sound intensity and power professor phil joseph
TRANSCRIPT
Departamento de
Engenharia Mecânica
Sound intensity and power
Professor Phil Joseph
IMPORTANCE OF SOUND INTENSITY AND SOUND
POWER MEASUREMENT
Sound pressure is the quantity usually used to quantify
sound fields. However, it is often satisfactory as an measure
of source because the pressure propagates as a wave
which, due to multi-path interference, may lead to
fluctuations with observer position.
Sound pressure, unlike measures of sound energy, are not
conserved.
Performance of noise control systems often specified in
terms of energy, e.g., transmission loss, absorption
coefficient.
Instantaneous sound intensity I(t) is the rate of acoustic energy flowing
through unit area in unit time (Wm-2). If, in a point in space, the
acoustic pressure p(t) produces at the same point a particle velocity
u(t), the rate at which work is done on the fluid per unit area I(t) at time
t is given by
I ut p t t
INSTANTANEOUS INTENSITY
Note that I is a vector quantity in the direction of the particle velocity u
‘PROOF’
The work done on the fluid by Force F
acting over a distance d in the
direction of the force is Fd
The work done per unit area A in unit
time T, i.e., the sound intensity, is
given by
uxI pTA
F
d
EXAMPLES FOR WHICH SOUND INTENSITY AND
MEAN SQUARE PRESSURE ARE SIMPLY RELATED
1. Plane progressive waves
2. Far field of a source in free field
3. Hemi-diffuse field
However, in general there is no simple relation between intensity and pressure
ENERGY CONSERVATION
yxt
Iyx
x
Iyx
t
E yx
Net rate of change of energy = Rate of energy in – Rate of energy out
In 3 - dimensions
0.
t
t
EI
x
I
x
I
x
I zyx
I.
RELATIONSHI[P BETWEEN SOUND IINTENSITY
AND SOURCE SOUND POWER
0.
I
t
E
Applying Gauss's divergence theorem
SV
dSdV nA.A ˆ.
SV
dSdVt
EW nI. ˆ
to
gives
GENERAL PROPERTIES OF SOUND INTENSITY FIELDS
Sound intensity (sometimes called sound power flux density) is a vector
quantity acting in the direction of the particle velocity vector u(t).
The instantaneous sound intensity I(t) is in general, rapidly oscillating. A
non-zero time averaged intensity represents a net overall flow of
energy and is called active intensity. A value is referred to as
reactive intensity and is characteristic of strong near fields comprising
strong circulations of energy, which do not propagate to the far field.
SO
UR
CE
Active intensity
Reactive intensity
I
I
INTERFERENCE BETWEEN SOUND INTENSITY FIELDS
Interfering monopoles
tttptp 2121 uuI
Intensity at the microphones is
Sum of intensities
generated by each
source individually.
Intensities are therefore
not generally additive.
ttpttpttpttp 12212211 uuuu
This term represents
correlations. It is zero for
statistically unrelated
source strengths, i.e., if the
sources are incoherent,
SOUND INTENSITY FIELD FOR INTERFERING (COHEENT)
MONOPOLES
Note presence of active ‘sinks’.
Thus, suppressing a portion of an
extended radiator may increase
total power radiation
PRINCIPLES OF SOUND INTENSITY MEASUREMENT
In general sound intensity can only be determined by the measurement
of acoustic pressure and particle velocity simultaneously. This has only
been possible fairly recently with the advent of fast signal processing
methods.
p t1 p t2
pt p t p t 12 1 2
u tp p
rdr
t
1 1 2
r
I ut p t t
tptptp 2212
1
t
dtr
tptptu
0
21
From Euler’s momentum
equation Spatial average
SPECTRAL FORMULATION OF INTENSITY FOR
USE WITH FFT ANALYSERS
The spectral (i.e., frequency) domain equivalent expression of
I ut p t t
r
G
12Im
I
G E p p12 1 2 * p p t e dti t1 2 1 2, ,
dtet ti II
is given by
where G12 is the pressure cross spectrum
and
A COMMERCIAL SOUND INTENSITY PROBE
EXAMPLE OF SOUND INTENSITY FIELDS
SIDE OF CAR AT 100Hz
EXAMPLE OF SOUND INTENSITY FIELDS
CELLO AT 160, 315 and 630Hz
EXAMPLE OF SOUND INTENSITY FIELDS
PISTON IN A BAFFLE AT ka = 2 and ka = 25.
ERRORS IN THE TWO-MICROPHONE SOUND INTENSITY
TECHNIQUE
Principal sources of error in the measurement of sound intensity using
the two-microphone technique in approximate order of importance are:
Bias (Systematic) Errors
a Finite difference and sum approximation error - increases with
increasing frequency and microphone separation distance r.
b Probe diffraction effects - Imposes an upper frequency limit on
their use.
c Phase mismatch error - Transducer and conditioning channel
mismatch. Must ensure phase matching as close as possible - reason why
intensity probe are disproportionately more expensive than single sensors
Random Errors
a Spectral estimation errors due to inadequate time average.
Normalized error , where B is the measurement bandwidth and T
is the effective analysis time window.
21
~
BT
Sound Power
SOURCE QUANTIFICATION The noise received at a location depends on the source strength and
also on the transmission of sound to that location.
