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JEE Main & Advanced Physics Wave Mechanics Question Bank Self Evaluation Test - Waves

  • question_answer
    When two sound waves travel in the same direction in a medium, the displacements of a particle located at 'x' at time 't' is given by: \[{{y}_{1}}=0.05\cos (0.50\pi x-100\pi t)\] \[{{y}_{2}}=0.05\cos (0.46\pi x-92\pi t)\] Where\[{{y}_{1}}\] , \[{{y}_{2}}\] and x are in meters and t seconds. The speed of sound in the medium is:

    A) 92m/s

    B) 200 m/s

    C) 100m/s

    D) 332m/s

    Correct Answer: B

    Solution :

    [b] Standard equation \[y(x,t)=A\cos \left( \frac{\omega }{V}x-\omega t \right)\] From any of the displacement equation Say \[{{y}_{1}}\] \[\frac{\omega }{V}=0.50\pi \] and \[\omega =100\pi \] \[\therefore \,\,\frac{100\pi }{V}=0.5\pi \] \[\therefore \,\,V=\frac{100\pi }{0.5\pi }=200m/s\]


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