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

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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