Two wires possessing different densities but the same area of cross section are joined together at one end and stretched to a tension T . The velocity of a transverse wave in the first wire is twice that in the second

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Quantrex Academy · Accepted Answer

Correct answer: D. 0.25

The velocity of a transverse wave in a stretched wire is given by

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

, where

\mu

is the linear mass density.

Since

\mu = \rho A

, where

\rho

is the density and

A

is the cross-sectional area, the velocity can be written as

v = \sqrt{\dfrac{T}{\rho A}}

.

For the two wires, the tension

T

and area

A

are the same. Thus,

v \propto \dfrac{1}{\sqrt{\rho}}

.

Given that

v_1 = 2v_2

, we have:

\sqrt{\dfrac{T}{\rho_1 A}} = 2 \sqrt{\dfrac{T}{\rho_2 A}}

Squaring both sides:

\dfrac{T}{\rho_1 A} = 4 \dfrac{T}{\rho_2 A}

\dfrac{1}{\rho_1} = \dfrac{4}{\rho_2}

\dfrac{\rho_1}{\rho_2} = \dfrac{1}{4} = 0.25

Two wires possessing different densities but the same area of cross...

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