First slide

Travelling wave

Question

A string of length L and mass M hangs freely from a fixed point. Then the velocity of transverse waves along the string at a distance x from the free end is

Moderate

A

$\sqrt{gL}$
B

$\sqrt{gx}$
C

gL
D

gx

Solution

Velocity $v = \sqrt{\frac{T}{m}}$ ; where T = weight of part of rope hanging below the point under consideration $= (\frac{M}{L}) xg$
$\Rightarrow v = \sqrt{\frac{(\frac{M}{L}) xg}{(\frac{M}{L})}} = \sqrt{xg}$

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