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

`T_2=13.5\ N`

Step-by-step explanation:

Given that,

Speed of transverse wave, v₁ = 20 m/s

Tension in the string, T₁ = 6 N

Let T₂ is the tension required for a wave speed of 30 m/s on the same string. The speed of a transverse wave in a string is given by :

`v=\sqrt{(T)/(\mu)}`........(1)

T is the tension in the string

`\mu` is mass per unit length

It is clear from equation (1) that :

`v\propto√(T)`

`(v_1)/(v_2)=\sqrt{(T_1)/(T_2)}`

`T_2=T_1* ((v_2)/(v_1))^2`

`T_2=6* ((30)/(20))^2`

`T_2=13.5\ N`

So, the tension of 13.5 N is required for a wave speed of 30 m/s. Hence, this is the required solution.