First slide

Speed of wave

Question

Velocity of transverse wave in a stretched string is ‘V’ when elongation produced in it is ‘x’, what will be the velocity of transverse wave in the same string when elongation produced in it is ‘2x’ ?

Moderate

A

$\frac{v}{\sqrt{2}}$
B

v /2
C

$\sqrt{2} v$
D

2 v

Solution

If Y be the young’s modulus of the material of the string, µ be the mass per unit length and S be the cross-sectional area, Then
$V = \sqrt{\frac{T}{μ}} and T = Area \times Stress = S . γ . \frac{x}{L} ∴ \begin{array}{l} V = \sqrt{\frac{S . Y . \frac{x}{L}}{μ}} and V' = \sqrt{\frac{S . Y . \frac{2 x}{L}}{μ}} \\ ∴ \frac{V'}{V} = \sqrt{2} \Rightarrow V' = \sqrt{2} . V \end{array}$

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