Reflection, Refraction and Superposition of Waves questions with solutions

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• MCQmediumWave MotionReflection, Refraction and Superposition of Waves

  Two waves are y₁ = 4 sin(kx-ωt) and y₂ = 2 sin(kx-ωt + 2π/3). The amplitude and phase of the resultant wave, relative to y₁, are:

  Options

  • Option A

    6, 2π/3

  • Option B

    6, π/3

  • Option C

    √3, π/6

  • Option D

    2√3, π/6

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• MCQeasyWave MotionReflection, Refraction and Superposition of Waves

  A sinusoidal transverse wave travels along a string towards a perfectly fixed end located at x = 0. Near the end, the incident wave is represented by yᵢ = A cos(kx-ωt). The origin is chosen at the reflecting end. Which expression correctly represents the reflected displacement wave?

  Options

  • Option A

    yᵣ = A cos(kx+ωt)

  • Option B

    yᵣ = -A cos(kx+ωt)

  • Option C

    yᵣ = -A cos(kx-ωt)

  • Option D

    yᵣ = A sin(kx+ωt)

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• A/RmediumWave MotionReflection, Refraction and Superposition of Waves

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

  Assertion

  A transverse displacement wave reflected from a perfectly free end does not undergo a phase reversal.

  Reason

  At a perfectly free end the transverse force must vanish, which imposes the boundary condition ∂y/∂x = 0 at the end.

  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 MotionReflection, Refraction and Superposition of Waves

  A wave travelling on string 1 is partially reflected at a junction with string 2. The two strings have impedances Z₁ and Z₂. What fraction of the incident average power is reflected?

  Options

  • Option A

    (Z₁-Z₂)/(Z₁+Z₂)

  • Option B

    [(Z₁-Z₂)/(Z₁+Z₂)]²

  • Option C

    4Z₁Z₂/(Z₁+Z₂)²

  • Option D

    Z₂/Z₁

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• NumericmediumWave MotionReflection, Refraction and Superposition of Waves

  Two strings are under the same tension and have linear densities μ₁ = 9μ and μ₂ = μ. A wave of displacement amplitude 8 mm is incident from string 1 onto string 2. If the reflected displacement amplitude is N mm, find N.

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• MCQmediumWave MotionReflection, Refraction and Superposition of Waves

  Two semi-infinite strings of linear mass densities μ₁ and μ₂ are joined and maintained under the same tension. A transverse wave is incident from string 1 towards string 2. If μ₂ > μ₁, which statement about the reflected displacement wave is correct?

  Options

  • Option A

    There is no reflected wave.

  • Option B

    The reflected displacement wave undergoes a phase change of π.

  • Option C

    The reflected wave always has zero phase difference from the incident wave.

  • Option D

    The transmitted displacement wave undergoes a phase change of π.

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• A/ReasyWave MotionReflection, Refraction and Superposition of Waves

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

  Assertion

  A transverse displacement wave reflected from a perfectly fixed end undergoes a phase change of π.

  Reason

  The total transverse displacement at the fixed end must remain zero at every instant.

  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 MotionReflection, Refraction and Superposition of Waves

  A sinusoidal wave of frequency f travels from a string of linear density μ₁ to another string of linear density μ₂. Both strings are under the same tension. Which relation correctly gives the ratio of transmitted wavelength λ₂ to incident wavelength λ₁?

  Options

  • Option A

    λ₂/λ₁ = √(μ₂/μ₁)

  • Option B

    λ₂/λ₁ = √(μ₁/μ₂)

  • Option C

    f₂/f₁ = √(μ₁/μ₂)

  • Option D

    f₂ = f₁ and λ₂ = λ₁

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• NumericmediumWave MotionReflection, Refraction and Superposition of Waves

  Two strings under the same tension have linear densities μ₁ = μ and μ₂ = 4μ. A displacement wave of amplitude 6 mm is incident from string 1. If the transmitted displacement amplitude is N mm, find N.

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• NumericmediumWave MotionReflection, Refraction and Superposition of Waves

  Two coherent waves have equal individual intensity I₀ and phase difference 120°. If their resultant intensity is NI₀, find N.

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