1. a brief revision of principles and calculations from Building Physics
building services applications
basic acoustics
a brief revision of principles and calculations from Building Physics

2. Note that individual molecules of air only move forwards and backwards, the energy is passed from one molecule to the next.

3. The black dot shows the variation of pressure at a point
as the wave travels past -- this would be the fluctuation
in pressure that we would hear.
Pressure

4.  f
c = f 
Wave velocity, c
────►
Pressure

5. PRESSURE Pressure is force acting upon a unit area
unit of force -- Newton, N
unit of area -- m2
Pressure, P = F/A in Nm-2
The usual unit for pressure is the Pascal A Pascal (Pa) is the same as 1.0 Nm-2

6. SUMMARY OF THE PROPERTIES OF SOUND
Frequency, f --- Hz (cycles per second)
Velocity, c --- ms-1 (about 330 ms-1)
depends on elasticity and density of air (see booklet)
Wavelength,  --- m
Relationship c = f 
Acoustic Pressure is between Pa (loud)

7. SOUND ENERGY
Although we measure sound waves using the variations of sound pressure, sound can also be thought of as energy.
All sound sources produce a flow of energy
unit of energy -- Joules, J
rate of flow of energy = power --- J/s or Js-1
of course, Js-1 are Watts, W

8. SOUND INTENSITY Defined as the flow of sound energy through a surface 1m2
Intensity at distance r
I = W/4r2
Area of sphere
= 4r2
Source with acoustic power
in Watts, W

9. BELS AND DECIBELS (reasons for using dB)
The range of sound intensities that can be heard is vast.
Threshold of hearing
(1 x Wm-2) or one million, millionth of a Watt per square metre
Threshold of pain
(100 Wm-2) or 100 Watts per square metre
The human ear is not linear
doubling the intensity does not double loudness

10. HOW LOGARITHMS COMPRESS THE RANGE
Number 10x log
1000,000,
Large
Range
Small
Range

11. Decibel Scale
Comparative sound pressures and their equivalent decibel levels
Logarithmic scales are also used in other branches of science

12. A few example sounds Single tone (100 Hz) Single tone (1 kHz)
White Noise (broadband, all frequencies)
Pink Noise (broadband, all frequencies)
Noise
1dB steps (decreasing)
3 dB steps (decreasing)

13. SOUND INTENSITY LEVEL
Once the intensity has been converted into logarithmic form it is referred to as a level
We have
Sound Intensity Level, Li
and also
Sound Pressure Level, Lp
Sound Power Level, Lw

14. Basic Definitions Sound Intensity Level Sound Pressure Level
The 20 is because intensity = pressure squared
Sound Power Level
(energy flow from a sound source)

15. Can we use dB for any quantity?
e.g travelling distance ?
Distance from here to the bar = 0.5 km (the ‘fundamental’ distance?)
Distance to home = 140 km
In decibels, my journey home will be

16. So, the distance from here to Uranus…
… measured in km, is 2.57 billion km
but in dB,
(reference distance to the bar)
… but how far is it if I want to go from here to the bar, then home, then on to Uranus?

17. ADDITION OF DECIBELS
Decibels can not be added directly since decibels are logarithmic units.
Adding 50 dB and 50 dB does not give the expected 100 dB but instead an answer of 53 dB.
In order to add decibels we need to convert them back into energy units, which can be added directly and then reconverted back into decibels.

18. Equations for Manipulating dB’s

19. Some examples of adding decibels
60 dB + 60 dB = 63 dB (the 3 dB rule)
Doubling the intensity is a 3 dB increase
= 70 dB
Ten times the intensity is a 10 dB increase
A 20 dB increase is100 x the intensity
A 30 dB increase is1000 x the intensity
60 dB + 50 dB  60 dB
50 dB is only 1/10 the intensity of 60 dB so the 50 dB has little effect when added to 60 dB

20. Human Hearing and Equal Loudness Contours

21. ‘A’ Weighted Levels
Corrections across the frequency spectrum to ‘model’ the auditory performance of human ears

22. Propagation of Sound Point, Line and Planar Sources
Houses
Point, Line and Planar Sources
Propagation Equations
Air Absorption
The Effects of Wind and Temperature
Diffraction, Reflections and Barriers

23. Geometric Spreading Point sound source of power W I
radiating equally in all directions
(Sphere) I =W/4r2
Lp = Lw - 20 log( r ) dB W r I
Same sound source on the ground
(Hemisphere) I =W/2r2
Lp = Lw -20 log( r ) dB

