Question

A wave pulse is generated in a string that lies along $x$ -axis. At the points $A$ and B, as shown in the figure, if $R_{A}$ and $R_{B}$ are the ratio of wave speed to the particle speed respectively then :

• A. $R_{A}>R_{B}$
• B. $R_{B}>R_{A}$
• C. $R_{A}=R_{B}$
• D. Information is not sufficient to decide.

Answer 1

Answer: (B)

$V_{\text{p}}=-\left(V\right)\left(\text{slope}\right)$
$\Rightarrow \quad \frac{V_p}{V}=-$ (slope) $=\frac{1}{R}$
$\Rightarrow \quad \frac{R_B}{R_A}=\frac{(\text { slope })_{\mathrm{A}}}{(\text { slope })_{\mathrm{B}}}$
as we can see
$(\text { slope })_{\mathrm{A}}>(\text { slope })_{\mathrm{B}}$
$\Rightarrow R_{\text{B}}>R_{\text{A}}$