The pressure wave, $P = 0.01\,sin\,[1000t -3x]\,Nm^{-2},$ corresponds to the sound produced by a vibrating blade on a day when atmospheric temperature is $0\,^oC.$ 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 .... $^oC$
JEE MAIN 2019, Medium
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Speed of wave from wave equation
$v=-\frac{(\text { coeffecient of } t)}{(\text { coeffecient of } x)}$
$v=-\frac{1000}{(-3)}=\frac{1000}{3}$
since speed of wave $\propto \sqrt{T}$
$\mathrm{So}=\frac{1000}{\frac{3}{336}}=\sqrt{\frac{273}{\mathrm{T}}}$
$\Rightarrow T=277.41 \mathrm{K}$
$\mathrm{T}=4.41^{\circ} \mathrm{C}$
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