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3 August, 17:53

A spherical source of sound radiates uniformly into a large volume of air at 25C and 101.3 kPa. The frequency of the sound wave is 274 Hz, and the acoustic power radiated from the source is 30mW. At a radial distance of 500mm from the source, determine a. the intensityb. the rms acoustic pressurec. the rms acoustic particle velocity

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  1. 3 August, 20:51
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    A. 0.0096 W/m²

    B. 11.603 dB

    C. 827.37 m/s

    Explanation:

    Parameters given:

    Frequency, f = 274Hz

    Pressure, P = 101.3 kPa

    Temperature, T = 25°C = 298K

    Power = 30 mW

    Radial distance, = 500 mm = 0.5 m

    A. Intensity = Power/Area

    Intensity = Power / (4*pi*r²)

    = (30 * 10^ (-3)) / (4 * 3.142 * 0.5²)

    = 0.0096 W/m²

    B. Pressure (rms) = √ (I*ρ*c)

    I = Intensity

    ρ = density

    c = speed of sound

    ρ = P/RT

    R = gas constant

    => ρ = (101.3 * 10^3) / (298 * 8.314)

    ρ = 40.89 kg/m³

    => Pressure (rms) = √ (0.0096 * 40.89 * 343)

    = √ (134.64)

    = 11.603 dB = 11.603 * 10^ (-6) Pa

    C. Acoustic Particle velocity = Intensity / Acoustic Pressure

    Acoustic Particle velocity = 0.0096 / (11.603 * 10^ (-6)

    Acoustic Particle velocity = 827.37 m/s
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