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How long will it take sound waves to tra...

How long will it take sound waves to travel a distance `l` between points A and B if the air temperature between them varies linearly from `T_1` and `T_2`? (The velocity of sound in air at temperature `T` is given by `v=alphasqrt(T)`, where `alpha` is a constant)

A

`(2l)/(alphasqrt(T_(1)T_(2))`

B

`alphalsqrt((T_1)/(T_2))`

C

`sqrt(T_1+T_2).alphal`

D

`(2l)/(alpha(sqrt(T_2)+sqrt(T_1)))`

Text Solution

Verified by Experts

The correct Answer is:
D
`lt vgt =(v_(1) +v_(2))/(2) =(alphasqrtT_(1) alpha sqrtT_(2))/(2)`
`rArr Time take =(2l)/(alpha (sqrtT_(1)+sqrtT_(2)))`
Alternate Solution:
`(dx)/(dt) =V= alpha sqrt(T_(1) +((T_(2)-T_(1))/(l)))x`
`int_(x=0)^(x=l)(dx)/(sqrt(T_(1)+((T_(2)-T_(1))/(l))x))=int_(0)^(t) alphadt`.
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