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)

Options

A. `t=(2l)/(alpha[sqrt(T_(2))+sqrt(T_(1))])`
B. `t=(4l)/(alpha[sqrt(T_(1))+sqrt(T_(2))])`
C. `t=(4l)/(alpha[sqrt(T_(1))sqrt(T_(2))])`
D. `t=(2l)/(alpha[sqrt(T_(1))+sqrt(T_(2))])`

Answer

A

Explanation

`V_(avg)=(V_(1)+V_(2))/(2)=(1)/(2)prop sqrt(T_(1))+prop sqrt(T_(2))`
`t=(l)/(V_(avg))=(l)/((1)/(2)[alphasqrt(T_(1))+alphasqrt(T_(2))])=(2l)/(alpha[sqrt(T_(1))+sqrt(T_(2))])`