Getting to Grips with Aircraft Noise
Getting to Grips with Aircraft Noise
Getting to Grips with Aircraft Noise
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9 - A BIT OF THEORY<br />
9.2. MATHEMATICAL APPROACH<br />
We will assume a punctual acoustic source and a homogeneous and obstacle free<br />
medium. These assumptions are close <strong>to</strong> the conditions encountered when the source<br />
is an airplane, provided that the observation point is far enough from the aircraft<br />
(typically at least the wave length of the lowest frequency emitted or several times the<br />
greatest dimension of the aeroplane).<br />
58<br />
Near Field<br />
Far Field<br />
(9.2-1)<br />
The far-field area sees the aircraft as a punctual source, while it is not the case <strong>with</strong>in<br />
the near-field area, where the sound pressure is much more complex <strong>to</strong> be expressed<br />
mathematically.<br />
9.2.1. AMPLITUDE MEASURE<br />
Note : For the sake of simplicity, we will base our reasoning upon one of the<br />
simplest form of sound wave emitted by a single source. All the conclusions<br />
demonstrated hereafter are applicable <strong>to</strong> the general case.<br />
In the far-field, the simplest form of the local sound pressure variation is a sine, which<br />
means a pure <strong>to</strong>ne (a mono-frequency sound).<br />
The local pressure variation of a pure <strong>to</strong>ne can be expressed as follows:<br />
Pmax<br />
2ππππ<br />
p = . cos( ωωωω t − r)<br />
(9.2.1-1)<br />
r<br />
λλλλ<br />
Where: Pmax/r is the amplitude of the wave<br />
r is the distance from the source (in meters)<br />
ω is the wave pulsation (in rad/s)<br />
λ is the wave length (in meters)<br />
Flight Operations Support & Line Assistance<br />
<strong>Getting</strong> <strong>to</strong> grips <strong>with</strong> aircraft noise
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