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A heavy uniform rope is held vertically by clam-ping it to a rigid support at the upper end. A transverse wave of a certain frequency is set up at the lower end. The wave will

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travel with same velocity along the string

travel with decreasing velocity along the string

travel with increasing velocity along the string

travel with increasing frequency along the string

answer is C.

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Detailed Solution

Velocity of transverse wave at a distance x from the lower end is,

$v = \sqrt{\frac{T}{μ}}$

where

$μ$ = Linear mass density

Here,

$T = μ x g$

$v = \sqrt{\frac{μ x g}{μ}}$

$v = \sqrt{x g}$

$v \propto \sqrt{x}$

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