general equation of wave questions with solutions

Showing 1–10 of 41 questions

• MCQmediumWave Motiongeneral equation of wave

  At t = 0, a localized pulse on a string has the shape y(x,0) = A/[1+(x/a)²]. It propagates towards the negative x-direction with speed v without changing shape. Which expression correctly represents the pulse at time t?

  Options

  • Option A

    y = A/{1+[(x-vt)/a]²}

  • Option B

    y = A/{1+[(x+vt)/a]²}

  • Option C

    y = A/{1+(x/a)²+vt}

  • Option D

    y = A/{1+[(vt-x)/a]}

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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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• 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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• 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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• A/RmediumWave Motiongeneral equation of wave

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

  Assertion

  A mechanical wave can transport energy over a large distance without producing a corresponding net transport of the particles of the medium.

  Reason

  Individual particles of the medium generally oscillate about their equilibrium positions while the disturbance propagates through the medium.

  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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• Multi-correctmediumWave Motiongeneral equation of wave

  Consider the ideal one-dimensional wave equation ∂²y/∂t² = v²∂²y/∂x². Which statements are correct?

  Select all that apply

  • Option A

    The parameter v has dimensions of velocity.

  • Option B

    Any sufficiently smooth function f(x-vt) satisfies the equation.

  • Option C

    A function g(x+vt) can never satisfy the equation.

  • Option D

    A sinusoidal progressive wave is a special solution of the equation.

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• MCQmediumWave Motiongeneral equation of wave

  A sinusoidal wave of wavelength 7.5 cm travels 1.2 cm along the +x direction in 0.3 s. At t = 0, a crest P is at x = 0 and the maximum displacement is 2 cm. Which equation correctly represents the wave?

  Options

  • Option A

    y = 2 sin(0.83x - 3.5t) cm

  • Option B

    y = 2 cos(3.35x - 0.83t) cm

  • Option C

    y = 2 cos(0.83x - 3.35t) cm

  • Option D

    y = 2 cos(0.13x - 0.5t) cm

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• A/RmediumWave Motiongeneral equation of wave

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

  Assertion

  A particle of a string can have a maximum transverse speed greater than the propagation speed of the wave for suitable wave parameters.

  Reason

  Particle speed and wave speed are different quantities: uₘₐₓ = Aω, whereas the wave speed is v = ω/k.

  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

  For the progressive wave y = A sin(kx-ωt), which expression gives the transverse acceleration aᵧ of a particle of the medium at displacement y?

  Options

  • Option A

    aᵧ = -ω²y

  • Option B

    aᵧ = +ω²y

  • Option C

    aᵧ = -v²y

  • Option D

    aᵧ = -k²y

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