Question

Transverse waves travel with a speed of 20 m/s on a string under a tension 0f 6.00 N. What tension is required for a wave speed of 30.0 m/s on the same string?

Answer 1

Answer:

The tension for a wave speed is 13.5 N.

Explanation:

Given that,

Speed of transverse wave = 20 m/s

Tension = 6.00 N

Speed of wave = 30.0 m/s

We need to calculate the tension

Using relation of velocity and tension

$v=\sqrt{\dfrac{T}{m}}$

Linear density, m is the same.

Squaring and dividing,

$(\dfrac{v_{1}}{v_{2}})^2=\dfrac{T_{1}}{T_{2}}$

Put the value into the relation

$(\dfrac{20}{30})^2=\dfrac{6.00}{T_{2}}$

$T_{2}=\dfrac{6.00}{(\dfrac{20}{30})^2}$

$T_{2}=13.5\ N$

Hence, The tension for a wave speed is 13.5 N.