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

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

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

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

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

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 0 - 1.0 Pa (loud)

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

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

BELS AND DECIBELS (reasons for using dB) The range of sound intensities that can be heard is vast. Threshold of hearing (1 x 10-12 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

HOW LOGARITHMS COMPRESS THE RANGE Number 10x log 1 100 0 10 101 1 100 102 2 1000 103 3 1000,000,000 109 9 Large Range Small Range

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

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)

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

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

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

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?

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.

Equations for Manipulating dB’s

Some examples of adding decibels 60 dB + 60 dB = 63 dB (the 3 dB rule) Doubling the intensity is a 3 dB increase 60+60+60+60+60+60+60+60+60+60 = 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

Human Hearing and Equal Loudness Contours

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

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

Geometric Spreading Point sound source of power W I radiating equally in all directions (Sphere) I =W/4r2 Lp = Lw - 20 log( r ) - 11 dB W r I Same sound source on the ground (Hemisphere) I =W/2r2 Lp = Lw -20 log( r ) - 8 dB

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 = L1 - 20 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

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 = L1 - 10 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

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 3 dB / doubling 6 dB / doubling

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

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) --- 3 dB /doubling Point source L2 =L1 – 20 lg(d2/d1) --- 6 dB /doubling

At 10m Lp = 75 - 10lg(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

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)

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

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 50 - 200 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.

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 9613 – 2)

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.

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.

  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