is best represented by
(${\rho }_o$ is the density of the medium at pressure $P_o$)

• A. $\rho ={\rho }_o\sin (\omega t-kx)$
• B. $\rho =-{\rho }_o\sin (\omega t-kx)$
• C. $\rho ={\rho }_o\cos (\omega t-kx)$
• D. $\rho =-{\rho }_o\cos (\omega t-kx)$

Answer 1

The correct option is C $\rho ={\rho }_o\cos (\omega t-kx)$

We know that if pressure is high in a particular region of a medium then density is also high and if pressure is low then density is also low.
This means pressure and density are in phase.
$\Rightarrow \Delta \varphi =0$
So, for pressure equation $P=P_o\cos (\omega t-kx)$, density equation will be $\rho ={\rho }_o\cos (\omega t-kx)$.