Question

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 $0^\circ C$. 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 $336\, ms^{-1}$ . Approximate value of $T$ is :

• A. 15°C
• B. 12°C
• C. 4°C
• D. 11°C

Answer 1

Answer: (C)

Speed of wave from wave equation
$v = - \frac{coeffecient \, of \, t}{coeffecient \, of \, x}$
$v = -\frac{1000}{(-3)} = \frac{1000}{3}$
since speed of wave \propto $\sqrt{T}$
so = $\frac{\frac{1000}{3}}{336} \, = \, \sqrt{\frac{273}{T}}$
$\Rightarrow \, \, T = 277.41 K$
T = $4.41 ^{\circ}C$