Question

A wave pulse is generated in a string that lies along x-axis. At the points A and B are as shown in figure, if $R_{A}and{R}_B$ are 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

The correct option is B $R_B>R_A$

Wave speed is always constant at every point in the wave.

$\therefore V_{A}w=V_{B}w$

Let the displacement of the particle be

$y=A\sin (wt-kx)V_p=A\cos (wt-kx)\times w{x}_B>x_A\Rightarrow wt-k{x}_B<wt-k{x}_A\Rightarrow \cos (wt-k{x}_B)>\cos (wt-k{x}_A)\Rightarrow V_{B}P>V_{A}P\frac{R_A}{R_B}=\frac{V_{A}w/V_{A}P}{V_{B}w/V_{B}P}\frac{R_A}{R_B}=\frac{V_{B}P}{V_{A}P}\therefore R_A>R_B$

Hence option (A) is correct.