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Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Wave Motion and Waves on a String

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Wave Motion and Waves on a String

A heavy but uniform rope of length L is suspended from a ceiling....

A heavy but uniform rope of length

L

is suspended from a ceiling. Determine the velocity of a transverse wave travelling on the string as a function of the distance

x

from the lower end.

Options

A $\sqrt{gx}$
B $\sqrt{2gx}$
C $\sqrt{\dfrac{gx}{2}}$
D $\dfrac{gx}{2}$

Correct answer

A. $\sqrt{gx}$

Step-by-step solution

Let the mass per unit length of the rope be

\mu

.

The tension

T

at a distance

x

from the lower end is equal to the weight of the rope below that point.

T = \mu x g

The velocity

v

of a transverse wave on a string is given by:

v = \sqrt{\dfrac{T}{\mu}}

Substituting the value of

T

, we get:

v = \sqrt{\dfrac{\mu x g}{\mu}} = \sqrt{gx}

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