Propagation of Sound and Vibration Hans Bodén

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

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

Sound Propagation in Rooms

Reverberation Time The time it takes the sound pressure to decay 10-6 (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

Equivalent Absorption Area Units: m2 Sabine or m2S

Measurement of Reverberation Time

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

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

Sound Field in Rooms

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

Directivity Index

Echo Radius Distance/ echo radius

Optimum Reverberation Time Catholic churches Concert halls Conference halls Sound studios

Control the Reverberation Sound absorbing baffles Sound absorbing suspended roof Traverse

Sound Transmission through Walls Transmission factor Sound reduction index

Sound transmission between two rooms

Single Wall Sound Reduction Index

Building Acoustics Transmission Paths, Flanking Transmission

Deterioration due to slits

Room Acoustics

Room Reflections

Ventilation Systems

Exhaust System

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

OUTDOOR SOUND PROPAGATION: FACTORS INFLUENCING Sound Source ? Receiver

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

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

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

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

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

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

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

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

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

Enclosures

Noise control of a compressor using a sound absorbing enclosure

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 15-20 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

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.

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