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° 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 :

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° 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

Tardigrade Admin · Accepted Answer

Speed of wave from wave equation v = - (coeffecient of t/coeffecient of x) v = -(1000/(-3)) = (1000/3) since speed of wave propto √T so = ((1000/3)/336) = √(273/T) ⇒ T = 277.41 K T = 4.41 °C

15°C

12°C

4°C

11°C

Speed of wave from wave equation v=−coeffecientofxcoeffecientoft​ v=−(−3)1000​=31000​ since speed of wave \propto T​ so = 33631000​​=T273​​ ⇒T=277.41K T = 4.41∘C

Speed of wave from wave equation
$v = - \frac{coe ff ec i e n t o f t}{coe ff ec i e n t o f x}$
$v = - \frac{1000}{( - 3 )} = \frac{1000}{3}$
since speed of wave \propto $T$
so = $\frac{\frac{1000}{3}}{336} = \frac{273}{T}$
$\Rightarrow T = 277.41 K$
T = $4.4 1^{\circ} C$