Sound is becoming an increasingly important aspect of air moving
operations. Requirements for low sound levels in industrial and
domestic environments are becoming more common place. This article will
run through the basic calculations of sound, as well as a brief blurb
regarding reflection and absorbtion. We will start with the latter and
progress through the basics of sound caculation and terminology.
Absorbtion and Reflection
When
sound comes into contact with a different medium three things will
happen. Some of the wave will reflect, some of the wave will go
through, and some of the wave will be absorbed. These three factors can greatly effect Sound Pressure Level (SPL).
Absorbtion
relates to the amount of energy that is absorbed by the medium. Various
materials can be used and are optimised for sound absorbtion, different
shapes can also help with the absorbtion of sound. Absorbtion is an
effective way to reduce your sound level.
However not all of
the energy will be absorbed, a portion of the sound will be reflected.
Dependant on your installation and the absorbtion factor of your
material reflections may in fact increase the SPL in certain areas near
the source. This is also where wall shapes can be of benefit by
redirecting reflections.
There is a lot of information available regarding absorbtion and reflection of sound the Woods Practical Guide to Noise Control is a good starting point for basic theory, and also has a chapter dedicated to ventilation.
Sound Pressure
Sound Pressure is the local change, from atmospheric, in pressure
caused by the sound wave. This is an instantaneous measurement and is
not the pressure measurement used for the calculation to find the Sound
Pressure Level in decibels (dB). Like all pressure measurements it is defined by Force divided by Area.
Sound
Pressure Level
The sound pressure level (SPL) is calculated from the root mean square
(rms) of the instantaneous pressure. For a sound wave this value is the
maximum pressure (amplitude) divided by the square root of 2.
The equation to transform the rms pressure to SPL in dB is as follows:
The reference pressure for the equation is the lowest audible pure tone
that can be heard by an undamaged ear. This has a value of 0.00002
Pascals, or 20µPa.
Below is a table of various sound sources showing their rms pressure
and SPL.
Source of sound
RMS sound pressure
SPL
Pa
dB
rocket launch equipment acoustic tests
approx. 165
threshold of pain
100
134
hearing damage during short-term effect
20
approx. 120
jet engine, 100 m distant
6–200
110–140
jackhammer,
1 m distant / discotheque
2
approx. 100
hearing
damage from long-term exposure
0.6
approx. 85
traffic noise on major road, 10 m distant
0.2–0.6
80–90
moving automobile, 10 m distant
0.02–0.2
60–80
TV set – typical home level, 1 m
distant
0.02
approx. 60
normal talking, 1 m distant
0.002–0.02
40–60
very calm room
0.0002–0.0006
20–30
quiet rustling leaves
0.00006
10
auditory
threshold at 2 kHz
0.00002
0
Sound Power
Level
Sound power level (SWL), not to be confused with Sound pressure level. Sound power level
is denoted by Lw. Sound power level is calculated
from the acoustic power that is generated by the source in Watts (W).
The SWL is calculated using the following equation:
Where W0 is the reference value:
Below is a table of examples converting the acoustic power to the SWL
for various sources.
Sound source
Sound Power
Watts
Lw
dB
Rocket engine
1,000,000 W
180 dB
Turbojet engine
10,000 W
160 dB
Siren
1,000 W
150 dB
Heavy truck engine or
loudspeaker rock concert
100 W
140 dB
Machine gun
10 W
130 dB
Jackhammer
1 W
120 dB
Excavator, trumpet
0.3 W
115 dB
Chain
saw
0.1 W
110 dB
Loud speech
0.001 W
90 dB
Usual talking,
Typewriter
10−5
W
70 dB
Refrigerator
10−7
W
50 dB
(Auditory
threshold at 2.8 m)
10-10
W
20 dB
(Auditory
threshold at 28 cm)
10-12
W
0 dB
SWL to SPL
As SWL is the power level of the source you can
calculate the SPL from the below equation. The equation describes the
ideal loss of sound for a free field propogation in air, it can be used
for other mediums with adjustments made to suit the different
resistance (acoustic impedance). S0 is the reference point of 1m² and r is the radius from the source.
The equation can also be modified for certain non free field calculations using correction factors. A few simple factors are;
1/2 spherical - 2(pi)r²
1/4 spherical - (pi)r²
1/8 spherical - (pi)r²/2
A-Weighting
Because the human ear is less sensitive to certain
frequencies of sound a weighting system can be used to create a
perceived sound level. The most common of these weighting systems is
A-Weighting. An adjustment weight is added to each octave band to
correct the octave to a perceived level. Below is a table for the
adjustment weights.
Frequency
(Hz)
63
125
250
500
1k
2k
4k
8k
16k
A-weighting (dB)
- 26.2
- 16.1
-8.6
- 3.2
0
+ 1.2
+ 1.0
-1.1
- 6.6
If you have any further questions regarding any of these topics please do not hesitate to contact Charles Burgess
