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Waves question

2003 · Shift 0 · Q164
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Waves question

2003 · Shift 0 · Q164

JEE MainPhysicsWavesMCQ+4 / −1
The displacement yyy of a wave travelling in the xxx-direction is given by y=10−4 sin⁡(600t−2x+π3)  metresy = {10^{ - 4}}\,\sin \left( {600t - 2x + {\pi \over 3}} \right)\,\,metresy=10−4sin(600t−2x+3π​)metres where xxx is expressed in metres and ttt in seconds. The speed of the wave - motion, in ms−1m{s^{ - 1}}ms−1, is
  1. A
    300300300
  2. B
    600600600
  3. C
    120012001200
  4. D
    200200200
View written solutionFree

Correct answer: A

  1. Write the given wave equation

    The wave is y=10−4 sin⁡(600t−2x+π3)y=10^{-4}\,\sin\left(600t-2x+\frac{\pi}{3}\right)y=10−4sin(600t−2x+3π​)

  2. Compare with the standard form

    A wave travelling in the positive xxx-direction is generally written as y=Asin⁡(ωt−kx+ϕ)y=A\sin(\omega t-kx+\phi)y=Asin(ωt−kx+ϕ) where:

    • ω\omegaω = angular frequency
    • kkk = wave number

    Comparing, ω=600 rad s−1,k=2 rad m−1\omega=600\ \text{rad s}^{-1}, \qquad k=2\ \text{rad m}^{-1}ω=600 rad s−1,k=2 rad m−1

  3. Use the wave speed formula

    The speed of the wave is v=ωkv=\frac{\omega}{k}v=kω​

    Substituting the values, v=6002=300 m s−1v=\frac{600}{2}=300\ \text{m s}^{-1}v=2600​=300 m s−1

  4. Match with the options

    300 m s−1300\ \text{m s}^{-1}300 m s−1 corresponds to Option A.

  5. Comparison with stored correct answer

    Stored correct answer: A

    Derived answer: A

    Hence, the derived answer agrees with the stored correct answer.

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