Page 688 - Automotive Engineering Powertrain Chassis System and Vehicle Body

Interior noise: Assessment and control C HAPTER 21.1

or interest here, so it will be removed by algebraic manip-
ulation, that is:
1
L pd ¼ L W1 þ 10 log 10 dB (21.1.47) 4 1
S H ¼ 10 ½L p1 L wŠ=10 (21.1.56)
R S 1
2
where S H is the surface area of a hemisphere (m ). 4 ½L p2 L wŠ=10 1
Now for a hemisphere R ¼ 10 (21.1.57)
S 2
1 4
L p1 ¼ L W1 þ 10 log 10 þ (21.1.48) Therefore,
S H R
1 1
1 4 10 ½L p1 L wŠ=10 ¼ 10 ½L p2 L wŠ=10 (21.1.58)
10 log 10 þ ¼ L p1 L W1 (21.1.49) S 1 S 2
S H R
1 1
1 4 10 ½L p1 L wŠ=10 10 ½L p2 L wŠ=10 ¼ (21.1.59)
þ ¼ 10 ½L p1 L W1Š=10 (21.1.50) S 1 S 2
S H R
Multiply both sides by 10 L w/10 ,
Now, it is known from equation (21.1.47) that:
1 1
1 10 L p1 =10 10 L p2 =10 ¼ 10 L w =10 (21.1.60)
L pd ¼ L W1 þ 10 log 10 (21.1.47) S 1
S H S 2
therefore, Take logarithms on both sides,

1 L p1 =10 L p2 =10 L w 1 1
L W1 ¼ L pd 10 log 10 (21.1.51) log 10 10 10 ¼ þ log 10
S H 10 S 1 S 2
(21.1.61)
so,
Multiply both sides by 10
1 4
þ ¼ 10 ½L p1 ðL pd þlog 10 ð1=S H Þފ=10
S H R L p1 =10 L p2 =10 1 1
10log 10 10 10 ¼ L w þ10log 10
1 4 10 ½L p1 L pdŠ=10 S 1 S 2
þ ¼ (21.1.62)
S H R S H
h i
4 1 ½L p1 L pdŠ=10 Now,
¼ 10 1 (21.1.52)
R S H
10 log 10 10 L p1 =10 10 L p2 =10
Now that the room constant is known, L p can be
determined over a hemisphere around the sound sour- L p2 =10 ðL p1 L p2Þ=10
ce, and the sound power determined directly according ¼ 10 log 10 10 10 1
to:
ðL p1 L p2Þ=10
1 4 L p2 þ 10 log 10 10 1
L w ¼ L p 10 log 10 þ (21.1.53)
2pr 2 R
1 1
¼ L w þ 10 log 10 (21.1.63)
A third alternative way of determining sound power S 1 S 2
levels involves obtaining the spatially averaged sound
pressure levels L p1 and L p2 over two different hemi- and finally
spherical surfaces of areas S 1 and S 2 both of which have 1 1
the acoustic source at their centres, that is: L w ¼ L p2 10 log 10
S 1 S 2

1 4 þ 10 log 10 ðL p1 L p2Þ=10 1 (21.1.64)
L p1 ¼ L w þ 10 log 10 þ (21.1.54) 10
S 1 R

1 4 This equation can be used directly to determine the
L p2 ¼ L w þ 10 log 10 þ (21.1.55)
S 2 R sound power from a source when
N
L w is to be determined. L p1 and L p2 are known, L p1;2 ¼ 10 log 1 X 10 ðL pi =10Þ dB (21.1.65)
measured quantities. The term 4/R is of no inherent 10 N
i ¼ 1

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