1. Beats are produced when two waves of slightly different frequencies interfere with one another. This results in a sound that alternates between loud and soft at a certain frequency known as the beat frequency. This is given by, f_beats = |f₁ - f₂| where - f_beats is the beat frequency - f₁ and f₂ arRead more

    Beats are produced when two waves of slightly different frequencies interfere with one another. This results in a sound that alternates between loud and soft at a certain frequency known as the beat frequency. This is given by,

    f_beats = |f₁ – f₂|

    where
    – f_beats is the beat frequency
    – f₁ and f₂ are the frequencies of the two interfering waves.

    This would commonly be observed in sound waves by experiencing periodic variation in amplitude, which leads to a pulsating sound.

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  2. The velocity of sound (v) in a gas is determined by the formula: v = √(γRT/M) where: - γ is the adiabatic index, - R is the universal gas constant, - T is the absolute temperature, - M is the molar mass of the gas. Since v ∝ √T, the velocity of sound increases with temperature. Pressure does not dirRead more

    The velocity of sound (v) in a gas is determined by the formula:
    v = √(γRT/M)

    where:
    – γ is the adiabatic index,
    – R is the universal gas constant,
    – T is the absolute temperature,
    – M is the molar mass of the gas.

    Since v ∝ √T, the velocity of sound increases with temperature. Pressure does not directly affect the speed of sound in an ideal gas because both pressure and density change proportionally, keeping their ratio constant.

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  3. The ratio of specific heats (γ = Cₚ / Cᵥ) for a monoatomic gas is given by: γ = (f + 2) / f where f is the degrees of freedom. For a monoatomic gas, f = 3 (translational motion only), so γ = (3 + 2) / 3 = 5/3 ≈ 1.67 So, the ratio of specific heats for monoatomic gas is 1.67. Click here for more: httRead more

    The ratio of specific heats (γ = Cₚ / Cᵥ) for a monoatomic gas is given by:
    γ = (f + 2) / f

    where f is the degrees of freedom. For a monoatomic gas, f = 3 (translational motion only), so
    γ = (3 + 2) / 3 = 5/3 ≈ 1.67

    So, the ratio of specific heats for monoatomic gas is 1.67.

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  4. According to the kinetic theory of gases, gas molecules are in constant random motion and exert pressure due to their collisions with the walls of the container. The pressure P is given by: P = (1/3) (N/V) m v̄² where: - N is the number of molecules, - V is the volume, - m is the mass of a molecule,Read more

    According to the kinetic theory of gases, gas molecules are in constant random motion and exert pressure due to their collisions with the walls of the container. The pressure P is given by:
    P = (1/3) (N/V) m v̄²
    where:
    – N is the number of molecules,
    – V is the volume,
    – m is the mass of a molecule,
    – v̄² is the mean square velocity.

    Every collision transfers momentum to the wall, and the result of many of these collisions is measurable gas pressure.

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  5. The root mean square speed of gases molecules is provided by: vₘₛ = √(3RT/M) - Here:, R: It is the Universal Gas Constant, T : This is Absolute temperature M : It refers to molar mass of a gas. Here this formula provides a condition showing that rms increases with an increment in temperature while tRead more

    The root mean square speed of gases molecules is provided by:
    vₘₛ = √(3RT/M)
    – Here:,
    R: It is the Universal Gas Constant,
    T : This is Absolute temperature
    M : It refers to molar mass of a gas.

    Here this formula provides a condition showing that rms increases with an increment in temperature while the rms declines as molar mass increases.

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