3. The velocity of waves on a rope under a tension of 40 N is 10 m/s. If the tension is reduced
to 10 N, what will be the new speed of the wave?
HAI

5 m/s

Explanation:

The speed of a wave in a string is related to the tension in the string by the equation

where

v is the speed of the wave

T is the tension in the string

is the linear density of the string

We can rewrite the equation as

In this problem, the tension in the string is changed; however, its linear mass density remains constant. So we can write:

where:

T1 = 40 N is the initial tension in the string

v1 = 10 m/s is the initial speed of the wave

T2 = 10 N is the final tension in the string

Solving for v2, we find the final speed of the wave:

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