Question

The displacement function $S(x,t)$ of three sound waves $1,2$ and $3$ at a certain time $t$ as marked on the curves that travel along $x-\text{axis}$ through air. If $P_1,P_{2}and{P}_3$ represent their pressure amplitudes respectively, then the correct relation between them is:

• A. $P_1>P_2>P_3$
• B. $P_3>P_2>P_1$
• C. $P_1=P_2=P_3$
• D. $P_2>P_3>P_1$

Answer 1

The correct option is B $P_3>P_2>P_1$

We know,
$\Delta P_o=B{S}_{o}k$
where, $B=$ Bulk modulus
$S_o=$ Displacement amplitude
$k=\frac{2\pi }{\lambda }=$ wave number
$\Rightarrow \Delta P_o=B{S}_o(\frac{2\pi }{\lambda })$
$\Rightarrow \Delta P_o\propto \frac{1}{\lambda }$..........(1)
[Parameters $B$ and $S_o$​ being same for all]
From graph,
${\lambda }_1>{\lambda }_2>{\lambda }_3$
$\Rightarrow P_1<P_2<P_3$ [ By using Eq.(1) ]
Thus, option $\left(b\right)$ is the correct answer.