1. Propagation of Sound and Vibration
Hans Bodén

2. CONTENTS Wave propagation in air Room acoustics
Sound propagation in ducts
Outdoor sound propagation

3. Wave Propagation in Fluids
Direction of propagation
Wavelength l
Pressure p / p0
Compressed
Rarified

4. Sound Propagation in Rooms

5. Reverberation Time
The time it takes the sound pressure to decay (60 dB) times the original value.
Sabine’s Formula:
T is reverberation time
V is volume of the room
A is the equivalent absorption area of the room
a is the absorption coefficient

6. Equivalent Absorption Area
Units: m2 Sabine or m2S

7. Measurement of Reverberation Time

8. Typical absorption factors for material
Description
Absorption factor ad
125 Hz
250 Hz
500 Hz
1 kHz
2 kHz
4 kHz
Tile
0.03
0.04
0.05
0.07
Concrete
Untreated
0.36
0.44
0.31
0.29
0.39
0.25
Painted
0.10
0.06
0.09
0.08
Plywood
1 cm
0.28
0.22
0.17
0.11
Window glass
0.35
0.18
0.12
Draperies
Pressed thin against wall
0.24
Thick, drawn up
0.14
0.55
0.72
0.70
0.65
Concrete floor
0.01
0.02
with linoleum layer
with thick mat
0.37
0.66
Wood floor
0.15
Ceiling
Gypsum slabs
Plywood 1cm

9. Added absorption area [m2S]
Typical absorption factors
Object
Description
Added absorption area [m2S]
125 Hz
250 Hz
500 Hz
1 kHz
2 kHz
4 kHz
Standing human
With coat
0.17
0.41
0.91
1.30
1.43
1.47
Without coat
0.12
0.24
0.59
0.98
1.13
1.12
Student, incl seat
Sitting
0.20
0.28
0.31
0.37
0.42
Chair
Cushioned
0.55
0.86
0.83
0.87
0.90

10. Sound Field in Rooms

11. Sound Field in Rooms ptot = total sound pressure
pdir = direct sound pressure
pd = diffuse sound pressure
Wdir = power sent out by the source
G = directivity index
A’ is the room constant

12. Directivity Index

13. Echo Radius
Distance/ echo radius

15. Optimum Reverberation Time
Catholic churches
Concert halls
Conference halls
Sound studios

16. Control the Reverberation
Sound absorbing baffles
Sound absorbing suspended roof
Traverse

17. Sound Transmission through Walls
Transmission factor
Sound reduction index

18. Sound transmission between two rooms

19. Single Wall Sound Reduction Index

20. Building Acoustics Transmission Paths, Flanking Transmission

21. Deterioration due to slits

22. Room Acoustics

23. Room Reflections

26. Ventilation Systems

27. Exhaust System

28. Reduce the Noise emitted form the engine
An engine is a variable noise source with a wide range of frequencies, amplitudes, flow rates, and gas temperatures
A muffler is a fixed, passive filter that is tuned for optimum noise control

29. OUTDOOR SOUND PROPAGATION: FACTORS INFLUENCING
Sound Source ?
Receiver

30. OUTDOOR SOUND PROPAGATION: FACTORS INFLUENCING
GEOMETRIC SPREADING
Due to the expansion of the wave fronts
Frequency independence
Dependent on the source, the distance and the propagation field
Geometric
Spreading
Sound Source
Receiver

31. OUTDOOR SOUND PROPAGATION: FACTORS INFLUENCING
Atmospheric
Absorption
ATMOSPHERIC ABSORPTION
Dissipation of acoustic energy into heat.
Proportional to the distance
Depends on frequency, humidity and temperature
Geometric
Spreading
Sound Source
Receiver

32. OUTDOOR SOUND PROPAGATION: FACTORS INFLUENCING
Atmospheric
Absorption
Geometric
Spreading
Sound Source
Receiver
Ground

33. OUTDOOR SOUND PROPAGATION: FACTORS INFLUENCING
TOPOLOGY
Noise barriers, hills, building etc.
Create reflections, diffractions and shadow zones
Effects greater if source closer to the ground
Geometric
Spreading
Sound Source
Topology
Receiver

34. OUTDOOR SOUND PROPAGATION: FACTORS INFLUENCING
IMPEDANCE
Attenuation of acoustic energy due to the losses at the boundaries
Depends on the nature of the ground and the angle of incidence of the waves
Atmospheric
Absorption
Ground impedance
Geometric
Spreading
Sound Source
Topology
Receiver

35. OUTDOOR SOUND PROPAGATION: FACTORS INFLUENCING
TEMPERATURE GRADIENTS
Atmospheric
Absorption
Temperature
decreases with
height
Sound Source
Ground
Shadow
Zone
increases with
Temperature
Ground impedance
Sound Source
Topology
Receiver

36. OUTDOOR SOUND PROPAGATION: FACTORS INFLUENCING
WIND GRADIENTS
Temperature
Wind
Sound
Source
Wind Direction
Ground
Shadow
zone
Ground impedance
Geometric
Spreading
Sound Source
Topology
Receiver

37. OUTDOOR SOUND PROPAGATION: FACTORS INFLUENCING
TURBULENCE
Local variations of temperature, wind velocity, etc.
create
fluctuations of sound waves
which induce
scattering of the sound energy.
Depends on distance, frequency and amplitude of the variations
Atmospheric
Absorption
Wind
Turbulence
Temperature
Geometric
Spreading
Sound Source
Topology
Receiver
Ground impedance

38. OUTDOOR SOUND PROPAGATION: FACTORS INFLUENCING
Atmospheric
Absorption
Temperature
Wind
Turbulence
Ground impedance
Geometric
Spreading
Sound Source
Topology
Receiver

39. Enclosures

40. Noise control of a compressor using a sound absorbing enclosure

41. Design Rules for Enclosures
Use a dense material, such as sheet metal or plasterboard, on the outside.
Use a sound absorbant material on the inside. A single hood of this type can reduce the sound level by dB(A).
Install mufflers on cooling air openings during enclosure of electric motors, etc.
Install easily opened doors as required for machine adjustment and service

42. Enclosure of a hydraulic system require muffled ventilation openings
Enclosure of a hydraulic system require muffled ventilation openings. Electric motors release both sound and heat, as do the pump and the oil tank.

43. Noise control of sand blasting operation using lead-rubber draping.