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Question:

The pressure wave, P=0.01sin[ 1000t-3x ] N m ^ -2, corresponds to the sound produced by a vibrating blade on a day when atmospheric temperature is 0^oC. On some other day, when temperature is T, the speed of sound produced by the same blade and at the same frequency is found to be 336ms^-1. Approximate value of T is

15oC

4oC

12oC

11oC

Solution:

Correct option is C.
4oC
speed of wave from wave equation
v=\frac{-coefficient of t}{coefficient of x}
v=\frac{-1000}{-3}=\frac{1000}{3}
since speed of wave \propto \sqrt{T}
so,\frac{1000}{336}=\sqrt{\frac{273}{T}}\implies T=277.41K
277.41k=4oC