The pressure wave, `P=0.01 sin [1000 t-3x]Nm^(-2)`, corresponds to the sound produced by a vibrating blade on a day when atmospheric temperature is `0^(@)C`. 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 `336 ms^(1)`. Approximate value of T is:

Options

A. `12^(@)C`
B. `15^(@)C`
C. `11^(@)C`
D. `4^(@)C`

Answer

D

Explanation

At `0^(@)C , v=(omega)/(k) = (1000)/(3) m//s ` `therefore (1000 // 3)/(336) = sqrt((273) / (273 + T)` `( because v prop sqrt(T))` ` therefore T ~~ 277 K=4^(@)C`