The pressure wave P=0.01sin[1000t-3x]Nm−2 correspond to the sound produced by a vibrating blade on a day when atmospheric temperature is 00C. 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 in 0C is...........

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Q.

The pressure wave $P = 0.01 \sin [1000 t - 3 x] {Nm}^{- 2}$ correspond to the sound produced by a vibrating blade on a day when atmospheric temperature is $0^{0} C$ . 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 in ⁰C is...........

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Detailed Solution

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Given, $P = 0.01 \sin (1000 t - 3 x) N / m^{2}$

$[∴ P = P_{0} \sin (ω t - k x)]$

Here, $ω = 1000, k = 3$

$V = \frac{ω}{K} \Rightarrow V = \frac{1000}{3}$

We , $V = \sqrt{\frac{r R T}{M}} \Rightarrow V \propto \sqrt{T}$

$\Rightarrow \frac{V_{2}}{V_{1}} = \sqrt{\frac{T_{2}}{T_{1}}}$

$\Rightarrow \frac{{V_{2}}^{2}}{{V_{1}}^{2}} = \frac{T_{2}}{T_{1}} \Rightarrow T_{2} = \frac{{(V_{2})}^{2}}{{(V_{1})}^{2}} \times T_{1}$

$\Rightarrow T_{2} = \frac{{(336)}^{2}}{{(\frac{1000}{3})}^{2}} \times 273 = 277.38 K$

$\Rightarrow T_{2} = {4.38}^{0} C = 4^{0} C$

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The pressure wave P=0.01sin[1000t-3x]Nm−2 correspond to the sound produced by a vibrating blade on a day when atmospheric temperature is 00C. 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 in 0C is...........