Question

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

• A. $4^{\circ }C$
• B. ${15}^{\circ }C$
• C. ${11}^{\circ }C$
• D. ${12}^{\circ }C$

Answer 1

The correct option is A $4^{\circ }C$

Given $P=0.01\sin [100t-3x]$
$\omega =1000$
$k=3$
Velocity of wave is$V=\frac{\omega }{k}$
$\Rightarrow V=\frac{1000}{3}\text{m/s}$
At Temperature $T$, velocity od sound is given as $V_2=336\text{m/s}$

Using $(v=\sqrt{\frac{\gamma RT}{M}})$
$\frac{V}{V_2}=\sqrt{\frac{T_1}{T_2}}$
$\frac{\frac{1000}{3}}{336}=\sqrt{\frac{273}{T_2}}$
$T=277.4K={4.4}^{\circ }C$