Physics Elasticity Question 30
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
[IIT 1996]
Options:
A) 1.22 v
B) 0.61 v
C) 1.50 v
D) 0.75 v
Show Answer
Answer:
Correct Answer: A
Solution:
Speed of sound in a stretched string $ v=\sqrt{\frac{T}{\mu }} $ ?(i) Where $ T $ is the tension in the string and $ \mu $ is mass per unit length. According to Hooke’s law, $ F\propto x $ \ $ T\propto x $ ?(ii) From (i) and (ii) $ v\propto \sqrt{x} $ $ v’=\sqrt{1.5}\ v=1.22\ v $
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