Comparative Representation of Sound Field Quantities

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Comparative representation of sound field quantities and sound energy quantities Assumption: German: http://www.sengpielaudio.com/VergleichendeDarstellungVonSchall.pdf Air temperarature = 20°C: (Atmospheric pressure 10,1325 Pa = 1013 hectopascal) Density of air at 20°C: = 1.204 kg / m3 (At 0°C is = 1.293 kg/m3) Speed of sound at 20°C: c = 343 m / s (At 0°C is c = 331 m/s) UdK Berlin p Sengpiel Specific acoustic impedance Z at 20°C: Z = · c = = 413 N · s / m3 (At 0°C is Z = 428 N·s/m3) 05.93 v Sound Reference sound field quantities: –5 2 –5 Reference sound pressure p0 = 2 · 10 N / m = 2 · 10 Pa (Fixed "threshold of audibility") p0 p0 –8 –8 Reference sound velocity v0 = = = 5 · 10 m / s (= 4.854 · 10 m / s) c Z0 Reference sound energy quantities: 2 p0 2 –12 2 –12 2 Reference sound intensity J0 = = Z0 · v = 10 W / m (= 0.9685 · 10 W / m ) Z0 J p v Reference sound energy density E = 0 = 00 = 3 · 10–15 W · m / s3 (= 2.824 · 10–15 J / m3) 0 c c –12 2 –12 Reference acoustic power W0 = J 0 · A = 10 W = 1 pW bei A = 1 m (= 0.9685 · 10 W) >>> Given: A plane sound wave of f = 1 kHz and the N Sound pressure p = 1 Pa = 1 = 10 bar 94 dBSPL – We use always the RMS value. m2 Calculated: c 343 Wavelength = = = 0.343 m = 34,3 cm f 1000 1 Periodic length T = = 0.001 s = 1 ms f p 1 Sound velocity v = 2 · · f · = = = 2.42 . 10–3 m / s = 2.42 mm / s Z0 413 v Sound particle displacement = = 0.385 · 10–6 m = 0.385 m 2 f p2 Acoustic intensity J = pv = = 2.42 · 10–3 W / m2 = 2.42 mW / m2 Intensity is not amplitude Z0 J Sound energy density E = = 7.06 · 10-6 W · s / m3 = 7.06 · 10-6 J / m3 c 2 –3 Sound power W0 (mit A = 1 m ) = JA = 2,42 · 10 W = 2.42 mW Level: Differentiate sound field quantities and sound energy quantities. p 1 Sound pressure level Lp = 20 · log = 20 · log = 94 dB (93.98 dB) 5 p0 210 v 3 Sound velocity level Lv = 20 · log = 20 · log 2.42 10 = 94 dB (93.70 dB) 8 v0 510 J 2.42 103 Acoustic intensity level LJ = 10 · log = 10 · log = 94 dB (93.84 dB) 12 J0 10 E 2.42 103 Sound energy density level LE = 10 · log = 10 · log = 94 dB (93.84 dB) 12 E0 10 3 LW 2.42 10 Sound power level LW = 10 · log = 10 · log = 94 dB (93.84 dB) 12 LWo 10 Don’t mix the pressure p with the power P, the sound power level is better called LW instead of LP. Theoretically interesting is, what sound level the 1.013 105 full modulation of the atmospheric pressure is: Lp = 20 · log = 194 dBSPL ≡ 1000237 Pa (RMS). But this is not the maximum possible 21 05 pressure! A previously used sound size was 1 µbar = 0,1 Pa. Since 1 W · s = 1 N · m, the result for the sound energy density 1 W · s / m³ 1 N / m² and that is the unit of sound pressure! Reminder: W · s = J (Joule). See also: http://www.sengpielaudio.com/RelationshipsOfAcousticQuantities.pdf "Relationship of acoustic quantities". .

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