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

The tension for a wave speed is 13.5 N.

Step-by-step 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{(T)/(m)}`

Linear density, m is the same.

Squaring and dividing,

`((v_(1))/(v_(2)))^2=(T_(1))/(T_(2))`

Put the value into the relation

`((20)/(30))^2=(6.00)/(T_(2))`

`T_(2)=(6.00)/(((20)/(30))^2)`

`T_(2)=13.5\ N`

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