Q14 of 118 Page 352

The absolute temperature of air in a region linearly increases from T1 to T2 in a space of width d. Find the time taken by a sound wave to go through the region in terms of T1, T2, d and the speed u of sound at 273 K. Evaluate this time for T1 = 280 K, T2 = 310 K, d =33m and u = 330 m s-1.

Given:
The absolute temperature of air in a region increases linearly from to in a space of width .



The speed of sound at 273 K is .



 is the velocity of the sound at temperature .



Let us find the temperature variation at a distance in the region.



Temperature variation is given by:




⇒


⇒


⇒


⇒


⇒


⇒


⇒


⇒--------------- (i)


Evaluating this time:
Initial temperature = 280 K
Final temperature = 310 K
Space width d = 33 m


On substituting the respective values in the above equation, we get:



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