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Waves question

2004 · Shift 0 · Q180
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Waves question

2004 · Shift 0 · Q180

JEE MainPhysicsWavesMCQ+4 / −1
The displacement yyy of a particle in a medium can be expressed as, y=10−6 sin⁡y = {10^{ - 6}}\,\siny=10−6sin (100t+20x+π4)\left( {100t + 20x + {\pi \over 4}} \right)(100t+20x+4π​) mmm where ttt is in second and xxx in meter. The speed of the wave is
  1. A
    20  m/s20\,\,m/s20m/s
  2. B
    5 m/s5\,m/s5m/s
  3. C
    2000 m/s2000\,m/s2000m/s
  4. D
    5 π m/s5\,\pi \,m/s5πm/s
View written solutionFree

Correct answer: B

  1. Write the given wave equation

    The displacement is y=10−6 sin⁡(100t+20x+π4) my = 10^{-6}\,\sin\left(100t + 20x + \frac{\pi}{4}\right)\text{ m}y=10−6sin(100t+20x+4π​) m

  2. Compare with the standard form

    A travelling wave can be written as y=Asin⁡(ωt±kx+ϕ)y = A\sin(\omega t \pm kx + \phi)y=Asin(ωt±kx+ϕ) where:

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

    From the given equation, ω=100 rad/s,k=20 rad/m\omega = 100\ \text{rad/s}, \qquad k = 20\ \text{rad/m}ω=100 rad/s,k=20 rad/m

  3. Use the wave speed formula

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

    Substituting the values: v=10020=5 m/sv = \frac{100}{20} = 5\ \text{m/s}v=20100​=5 m/s

  4. Identify the correct option

    v=5 m/sv = 5\ \text{m/s}v=5 m/s

    So, the correct option is B.

  5. Compare with stored answer

    Stored correct answer: B

    This matches our derived answer.

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