Q 11-14-120JEE MainJEE Main 2019 (9 Apr, Shift 1)Medium
The pressure wave, $P = 0.01\sin(1000t - 3x)\ \text{N m}^{-2}$, 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 $336\ \text{m s}^{-1}$. Approximate value of $T$ is
Answer: (C) $4^\circ\text{C}$
At $0^\circ\text{C}$: $v_0 = \dfrac\omega k = \dfrac{1000}{3} = 333.3\ \text{m/s}$.
Speed of sound $\propto\sqrt T$ (kelvin):
$$\frac{T}{273} = \left(\frac{336}{333.3}\right)^2 \approx 1.016 \Rightarrow T \approx 277.4\ \text{K} \approx 4^\circ\text{C}$$
Solution by Sreeraj P, M.Sc Physics