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 $0^{\circ }\text{C}$. 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. ${15}^{\circ }\text{C}$
• B. ${11}^{\circ }\text{C}$
• C. ${12}^{\circ }\text{C}$
• D. $4^{\circ }\text{C}$

Answer 1

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

On comparing with $P=P_0\sin (\omega t-kx)$,

we have
$\omega =1000\text{rad}/\text{s},K=3{\text{m}}^{-1}$

$\therefore v_0=\frac{\omega }{k}=\frac{1000}{3}=333.3\text{m/s}$

We know that speed of sound is given as
$v=\sqrt{\gamma RT}$
$\frac{v_1}{v_2}=\sqrt{\frac{T_1}{T_2}}$
$\frac{333.3}{336}=\sqrt{\frac{273+0}{273+t}}\therefore t=4^{\circ }C$