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

Answer

C

Explanation

At `0^(@)C`
`y=Asin(1000t-3x)`
`v_(1)=(omega)/(k)=(1000)/(3)`
at temperature T, `v_(2)=336m//s`
`(v_(1))/(v_(2))=sqrt((T_(1))/(T_(2)))`
`implies ((1000)/(3))/(336)=sqrt((273)/(T))implies T=277.41k`
i.e. `T=4.4^(@)C=4^(@)C`.