Question

Transverse waves travel at 24 m/s on a string that is under a tension of 5.34 N. What tension is required for a wave the speed of 22.2 m/s in the same string

Answer 1

the required tension is 4.57 N.

Step-by-step explanation:

Given;

first velocity of the wave, v₁ = 24 m/s

first tension on the string, T₁ = 5.34 N

second velocity of the wave, v₂ = 22.2 m/s

second tension of the string, T₂ = ?

`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) \\\\T_2 =(T_1v_2^2)/(v_1^2) \\\\T_2 = (5.34 * 22.2^2)/(24^2) \\\\T_2 = 4.57 \ N`

Therefore, the required tension is 4.57 N.