sound wave questions with solutions

Showing 1–10 of 33 questions

• MCQeasyWave Motionsound wave

  At a certain point of a travelling sound wave, the instantaneous excess pressure is positive, so Δp > 0. Which statement correctly identifies the local state of the medium?

  Options

  • Option A

    The point is in a rarefaction and its density is below the equilibrium density.

  • Option B

    The point is in a compression and its density is above the equilibrium density.

  • Option C

    The particle displacement must be maximum at that point.

  • Option D

    The particle velocity must necessarily be zero at that point.

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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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• NumericmediumWave Motionsound wave

  The speed of sound in an ideal gas is 330 m/s at 300 K. At another temperature the speed becomes 363 m/s. Assuming γ is unchanged, if the new temperature is N K, find N.

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• MCQeasyWave Motionsound wave

  Which pair gives the standard expressions for the longitudinal speed of sound in a thin solid rod of Young's modulus Y and density ρ, and in a fluid of bulk modulus B and density ρ?

  Options

  • Option A

    Solid rod: v = √(Y/ρ); fluid: v = √(B/ρ)

  • Option B

    Solid rod: v = √(ρ/Y), fluid: v = √(ρ/B)

  • Option C

    Solid rod: v = Y/ρ, fluid: v = B/ρ

  • Option D

    Both velocities depend only on density.

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• Multi-correctmediumWave Motionsound wave

  Which expressions are correct in the standard ideal approximations for the speed of sound?

  Select all that apply

  • Option A

    In a fluid, v = √(B/ρ).

  • Option B

    In a thin solid rod, v = √(Y/ρ).

  • Option C

    In an ideal gas, v = √(γP/ρ).

  • Option D

    In an ideal gas, v = √(γRT/M).

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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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• 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-correctmediumWave Motionsound wave

  Which statements correctly compare Newton's original theory and Laplace's correction for the speed of sound in a gas?

  Select all that apply

  • Option A

    Newton treated compressions and rarefactions as isothermal.

  • Option B

    Newton used the effective bulk modulus B = P.

  • Option C

    Laplace treated the rapid changes as approximately adiabatic.

  • Option D

    Laplace's corrected speed is √γ times Newton's value.

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• MCQmediumWave Motionsound wave

  A longitudinal sound wave travels in the positive x-direction through a fluid of equilibrium density ρ₀ and bulk modulus B. The longitudinal displacement of the particles is s = sₘ cos(kx-ωt). Which expression correctly represents the excess pressure Δp produced by the sound wave?

  Options

  • Option A

    Δp = -Bksₘ cos(kx-ωt)

  • Option B

    Δp = Bksₘ sin(kx-ωt)

  • Option C

    Δp = -Bksₘ sin(kx-ωt)

  • Option D

    Δp = Bωsₘ cos(kx-ωt)

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• MCQmediumWave Motionsound wave

  Laplace corrected Newton's calculation of sound speed in a gas by treating the rapid compressions and rarefactions as adiabatic. Which expression results?

  Options

  • Option A

    v = √[P/(γρ)]

  • Option B

    v = √(γP/ρ)

  • Option C

    v = γ√(P/ρ)

  • Option D

    v = √[ρ/(γP)]

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