A wire is under tension of 2 kg wt and a wave is travelling through it with some speed. Tension in the wire is so increased that the wave travels through it with thrice the original speed. The increas

Question

A wire is under tension of 2 kg wt and a wave is travelling through it with some speed. Tension in the wire is so increased that the wave travels through it with thrice the original speed. The increase in tension is (in kg wt)

TestHub · Accepted Answer

The speed of a transverse wave in a stretched wire is given by $v = \frac{T}{μ}$

where $T$ is the tension and $μ$ is the linear mass density.

Since the speed is proportional to the square root of tension, we have $v \propto T$

Given that the new speed is thrice the original speed, $v_{2} = 3 v_{1}$

$T_{2} = 3 T_{1}$

$T_{2} = 9 T_{1}$

Given the initial tension $T_{1} = 2$ kg wt, the new tension is $T_{2} = 9 \times 2 = 18$ kg wt.

The increase in tension is $Δ T = T_{2} - T_{1} = 18 - 2 = 16$ kg wt.

Answer: $16$

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