Waves

JEE Main level, single correct, medium

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Question 138 of 142

The pressure wave, P=0.01sin⁡⁡[1000t−3x]Nm–2P=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∘C0^{\circ}C . On some other day when temperature is TT , the speed of sound produced by the same blade and at the same frequency is found to be 336ms–1336m{s}^{–1} . Approximate value of TT is:

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Answer: (C) 4∘C4^{\circ}C

at 0∘C0^{\circ}C
y=Asin(1000t−3x)y=Asin(1000t-3x)
v1=ωk=10003{v}_{1}=\dfrac{\omega }{k}=\dfrac{1000}{3}
at temperature T,v2=336m/sT,{v}_{2}=336m/s
v1v2=T1T2\dfrac{{v}_{1}}{{v}_{2}}=\sqrt{\dfrac{{T}_{1}}{{T}_{2}}}
⇒1000336=273T⇒T=277.41K\Rightarrow \dfrac{1000}{336}=\sqrt{\dfrac{273}{T}}\Rightarrow T=277.41\text{K}
i.e.T=4.4∘C=4∘Ci.e.T=4.4^{\circ}C=4^{\circ}C

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