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inn [45]
3 years ago
15

A string of mass m and length L is under tension T. The speed of a wave in the string is v. What will be the speed of a wave in

the string if the mass of the string is increased to 2m, with no change in length?
Physics
1 answer:
Gekata [30.6K]3 years ago
3 0

Answer:

\frac{1}{\sqrt{2}}

Explanation:

The speed of a wave in a string is given by:

v=\sqrt{\frac{T}{m/L}}

where

T is the tension in the string

m is the mass of the string

L is the length

In this problem, the mass of the string is increased to 2m: m' = 2 m, while the length is not changed, L'=L. If the tension in the string is not changed, then the new speed of the wave in the string will be:

v'=\sqrt{\frac{T}{m'/L'}}=\sqrt{\frac{T}{2m/L}}=\frac{1}{\sqrt{2}}\sqrt{\frac{T}{m/L}}=\frac{v}{\sqrt{2}}

so, the speed of the wave decreases by a factor \frac{1}{\sqrt{2}}

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