The extension in a string obeying Hooke's law is x. The speed of a transverse wave in a stretched string is v. If the extension in the string is increased to 1.5x, the speed of the wave will be
1.22 v
Speed of a transverse wave in a stretched string ν=√Tμ......(i)
Where T is the tension in the string and μ is mass per unit length.
Since the string obeys Hooke's law, T ∝ x ...(ii)
From (i) and (ii) ν∝√x∴ν′=√1.5ν=1.22ν