The pressure wave, P = 0.01 [1000t - 3x]N m ^ – 2 , corresponds to...

The pressure wave,

P = 0.01\sin \left[1000t - 3x\right]N{m}^{– 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

336m{s}^{– 1}

. Approximate value of

T

is:

Options

A $12 ° C$
B $15 ° C$
C $4 ° C$
D $11 ° C$

Correct answer

C. $4 ° C$

Step-by-step solution

at $0 ° C$
$y = Asin ( 1000t - 3x )$
${v}_{1} = \dfrac{\omega}{k} = \dfrac{1000}{3}$
at temperature $T, {v}_{2} = 336m / s$
$\dfrac{{v}_{1}}{{v}_{2}} = \sqrt{\dfrac{{T}_{1}}{{T}_{2}}}$

$⇒ \dfrac{1000}{336} = \sqrt{\dfrac{273}{T}} ⇒ T = 277 . 41\text{K}$
$i . e . T = 4 . 4 ° C = 4 ° C$

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