Question

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

• A. 1.22 v
• B. 0.61 v
• C. 1.50 v
• D. 0.75 v

Answer 1

Answer: (A)

1.22 v

Answer 2

From Hooke's law Tension in a string (T) $\propto$ extension (x) and speed of sound in string \hspace20mm v = \sqrt{T/\mu} or $\, \, v = \propto \sqrt T$ Therefore, \hspace15mm v \propto \sqrt x x is increased to 1.5 times i.e. speed will increase by $\sqrt{1.5}$times or 1.22 times. Therefore, speed of sound in new position will be 1.22 v.