Getting to Grips with Aircraft Noise

⎛ dr ⎞
⎜⎝
c + ⎟⎠
' dr ⎛ dr ⎞ dt
λλλλ = cT + T = T⎜⎝
c + ⎟⎠
=
(9.1.5-2)
dt dt f
Flight Operations Support & Line Assistance
Getting to grips with aircraft noise
9 - A BIT OF THEORY
The ration between the frequency from the source and the frequency perceived by the
observer is then:
f
f
'
=
1 +
1
dr
dt
c
(9.1.5-3)
2
dr d 2 2 2 V t
In our case, = ( h + V t ) =
(9.1.5-4)
dt dt
r
As
r = −
Vt
cos
( θθθθ )
And the Mach number M = V / c
We get:
f
f
'
1
= (9.1.5-5)
1 − M cos
( θθθθ )
Consequently, the sound perceived on ground is more high-pitched when the aircraft is
approaching (θθθθ below 90°) and louder when moving away from the observer (θθθθ above
90°).
9.1.6. DIRECTIONALITY - DIRECTIVITY
Generally speaking, a sound source the characteristic dimensions of which are large
compared to the wavelength prove to be directional. This is the case for airplanes.
Consequently, the sound field around an aircraft depends both on distance and angular
direction.
The descriptor used to assess the directivity of a source is called the directivity index
and corresponds to the difference between the Sound Pressure Level (see §9.3.2) in a
specified angular direction θ to the average Sound Pressure Level at the same distance
r:
DI = SPL θθθθ
−
( ) SPLaverage
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