Wave Motion and General Equation of Travelling Waves questions with solutions

Showing 1–10 of 42 questions

• MCQeasyWave MotionWave Motion and General Equation of Travelling Waves

  A mechanical disturbance is to propagate through a material medium as a wave. The particles of the medium are not transported permanently with the disturbance; instead, each particle oscillates about its equilibrium position while the disturbance moves forward. Which pair of properties of the medium is fundamentally responsible for this propagation?

  Options

  • Option A

    Inertia and elasticity

  • Option B

    Density and temperature only

  • Option C

    Momentum and pressure only

  • Option D

    Viscosity and surface tension only

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• NumericeasyWave MotionWave Motion and General Equation of Travelling Waves

  A travelling wave is given by y = 0.01 cos(6πx+30πt), where x and y are in metres and t in seconds. If the frequency is N Hz, find N.

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• MCQeasyWave MotionWave Motion and General Equation of Travelling Waves

  A one-dimensional disturbance y(x, t) propagates in a uniform medium with constant wave speed v. Which differential equation is the standard one-dimensional wave equation satisfied by the displacement?

  Options

  • Option A

    ∂²y/∂t² = v²∂²y/∂x²

  • Option B

    ∂y/∂t = v²∂y/∂x

  • Option C

    ∂²y/∂x² = v²∂²y/∂t²

  • Option D

    ∂²y/∂x² + v²∂²y/∂t² = 0

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• NumericeasyWave MotionWave Motion and General Equation of Travelling Waves

  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.

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• Multi-correcteasyWave MotionWave Motion and General Equation of Travelling Waves

  Which statements correctly describe the direction of propagation of one-dimensional travelling waves?

  Select all that apply

  • Option A

    f(x-vt) propagates towards +x.

  • Option B

    f(x+vt) propagates towards -x.

  • Option C

    sin(kx-ωt) propagates towards +x.

  • Option D

    sin(kx+ωt) propagates towards -x.

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• Multi-correctmediumWave MotionWave Motion and General Equation of Travelling Waves

  Which of the following expressions can represent an undistorted wave travelling with constant speed v?

  Select all that apply

  • Option A

    y = f(x-vt)

  • Option B

    y = g(x+vt)

  • Option C

    y = A exp[-(x-vt)²/a²]

  • Option D

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

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• MCQmediumWave MotionWave Motion and General Equation of Travelling Waves

  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 MotionWave Motion and General Equation of Travelling Waves

  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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• MCQeasyWave MotionWave Motion and General Equation of Travelling Waves

  A plane progressive wave is described by y = 5 cos{π[200t-(x / 150)]}, where x and y are measured in centimetres and t in seconds. What is the speed of the wave in m·s⁻¹?

  Options

  • Option A

    120

  • Option B

    150

  • Option C

    200

  • Option D

    300

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• MCQmediumWave MotionWave Motion and General Equation of Travelling Waves

  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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