Question

A wave travels with a speed vo along a string under tension. If the mass of the string is doubled, but its length and tension are unchanged, what would be the speed of the wave? (a) vo/ V2 (b) v2 vo (C) 2vo (d) vo

Answer 1

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Answer 2

Answer:

Option A is the right choice. Velocity of the wave becomes $\frac{v_{0} }{\sqrt{2} }$.

Explanation:

Given is a wave that travels with a speed of $v_{0}$ on a string under tension.

Velocity of the wave on a string is given by the relation,

$v=\sqrt{\frac{Tl}{m} }$

where T is the tension on the string, l is the length of the string and m is the mass of the string.

If the mass of the string is doubled keeping its length and tension same then v becomes,

$v=\sqrt{\frac{Tl}{2m} }=\frac{v}{\sqrt{2} }$

Hence, Velocity of the wave becomes $\frac{v_{0} }{\sqrt{2} }$