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

JEE Main · 2019 · 09 Apr 2019 · Shift 1 · Waves & Sound

The pressure wave,

P = 0.01 sin [1000 t - 3 x] 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:

Answer: (D)

From

P = 0.01 sin (1000 t - 3 x)

the speed at

0^{\circ}

C is

v_{1} = \frac{ω}{k} = \frac{1000}{3}

m/s. Sound speed scales as

T

in absolute temperature, so

\frac{v _{1}}{v _{2}} = \frac{T _{1}}{T _{2}}

with

T_{1} = 273

K and

v_{2} = 336

m/s. Then

T_{2} = 273 (\frac{336 \times 3}{1000})^{2} = 273 (\frac{1008}{1000})^{2} \approx 277.4

K, which is about

4^{\circ}

JEE Main · 2019 · 09 Apr 2019 · Shift 1 · Single correct option