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:

$T_2=13.5\ N$

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 :

$v=\sqrt{\dfrac{T}{\mu}}$........(1)

T is the tension in the string

$\mu$ is mass per unit length

It is clear from equation (1) that :

$v\propto\sqrt{T}$

$\dfrac{v_1}{v_2}=\sqrt{\dfrac{T_1}{T_2}}$

$T_2=T_1\times (\dfrac{v_2}{v_1})^2$

$T_2=6\times (\dfrac{30}{20})^2$

$T_2=13.5\ N$

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