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

 

Answers (1)

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 T,

  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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