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Reflection from an Open End

A wave pulse ...

Question

A wave pulse is generated in a string that lies along $x -$ axis. At the points $A$ and $B$ , 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}

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B

R_{B} > R_{A}

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C

R_{A} = R_{B}

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D

Information insufficient

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Solution

The correct option is B $R_{B} > R_{A}$
The wave speed $(V_{W})$ at all points is the same.
The particle speed depends on displacement from the mean position. Since, $A$ is closer to mean position than $B$
$\Rightarrow V_{A} > V_{B}$
Now, $R_{A} = \frac{V_{W}}{V_{A}} a n d R_{B} = \frac{V_{W}}{V_{B}} \Rightarrow \frac{R_{A}}{R_{B}} = \frac{V_{B}}{V_{A}} < 1 \Rightarrow R_{A} < R_{B}$

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