24. Attenuation with distance
POINT SOURCE
At double the distance
away from a point source
the intensity is only ¼
because the area increases
by x4 as the radius is doubled
L2 = L log ( r2/r1)
L2 is the level at distance 2
L1 is the level at distance 1
r2& r1 are the distances 2&1
6 dB / doubling of distance

25. Attenuation with distance
LINE SOURCE
At double the distance
away from a line source
the intensity is ½ because
the area increases by x2
as the radius is doubled
L2 = L log ( d2/d1)
L2 is the level at distance 2
L1 is the level at distance 1
d2& d1 are the distances 2&1 A 2A d 2d
3 dB / doubling of distance

26. Attenuation with distance
PLANAR SOURCE
Close to the planar source the radiated sound does not spread out so there is no attenuation
Further from the area source the radiated sound starts to wrap around the longest edges – a bit like a line source
Further away still the radiated sound starts to wrap around the all the edges – a bit like a point source
No attenuation dB / doubling dB / doubling

27. Attenuation with distance
Transition from planar – line – point
a & b are the dimensions of the source b a
a/
b/
3 dB/ doubling
6 dB/ doubling Lp
Distance from source

28. Example
The sound pressure level, Lp just in front of a factory façade 10m high by 50m long is 75dBA.
Find the distances when the propagation changes from planar to line & from line to point.
Determine the Lp at 10m and at 50m from the façade
Planar to line = a/π = 10/3.142 = 3.18m
Line to point = b/π = 50/3.142 = 15.91m
So, the level stays constant at 75dBA up to 3.18m then reduces by 3dB every doubling of this distance up to 15.91m and then reduces by 6 dB per double of this distance.
Line source L2 =L1 – 10 lg(d2/d1) dB /doubling
Point source L2 =L1 – 20 lg(d2/d1) dB /doubling

29. At 10m Lp = lg(10/3.18) = 70dBA
To find the level at 50m we first need to find the level at the line-point cut-off at 15.91m
At 15.19m Lp = 75 – 10lg(15.19/3.18) = 68dBA
So, at 50m Lp = 68 – 20lg(50/15.91) = 58 dBA
3.18m
15.19m Lp 75 68 70 58
10m
50m

30. Effect of the Ground Surface
All the basic formulae assume perfectly reflecting ground – a reasonable assumption for hard surfaces such as concrete.
Soft ground – grassland, etc will absorb sound and also change the phase of the reflected sound giving rise to interference between the direct and reflected waves (mostly at low frequencies around 400 Hz)
This is the GROUND EFFECT
Only important over larger distances & receivers close to the ground
Sometimes presented as EXCESS ATTENUATION (i.e. the attenuation that you get in excess of that you would expect from distance alone
(Note that some modern roads have specially designed porous surfaces which can reduce road traffic noise by up to 6 dB for fast moving traffic)

31. The Effect of the Atmosphere
cooler air at higher altitude
Ground level
Shadow zones near ground
NORMAL
LAPSE RATE
TEMPERATURE EFFECTS
Focusing of the sound
warmer air at higher altitude
TEMPERATURE
INVERSION

32. The Effect of the Atmosphere
AIR ABSORPTION
As sound travels through air some of the energy is
absorbed due to molecular friction. The amount of
absorption depends on the air temperature and humidity.
At low frequencies the attenuation is negligible
(at less than1 dB per 1000 m for frequencies less than 200 Hz)
but at high frequencies can be considerable
(between dB per 1000 m at 8 kHz )
Noise from a distant motorway is heard as a rumble
because the high frequencies have been absorbed
by the atmosphere.

33. The Effect of the Atmosphere
WIND EFFECTS
Velocity Profile
Sound rays ‘bent’ by the wind
Ground level
Height
Shadow
Focusing
The effect of this can be to reduce the sound level by up to 30 dB in the shadow zone
and increase the sound level by 20 dB where focusing occurs.
Also, the turbulence of the atmosphere can also cause scattering even at relatively
low wind speeds. Wind effects are difficult to predict (see ISO – 2)

34. Reflections Sound Source Reflections can increase the
Incident and reflected sound adds together
Sound Source
Reflections can increase the
level by 3 dB (6db for some tones)
Reflection should be avoided
or included in measurements.

35. Barriers Illuminated Zone Shadow Zone Sound Source Barrier
Part of the sound wave is reflected back off the barrier
The sound wave passing over the barrier is diffracted so that the sound can still be heard even though its source can not be seen.

36.   Path difference (δ) = a + b - c b a Receiver c Source r s
Close to source
good attenuation
least intrusion
Mid position
poor attenuation
some intrusion
Close to receiver
very intrusive  
The path difference is always greatest when the barrier is close to the source or
close to the receiver