Sound Waves: Wave Equation, Propagation and Speed of Sound questions with solutions

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• MCQeasyWave MotionSound Waves: Wave Equation, Propagation and Speed of Sound

  The equilibrium pressure of a gas is P₀. A sinusoidal sound wave travelling through the gas has pressure amplitude Δpₘ. Which expressions correctly give the maximum and minimum absolute pressures during the oscillation?

  Options

  • Option A

    Pₘₐₓ = P₀+Δpₘ and Pₘᵢₙ = P₀-Δpₘ

  • Option B

    Pₘₐₓ = Δpₘ and Pₘᵢₙ = -Δpₘ

  • Option C

    Pₘₐₓ = P₀+Δpₘ/2 and Pₘᵢₙ = P₀-Δpₘ/2

  • Option D

    Pₘₐₓ = P₀+Δpₘ² and Pₘᵢₙ = P₀-Δpₘ²

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• MCQeasyWave MotionSound Waves: Wave Equation, Propagation and Speed of Sound

  The speed of sound in the same ideal gas is v₁ at absolute temperature T₁ and v₂ at temperature T₂. The ratio of specific heats γ remains unchanged. Which relation is correct?

  Options

  • Option A

    v₂/v₁ = T₂/T₁

  • Option B

    v₂/v₁ = √(T₂/T₁)

  • Option C

    v₂/v₁ = √(T₁/T₂)

  • Option D

    v₁ = v₂

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• MCQmediumWave MotionSound Waves: Wave Equation, Propagation and Speed of Sound

  Newton originally obtained the speed of sound in a gas as vₙ = √(P/ρ). Which physical assumption about the compressions and rarefactions led to this result?

  Options

  • Option A

    The compressions and rarefactions were assumed to be adiabatic.

  • Option B

    The compressions and rarefactions were assumed to be isothermal.

  • Option C

    The gas pressure was assumed to remain zero.

  • Option D

    The gas density was assumed to remain exactly constant.

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• MCQeasyWave MotionSound Waves: Wave Equation, Propagation and Speed of Sound

  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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• A/RmediumWave MotionSound Waves: Wave Equation, Propagation and Speed of Sound

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

  Assertion

  Newton's calculated speed of sound in air was lower than the experimentally observed value.

  Reason

  Newton assumed the sound-wave compressions and rarefactions to be isothermal, whereas the actual rapid changes are approximately adiabatic and have effective bulk modulus γP.

  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 MotionSound Waves: Wave Equation, Propagation and Speed of Sound

  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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• NumericmediumWave MotionSound Waves: Wave Equation, Propagation and Speed of Sound

  Two coherent sound waves of intensities 9 W/m² and 4 W/m² arrive at the same point with phase difference π. If the resultant intensity is N W/m², find N.

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• MCQmediumWave MotionSound Waves: Wave Equation, Propagation and Speed of Sound

  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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• MCQmediumWave MotionSound Waves: Wave Equation, Propagation and Speed of Sound

  A small-amplitude plane sound wave propagates through a fluid with wave speed v. At a particular position and time the excess pressure is Δp and the corresponding excess density is Δρ. Which relation is correct?

  Options

  • Option A

    Δp = vΔρ

  • Option B

    Δp = v²Δρ

  • Option C

    Δp = ρ₀vΔρ

  • Option D

    Δp = Δρ/v²

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• MCQmediumWave MotionSound Waves: Wave Equation, Propagation and Speed of Sound

  The speed of a longitudinal wave in a metallic bar is 400 m/s. If the density and Young's modulus of the bar material are increased by 0.5% and 1% respectively then the speed of the wave is changed approximately to _____ m/s.

  Options

  • Option A

    399

  • Option B

    398

  • Option C

    402

  • Option D

    401

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