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JEE Main & Advanced Physics Wave Mechanics JEE PYQ-Wave Mechanics

  • question_answer
    The pressure wave, \[P=0.01\] \[\sin \left[ 1000t3x \right]\]\[N{{m}^{2}},\]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 \[336m{{s}^{-1}}.\]Approximate value of T is: [JEE Main 9-4-2019 Morning]

    A)  \[15{}^\circ C\]                       

    B)  \[12{}^\circ C\]

    C)  \[4{}^\circ C\]

    D)  \[11{}^\circ C\]

    Correct Answer: C

    Solution :

    [c] Speed of wave from wave equation
    \[\text{v=-}\frac{\text{(coeffecient}\,\text{of}\,\text{t)}}{\text{(coeffecient}\,\text{of}\,\text{x)}}\]
    \[\text{v=-}\frac{1000}{(-3)}=\frac{1000}{3}\]
    since speed of wave\[\propto \sqrt{T}\]
    so\[=\frac{1000}{\frac{3}{336}}=\sqrt{\frac{273}{T}}\]\[\Rightarrow T=277.41K\]
    \[T=4.41{}^\circ C\]
    Option (c)                     


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