Question

5. The speed of a transverse wave on a string is 170 m/s when the string tension is 120 ????. To what value must the tension be changed to raise the wave speed to 180 m/s?

Answer 1

The tension on string when the speed was raised is 134.53 N

Step-by-step explanation:

Given;

Tension on the string, T = 120 N

initial speed of the transverse wave, v₁ = 170 m/s

final speed of the transverse wave, v₂ = 180 m/s

The speed of the wave is given as;

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

where;

μ is mass per unit length

`v^2 = (T)/(\mu) \\\\\mu = (T)/(v^2) \\\\(T_1)/(v_1^2) = (T_2)/(v_2^2)`

The final tension T₂ will be calculated as;

`T_2 = (T_1 v_2^2)/(v_1^2) \\\\T_2 = (120*180^2)/(170^2) \\\\T_2 = 134.53 \ N`

Therefore, the tension on string when the speed was raised is 134.53 N