general equation of wave questions with solutions

Showing 1–10 of 42 questions

• MCQeasyWave Motiongeneral equation of wave

  A plane progressive wave is given by y = 2 cos 2π(330t - x) m. The frequency of the wave is:

  Options

  • Option A

    165 Hz

  • Option B

    330 Hz

  • Option C

    660 Hz

  • Option D

    340 Hz

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• A/RmediumWave Motiongeneral equation of wave

  Choose the correct option for the following Assertion (A) and Reason (R).

  Assertion

  For a wave travelling in the positive x-direction in the form y = f(x-vt), the transverse particle velocity and the local slope of the wave have opposite signs.

  Reason

  For a right-moving wave, ∂y/∂t = -v∂y/∂x.

  Options

  • Option A

    Both A and R are true and R is the correct explanation of A.

  • Option B

    Both A and R are true but R is NOT the correct explanation of A.

  • Option C

    A is true but R is false.

  • Option D

    A is false but R is true.

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• MCQeasyWave Motiongeneral equation of wave

  A progressive wave is described by y = 0.04 sin(2πx-8πt+π/6), where x and y are in metres and t is in seconds. What is the speed of propagation of the wave?

  Options

  • Option A

    2 m/s

  • Option B

    4 m/s

  • Option C

    8 m/s

  • Option D

    16 m/s

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• MCQeasyWave Motiongeneral equation of wave

  A sinusoidal wave of amplitude A and angular frequency ω travels through a medium. What is the maximum magnitude uₘₐₓ of the oscillatory velocity of a particle of the medium?

  Options

  • Option A

    uₘₐₓ = Aω

  • Option B

    uₘₐₓ = Aω²

  • Option C

    uₘₐₓ = Ak

  • Option D

    uₘₐₓ = ω/k

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• MCQmediumWave Motiongeneral equation of wave

  A transverse wave travels towards the positive x-direction with speed v and is written in the general form y = f(x-vt). If the local slope of the string at a point is ∂y/∂x, which relation gives the transverse particle velocity uᵧ at that point?

  Options

  • Option A

    uᵧ = +v∂y/∂x

  • Option B

    uᵧ = -v∂y/∂x

  • Option C

    uᵧ = v²∂y/∂x

  • Option D

    uᵧ = -(1/v)∂y/∂x

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• MCQeasyWave Motiongeneral equation of wave

  A sinusoidal wave is described by y = A sin(kx-ωt). At a fixed position x, what is the instantaneous transverse velocity uᵧ of the particle of the medium?

  Options

  • Option A

    uᵧ = Aω sin(kx-ωt)

  • Option B

    uᵧ = -Aω cos(kx-ωt)

  • Option C

    uᵧ = Ak cos(kx-ωt)

  • Option D

    uᵧ = Aω cos(kx-ωt)

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• MCQmediumWave Motiongeneral equation of wave

  Which of the following displacement expressions does NOT represent an undistorted wave profile propagating with one constant speed along the x-axis?

  Options

  • Option A

    y = A sin(kx-ωt)

  • Option B

    y = A exp[-(x-vt)²/a²]

  • Option C

    y = A sin(kx²-ωt)

  • Option D

    y = A cos[k(x+vt)]

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• MCQmediumWave Motiongeneral equation of wave

  Which of the following displacement expressions can represent an undistorted travelling wave moving with a single constant speed?

  Options

  • Option A

    y = A sin(kx-ωt)

  • Option B

    y = A exp[-(x-vt)²/a²]

  • Option C

    y = A cos[k(x+vt)]

  • Option D

    All of the above

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• NumericeasyWave Motiongeneral equation of wave

  A progressive sinusoidal wave is described by y = 5×10⁻³ sin(4πx-20πt), with SI units. If the wavelength is N/2 metres, find N.

  Your answer

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• MCQmediumWave Motiongeneral equation of wave

  A transverse wave is represented by y = 4 sin(5x+20t), where x is measured in metres and t in seconds. By examining the constant-phase condition, determine the direction of propagation of the wave.

  Options

  • Option A

    Positive x-direction

  • Option B

    Negative x-direction

  • Option C

    The wave is stationary.

  • Option D

    The direction cannot be obtained from the equation.

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