Page 690 - Automotive Engineering Powertrain Chassis System and Vehicle Body

Interior noise: Assessment and control C HAPTER 21.1

The sound power level (re 10 12 W) is thus: where

rcSs v 2 h ¼ plate thickness (m)
L w ¼ 10 log 10 (21.1.71)
10 12 c L ¼ phase speed of longitudinal waves in plate
1
(ms )
2
1
L w ¼ 10 log 10 hv i þ 10 log S þ 10 log s c ¼ speed of sound in fluid (air) (ms )
10
10
The radiation efficiency is generally greater than 100% at
rc
þ 10 log 10 frequencies around the critical frequency. At frequencies
10 12 greatly above the critical frequency, the radiation effi-
ciency is usually 100% whereas at frequencies greatly
2
L w x 10 log 10 hv i þ 10 log S þ 10 log s below the critical frequency the radiation efficiency can
10
10
be as low as a fraction of 1%.
12
þ 146 dB re10 W
Radiation efficiencies can be predicted using boundary
(21.1.72) element techniques (SYSNOISE), or approximations
may be obtained from generalised curves such as those
The determination of sound power from surface vi- presented by Ve ´r and Holmer (1971), reported in Fahy
bration measurements is an approximate method due to (1985), reproduced in Fig. 21.1-5.
uncertainties in:
(i) the surface-averaged vibration velocity;
(ii) the radiation efficiency.
21.1.3.8 Determination of sound power
Ideally, the surface-averaged vibration velocity should be using an intensity meter
obtained using an accelero-meter and an integrating cir-
cuit, making a large number of narrow band measure- It has already been stated that sound power is directly
ments at points away from the edges of the structure, and related to sound intensity by the bounding area, thus:
averaging each band result as follows:
N W ¼ I$S
1 X =10
¼ 10 log 10 L v i (21.1.73)
L v i 10 N The fact that for free-field conditions at room
i ¼ 1
temperature
However, care should be taken when using integrating
circuits that the signal-to-noise ratio for the measurement L p x L i
chain is not too severely reduced. If this is the case, or if was also employed when determining the sound
a reasonable quality integrating circuit is not available, power of a source using sound pressure measurements.
then the vibration velocity can be estimated from the This relationship breaks down for non-free-field condi-
vibration acceleration as follows:
tions, but the relationship between sound power and
ð sound intensity still holds. Therefore, if one can measure
N
jvje iut ¼ jaje iut dt (21.1.74) sound intensity directly then sound power may be de-
0 termined even in non-free-field conditions.
jaj Sound intensity is the long-term average integral of
jvj ¼ (21.1.75)
iu acoustic pressure and acoustic particle velocity
2
2 a ð T
v z 2 (21.1.76) 1
ð2pfÞ I ¼ lim p$u dt (21.1.29)
T/N T 0
f is the band centre frequency (Hz). If this approximate An intensity meter has been developed by Fahy and
integration technique is used on third octave bands, then others (Fahy, 1989) which measures intensity directly by
significant errors can occur at higher frequencies where using two phase-matched microphones at a known
the bandwidths are greater. spacing apart to infer acoustic particle velocity from the
The radiation efficiency of a vibrating structure is pressure gradient. It should be appreciated that sound
notoriously difficult to determine. The key parame- intensity is a vector product having both magnitude and
ter is the critical frequency, which for uniform flat direction.
plates is: Sound power is determined from the intensity aver-
aged over a notional surface placed around the source.
2
f c ¼ c =1:8 hc L ðHzÞ ðFahy; 1985Þ (21.1.77) The same restrictions on accuracy regarding the number

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