Transmission path
LW Lp
ReceiverSource
Noise control strategies can be divided into:
• Reductions at source
• Reductions in the transmission path between source and receiver
In both cases it is useful to quantify the source, independent of its location.
For this we need a suitable measurement quantity representing the source
strength, not a receiver quantity. It should therefore be
• A property of the source alone, independent of its location
• Representative of the sound from the whole source
• Related to the receiver quantity
OBJECTIVES OF SOURCE QUANTIFICATION
Why do we want to quantify the source output?
1. to compare different machines or plant for user selection
2. for a manufacturer to check acceptability of components from sub-
suppliers
3. for source labelling
4. to check that the machine complies with regulatory or legal
requirements
5. for predicting the sound pressure at an operator position (for
assessing hearing hazard) or in the neighbourhood (environmental
impact)
6. to identify source mechanisms (diagnostics)
7. to understand the physics of the source in order to develop models
for the purpose of improving the design
as input to models of transmission paths for noise control
by reducing transmission
SOUND POWER MEASUREMENT
In view of the importance of sound power as a measure of source
‘strength’, its accurate measurement is extremely important. The
commonest techniques for measuring sound power may be organized as
follows: Sound Power Measurement
Techniques
Direct Indirect
Free Field
Technique
Diffuse FieldTechnique
Sound PressureMeasurements
Sound IntensityMeasurements
In-situ
Source
Substitution
Source Surface
Vibration MeasurementTechnique
DEFINITION OF SOUND POWER:
INTEGRAL FORMULATION
S
I
n
W dSS
I n. This integral expression follows from
Gauss’s theorem
The choice of control surface S is
arbitrary, as long as it completely
encloses the source
Time-stationary sources do not
contribute to the integral
Expression assumes that intensity can
be measured directly
SOURCE POWER IS WEAKLY AFFECTED BY ITS
ENVIRONMENT
It is important to be aware that strong reflections back on the source, for
example when the source is situated close to a reflecting surface, may alter
the source radiation resistance and hence increase (or decrease) its sound
power output. The acoustic behavior environment may therefore modify the
source power output although this is generally a weak effect at mid to high
frequencies.
Example
0 2 4 6 8 10 12 14
0.8
1
1.2
1.4
1.6
1.8
2
2kd
FREE-FIELD (or ANECHOIC CHAMBER) TECHNIQUE
(ISO 3745 (3744)) A measurement surface is constructed around the source and divided
into N segments. It is assumed that in the absence of reflections the
intensity may be deduced from the acoustic pressure
(i.e. LI = LP)
This assumes that the wave fronts are
planar, or spherical, and lie normal to
the measurement surface. The sound
power then follows as
W p c Si ii
N
2
1
/
Advantages: Very simple to implement
Disadvantages: Requires costly use of anechoic chamber. Measurements
cannot be made in-situ. Makes potentially very erroneous assumptions about
the radiated field.
DIFFUSE FIELD TECHNIQUE
(ISO 3741 (3742 - 1/2)) Here, it is assumed that under steady state conditions the rate of sound
power input by the source to the room equals the power dissipated by the
walls. From previous results
W I Ad I p cd 2 4/
where is the space-averaged mean square pressure in the room and
A is the random incidence (Sabine) absorption estimated from the rate of
decay of following transient excitation of the sound field via the
relationship, A=0.161T60/V, where T60 is the time taken for the sound field to
decay by 60dB and V is the room volume.
p2
Advantages: Simple to implement. Uses only measurements of acoustic
pressure.
Disadvantages: Assumes ‘large room’ acoustics, which implies high
frequencies or large rooms. Potentially costly.
p2
INTENSITY-BASED METHODS
(ISO 9614-1 and 9614-2)
Here the normal component of sound intensity normal to a hypothetical
surface enclosing the source is measured directly by the use of a sound
intensity probe.
W I Sni ii
N
1
The intensity estimate at each segment may be made by
either
(i). Point-sampling. A single intensity measurement
at the centre of each segment (ISO9614 – 1)
(ii). Scanning the intensity probe over the each
segment surface (ISO9614 – 2)
SOURCE SUBSTITUTION METHOD
(ISO 3747)
A special reference source of known radiated sound power spectrum
(determined by, for example, one of the methods above) is located in the
position (or as close as possible) to the source under test. Measurements
of the sound pressure level with the reference source are compared with
those due to the source under test. The ratio between sound power and
space average mean-squared pressure is assumed to be identical for
both sources.
L LW Wref
L Lp p ref
Advantages: Very simple to implement.
Disadvantages: Potentially large errors for sources of high directionality in
highly reverberant enclosures. Large errors may also arise
from interference in the pressure measurements from
coherent extraneous sources.
SOURCE SURFACE VIBRATION MEASUREMENT
Radiated sound power is inferred directly from the space-averaged mean
square surface vibration velocity. This can be measured using an
accelerometer, or by using a non-contact sensor such as a laser velocimeter
or a volume velocity transducer.
W v S crad 2
Radiation efficiency differs for different structures and is frequency
dependent. It must be obtained from predicted and measured values
published in the literature.
Advantages: Simple to implement. Offers a non-contact measurement
technique. Technique may be performed in-situ with
extraneous source operating simultaneously.
Disadvantages: Assumes radiation efficiency is known which is unlikely for
complex structures. Requires complicated structure to be
decomposed, arbitrarily, into simpler sub-structures.