Wave Mechanics Question 612
Question: 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 1.5x, the speed of sound will be
Options:
A) 1.22v
B) 0.61v
C) 1.50v
D) 0.75v
Show Answer
Answer:
Correct Answer: A
Solution:
[a] According to Hooke’s law $ F _{R}\propto x $ [Restoring force $ F _{R}=T $ , tension of spring] Velocity of sound by a stretched string $ v=\sqrt{\frac{T}{m}} $ where w is the mass per unit length Hence $ v\propto \sqrt{T}or\frac{v}{v’}=\sqrt{\frac{T}{T’}} $
$ orv’=v\sqrt{\frac{T’}{T}}=v\sqrt{\frac{1.5x}{x}}=1.22v $
BETA
