The extension in a string obeying Hooke's law is x. The speed of sound in the stretched string is v. If the extension in the string is increased to 1.5 x, the speed of sound will be

a) 1.22 v

b) 0.61 v

c) 1.50 v

d) 0.75 v

Answer: a) 1.22 v

Solution:

Velocity of sound by a stretched string, v = (1/λ)√(T/m)

Young’s modulus = Stress/Strain 

Y = (T/A)/(x/l) = Tl/Ax

T = YAx/l

T ∝ x

v ∝ √T ⇒ v ∝ √x

(v/v’) = √(x/x’)

v’ = v√(x’/x)

= v√(1.5x/x)

= 1.22v