Answer:
[tex]T_2=13.5\ N[/tex]
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 :
[tex]v=\sqrt{\dfrac{T}{\mu}}[/tex]........(1)
T is the tension in the string
[tex]\mu[/tex] is mass per unit length
It is clear from equation (1) that :
[tex]v\propto\sqrt{T}[/tex]
[tex]\dfrac{v_1}{v_2}=\sqrt{\dfrac{T_1}{T_2}}[/tex]
[tex]T_2=T_1\times (\dfrac{v_2}{v_1})^2[/tex]
[tex]T_2=6\times (\dfrac{30}{20})^2[/tex]
[tex]T_2=13.5\ N[/tex]
So, the tension of 13.5 N is required for a wave speed of 30 m/s. Hence, this is the required solution.
