sound wave questions with solutions

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• NumericeasyWave Motionsound wave

  A sound pressure wave is represented by Δp = 0.02 sin(1000t-4x), with all quantities in SI units. If the speed of the sound wave is N m/s, find N.

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• NumericmediumWave Motionsound wave

  For a gas having γ = 7/5, define vₗ as the sound speed predicted after Laplace's correction and vₙ as Newton's isothermal prediction. If (vₗ/vₙ)² = N/5, find N.

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• NumericmediumWave Motionsound wave

  A plane sound wave in a gas has pressure amplitude Δpₘ = 3 Pa, angular frequency 1000 rad/s, sound speed 300 m/s and equilibrium density ρ₀ = 1 kg/m³. If the particle-displacement amplitude is N μm, find N.

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• Multi-correcteasyWave Motionsound wave

  Which statements correctly describe compression and rarefaction in a small-amplitude sound wave?

  Select all that apply

  • Option A

    Compression corresponds to Δp > 0.

  • Option B

    Compression corresponds to Δρ > 0.

  • Option C

    Rarefaction corresponds to absolute pressure below the equilibrium pressure.

  • Option D

    Pressure and density reach their respective maxima at the same phase.

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• MCQmediumWave Motionsound wave

  Two ideal gases at the same absolute temperature have adiabatic indices γ₁ and γ₂ and molar masses M₁ and M₂. Their sound speeds are v₁ and v₂. Which relation is correct?

  Options

  • Option A

    v₁/v₂ = √(γ₁M₁/(γ₂M₂))

  • Option B

    v₁/v₂ = √(γ₁M₂/(γ₂M₁))

  • Option C

    v₁/v₂ = M₂/M₁

  • Option D

    v₁/v₂ = √(M₁/M₂)

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• MCQmediumWave Motionsound wave

  Two coherent sound waves have intensities I₁ and I₂ at a point and a phase difference φ. Which expression gives the resultant intensity?

  Options

  • Option A

    I = I₁+I₂

  • Option B

    I = I₁+I₂+2√(I₁I₂) cosφ

  • Option C

    I = (I₁+I₂) cosφ

  • Option D

    I = √(I₁²+I₂²)

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• A/RmediumWave Motionsound wave

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

  Assertion

  Pressure variation and density variation in a progressive sound wave are in phase.

  Reason

  For a small-amplitude sound wave, Δp = v²Δρ.

  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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• Multi-correctmediumWave Motionsound wave

  Which statements are correct for a plane sinusoidal sound wave of pressure amplitude Δpₘ and particle-displacement amplitude sₘ?

  Select all that apply

  • Option A

    I = Δpₘ²/(2ρ₀v)

  • Option B

    I = ½ρ₀vω²sₘ²

  • Option C

    Average intensity is proportional to Δpₘ².

  • Option D

    Average sound power through an area A normal to propagation is P̄ = IA.

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• NumericeasyWave Motionsound wave

  Two ideal gases have the same value of γ and are at the same absolute temperature. Their molar masses are 4 g/mol and 36 g/mol. If the ratio of the sound speed in the lighter gas to that in the heavier gas is N, find N.

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• MCQmediumWave Motionsound wave

  A right-moving sound wave has particle displacement s = sₘ cos(kx-ωt). Let u be the instantaneous particle velocity and Δp the excess pressure at the same point. Which relation is correct?

  Options

  • Option A

    Δp = ρ₀vu

  • Option B

    Δp = -ρ₀vu

  • Option C

    Δp = ρ₀v²u

  • Option D

    Δp = u/(ρ₀v)

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