Getting to Grips with Aircraft Noise

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9 - A BIT OF THEORY Consequently, the average intensity of the sound wave over a period of time is given by: 60 T 1 I( r) = ∫ pv r ( t). dt (9.2.2-3) T 0 The linearized equation of the dynamics first principle (the particle acceleration is mainly due to pressure forces) gives: ∂vr ∂p ρρρρ ∞ = − (9.2.2-4) ∂t ∂r Where: ρρρρ ∞ is the density of the medium (in kg/m 3 ) for the air at sea level, ρρρρ ∞ =1.29 kg/m 3 Consequently: − 1 ∂p t) = ∫ dt = p ρρρρ ∂r ⎛ 2ππππ ⎛ 2ππππ ⎞ 1 ⎜ cos⎜⎝ ωωωω t − r ⎟⎠ − ⎝ λλλλ rωωωω λλλλ ωωωω r vr ( max 2 ∞ pv r = pmax ρρρρ r ∞ 2 cos 2 ⎛ 2ππππ ⎞⎛ 2ππππ ⎛ 2ππππ ⎞ 1 ⎜⎝ ωωωω t − r ⎟⎠ ⎜ cos⎜⎝ ωωωω t − r ⎟⎠ − λλλλ ⎝ λλλλ rωωωω λλλλ ωωωω r ⎛ 2ππππ ⎞⎞ sin⎜⎝ ωωωω t − r ⎟⎠ ⎟ λλλλ ⎠ ⎛ 2ππππ ⎞⎞ sin⎜⎝ ωωωω t − r ⎟⎠ ⎟ λλλλ ⎠ Averaging the above equation over one period, leads to (as the product of a sine by a cosine has got a nil average over one period and the average of the squared cosine is equal to 0.5): 2ππππ pmax I( r) = 2 2ρρρρ ωωωω r λλλλ As λλλλ =cT and ωωωω =2ππππ /T, then ∞ 2 2 2 1 ⎛ pmax ⎞ pe I( r) = ⎜⎝ ⎟⎠ = (9.2.2-5) ρρρρ ∞c r 2 ρρρρ ∞c This equation is the equivalent of the Ohm’s law in electricity (Intensity=potential difference divided by the resistance). By analogy, the quantity ρρρρ ∞c is called the acoustic resistance of the medium. Flight Operations Support & Line Assistance Getting to grips with aircraft noise
9.3. PSYCHO-ACOUSTICS Flight Operations Support & Line Assistance Getting to grips with aircraft noise 9 - A BIT OF THEORY 9.3.1. NOTION OF SOUND INTENSITY LEVEL (SIL) The human eardrum is sensitive to sound intensity. Practically, the human ear perceives sounds, the intensity of which varies from 1.10 -12 W/m 2 (threshold of perception) to 100 W/m 2 , (threshold of pain). In order to cope with this wide range, a logarithmic scaling has been defined. It is called the Sound Intensity Level (SIL) and its unit is the decibel (dB): ⎛ I ⎞ SIL = 10 log ⎜⎜ ⎟⎟ ⎝ I 0 ⎠ , in decibel (dB) (9.3.1-1) Where: I is the actual average sound intensity I0 is the average intensity at the threshold of perception for a pure sound The following chart gives some typical noise levels in our everyday life Sound Intensity Level (dB) Item 140 Threshold of pain 110 Pneumatic drill 100 Concorde (at takeoff) 90 Truck 60 Conversation 35/40 Library 25 Bedroom 61
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Getting to Grips with Aircraft Noise

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