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JEE Main & Advanced Sample Paper JEE Main Sample Paper-8

  • question_answer
    DIRECTION (Qs. 52) Read the following passage and answer the questions that follows: A sinusoidal wave is propagating in negative x-direction in a string stretched along x-axis. A particle of string at \[x=2m\]is found at its mean position and it is moving in positive y-direction at \[t=1\text{ }\sec .\]The amplitude of the wave, the wavelength and the angular frequency of the wave are 0.1 meter, \[\pi /2\]meter and In \[2\pi \,rad/\sec \]respectively. The equation of the wave is

    A)  \[y=0.1\text{ }\sin \,(4\pi (t-1)+8(x-2))\]

    B)  \[y=0.1\text{ }\sin \,((t-1)-(x-2))\]

    C)  \[y=0.1\text{ }\sin \,(2\pi (t-1)+4(x-2))\]

    D)  None of these

    Correct Answer: C

    Solution :

     The equation of wave moving in negative x-direction, assuming origin of position at x = 2 and origin of time (i.e. initial time) at t = 1 sec. \[y=0.1\sin (2\pi t+4x)\] Shifting the origin of position to left by 2m, that is, to x = 0. Also shifting the origin of time backwards by 1 sec, that is to t = 0 sec. \[y=0.1\sin (2\pi (t-1)+4(x-2)\]


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