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AMU Medical AMU Solved Paper-2010

  • question_answer
    A travelling wave is represented by the equation \[\text{y}=\frac{1}{10}\text{ sin}\left( \text{6}0\text{t}+\text{2x} \right),\]where x and \[\text{y}\]are in metre and c is in second. This represents a wave   1. travelling with a velocity of 30 \[\text{m}{{\text{s}}^{\text{-1}}}\]30 2. of frequency \[\frac{30}{\pi }\] Hz                  3. of wavelength 7t metre 4. of amplitude 10 cm 5. moving in the positive x - direction Pick out the correct statements from the above.

    A)  1, 2, 4                                  

    B)  3, 4, 5      

    C)  1,2,3,4                                 

    D)  All of these

    Correct Answer: C

    Solution :

                     The equation of travelling wave                 \[y=\frac{1}{10}\sin (60\,t+2x)\] Compare with the standard wave equation                 \[y=a\sin \,(\omega \,t+kx)\] we get Amplitude, \[a=\frac{1}{10}m=10\,cm\] Angular frequency, \[\omega =60\] rad/s and Angular wave number, k = 2 rad/m \[\therefore \] Velocity of the wave                 \[v=\frac{\omega }{k}=\frac{60}{2}=30\]m/s \[\therefore \] Frequency of the wave                 \[f=\frac{\omega }{2\pi }=\frac{60}{2\pi }=\frac{30}{\pi }H\] Wavelength of the wave                 \[\lambda =\frac{2\pi }{k}=\frac{2\pi }{2}=\pi \,m\] There is positive sign between t and x terms, the given wave is moving in the negative x-direction.


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