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

Answer

a

Explanation

On comparing with `P= P_(0) sin (omegat-kx)`, we have `omega = 1000 rad//s, K= 3 m^(-1)`
`:. V_(0)= (omega)/(k)= (1000)/(3)= 333.3m//s`
`(v_(1))/(v_(2))= sqrt((T_(1))/(T_(2))`
or `(333.3)/(336)= sqrt((273+0)/(273+t)) :. T= 4^(@)C`