Given Information:
Frequency = 214 Hz
Temperature = 358° C = 308.2 K
Sound Pressure = p = 100 dB = 2 pascal
Distance = 600 mm = 0.60 m
Required Information:
(a) Acoustic Power Level = ?
(b) Acoustic Particle Velocity = ?
and Velocity level at a distance of 600 mm = ?
Answer:
Acoustic Power Level = Lw = 106.44 dB
Acoustic Particle Velocity = v = 0.0106 m/s
Velocity level = 60.25 dB
Explanation:
(a) Acoustic Power Level
Acoustic Power = W = 4πr²
I
Acoustic Intensity = I = p
²/Z₀
Where Z₀ is the characteristic impedance of air Z₀ = 409.8 rayl
I = p
²/Z₀ = (2)²/409.8 = 0.00976 W/m²
W = 4πr²
I = 4*π(0.60)²*0.00976 = 0.0441 W
Acoustic Power Level = Lw = 10log(W/Wref)
Where Wref is Reference Acoustic Power Wref = 1x10⁻¹² W
Lw = 10log(W/Wref) = 10log(0.0441/1x10⁻¹²) = 106.44 dB
Lw = 106.44 dB
(b) Acoustic Particle Velocity
Acoustic Particle velocity = v = p
²/Zs
Where Zs is specific acoustic impedance
Zs = Z₀kr/(1 + k²r²)⁰°⁵
Where k = 2πf/c and c = 346.1 m/s is the speed of sound in air
k = 2π*214/346.1 = 3.885 per m
Zs = 409.8*3.885*0.60/(1 + (3.885)²(0.60)²)⁰°⁵
Zs = 376.6 rayl
v = p
²/Zs = 2²/376.6 = 0.0106 m/s
v = 0.0106 m/s
Velocity level = 10log(v/vref) where vref = 10x10⁻⁹ m/s
Velocity level = 10log(0.0106/10x10⁻⁹) = 60.25 dB
Velocity level = 60.25 dB
