# The pressure wave,$P=0.01sin\left [ 1000t-3x \right ]Nm^{-2},$ 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 : Option 1) $4^{\circ}C$            Option 2) $11^{\circ}C$ Option 3) $12^{\circ}C$     Option 4) $15^{\circ}C$

S solutionqc

at $0^{\circ}C$

$P=0.01sin\left ( 1000\; t-3x \right )Nm^{-2}$

$V_{1}=\frac{\omega }{k}$

$V_{1}=\frac{1000}{3}$

at temp $\inline T,$

$\inline V_{2}=336\; ms^{-1}$

$\frac{V_{1}}{V_{2}}=\sqrt{\frac{T_{1}}{T_{2}}}$       (Where T is in Kelvin)

$\frac{\frac{1000}{3}}{336}=\sqrt{\frac{273}{T}}$

$\Rightarrow T=277.41 k$

$=T=4.4^{\circ}C$

Option 1)

$4^{\circ}C$

Option 2)

$11^{\circ}C$

Option 3)

$12^{\circ}C$

Option 4)

$15^{\circ}C$

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