Building Environment 1: Acoustics

David Coley (6E2.22, d.a.coley@bath.ac.uk)

The uproar of humanity is intolerable and the confusion

is such that it is not possible to sleep

Epic of Gilgamesh, Mesopotamia, ~3000 BC

Speech communication

Music

Environmental conditions (and potential threats)

Sound source detection (possible in 3D)

Excessive noise (causing sleep disturbance perhaps)

What is the significance of sound in your life?

Buildings have an impact on all of these

Dont just think offices

We are all different

What do we feel?

100 dB

1m

1s

1x10-11C

Thinking in numbers

I have two children, one of which is a girl.

What is the probability the other is a boy?

Can you hear at the back?

American school ca. 1917!

Acoustics of new school buildings in Britain is now carefully controlled.

Absorbing material included for nearly all spaces used by students

Sound insulation between

dwellings (semi-detached,

terraced housing or flats/

apartments)

Good sound insulation

required for party walls

and in flats, party floors

as well.

Lines of party walls

Acoustic performance of party walls and floors

is covered by Building Regulations

Acoustics of large spaces

Paddington Station

A noisy environment

Terminal building at Bristol Airport

A much calmer space with sound

absorbing material on the ceiling

Acoustics of auditoria

Royal Festival Hall,

London (1951)

2900 seats

The Egg Theatre, Bath

150 seats

Wave patterns in two dimensions

Sound waves

Sound is a wave motion involving movement of air particles

Wave behaviour is most easily observed on water surfaces

(and that is where the word wave comes from)

Different types of wave motion exhibit similar characteristics

Waves involve energy travelling through a medium which

returns to its original condition after the wave has passed

There are basically three types of wave:

Longitudinal - longitudinal wave on a string

acoustic waves

Transverse lateral wave on a string

electromagnetic waves

Combined - surface wave on water

Types of wave

Longitudinal

Transverse

Combined

Any vibrating surface will generate sound. In this case, a piston produces sound

that travels along the tube at a fixed frequency

Speed of sound, c = 331.4 (273 + toC)/273

A fundamental wave equation:

Speed of wave = Frequency x Wavelength

Frequency is measured in cycles/second or Hertz (Hz)

Light (colour green)

Speed of light = 3.108 m/s

= 5.1014 Hz x 6.10-7 m

Range of visual wavelength = 4 to 7.5.10-7 m

Sound (middle C)

Speed of sound = 343 m/s at 20oC

= 262 Hz x 1.31 m

Range of audible wavelength = 17 m to 17 mm

Range of audible frequency = 20 to 20,000 Hz

Speed different in different materials

Size of rooms = wave length of some

sound

20 50 100 200 500 1k 2k 5k 10k 20k

Frequency (Hz)

Piccolo

Bassoon

Violin

Double bass

Soprano

Bass

Piano

Fundamental frequencies of different musical instruments

Frequency and wavelength are related

Note that frequency scale is logarithmic, piano keyboard is correctly scaled

Outer ear

Analogue/digital convertor

The ear responds to acoustic pressure. Sound is transmitted to the

brain as a series of nerve pulses

The ear Hearing and balance

The basilar membrane is around 35mm in humans and contains around 15,000

sensory hairs

Most neurons in the auditory pathway show a preferred frequency, with

frequency encoded by which neurons are active and loudness by the rate they

are responding.

The human ear has a sensitivity less than one billionth of atmospheric pressure,

and equal to 10-16 watts/cm2 , and pain doesnt set in until 13 orders of

magnitude later, i.e. 10-3watts/cm2. To put this range into perspective, human

skin has a thermal output of 80W/1.8m2 = 44W/m2; thirteen orders of magnitude

greater would be 44x1013W/m2 and is over 20 million times greater than the

output per m2 of the sun.

Source: http://hyperphysics.phy-astr.gsu.edu/hbase/sound/ear.html

A pure tone represented as a time variation and as a spectrum (single frequency)

Spectrum of road traffic noise, which is a mixture of lots of frequencies

Divide up the audible frequency range (20 20,000 Hz) into octave bands

(like a cake)

Ignore 16 and 32Hz octaves, also ignore 8 and 16kHz octaves, note that spectrum

decreases as frequency increases

Octave

band

frequencies

important range

The magnitude of sound?

A sound wave involves changes of density, temperature and pressure,

the transport of energy as well as movement of air particles.

It proves most convenient to deal mostly with acoustic pressure

Acoustic pressure is super-imposed on atmospheric pressure

(acoustic pressure is normally very much smaller than atmospheric pressure)

An advantage of using pressure is that it is a scalar quantity without direction

The effects of high noise levels depend on duration

and intensity: hearing loss from poor acoustics in

buildings is possible.

Not just an issue of audible vibrations: Buildings that

vibrate excessively, possibly in response to the wind,

can cause motion sickness because of inconsistent

sensory information.

How loud is it, really?

Answer: the decibel

The problem: acoustic pressure varies between 2.10-5 N/m2 and 20 N/m2

with a range of 1:1 million from threshold of hearing to pain threshold

Sound intensity varies between 10-12 and 1 W/m2 (watts per sq. metre)

(intensity relates to sound energy, which is proportional to pressure2)

Relevant question: how does the ear handle this?

Answer: logarithmically

changes with the same ratio are judged as of equal magnitude

Example: a doubling of pressure (= 6 dB change), doubling of energy (=3

dB change)

Intensity range of 10-12 1 W/m2 is reduced to 0 120 dB

Where Pref is the reference sound pressure and Prms is the sound

pressure being measured.

The commonly used reference sound pressure in air is 20 micro

pascal which is considered the threshold of human hearing (roughly

the sound of a mosquito flying 3m away).

Most sound measurements made relative to this level, i.e. 1 pascal

equals 49 dB.

What is the loudest possible noise (in air)?

Why is it a decibel?

Intensity range of 10-12 1 W/m2 is reduced to 0 120 dB

This range is also 0 12 bels, named after Alexander Bell,

the inventor of the telephone

Since 0.1 bels is the smallest interval we can detect, a range of 0 12

is too small, therefore multiply by 10 to get deci-bels

Decibels are abbreviated to dB

Since sound intensity is proportional to acoustic pressure squared, the

range of pressure from 2.10-5 N/m2 to 20 N/m2 is also represented by

0 120 dB.

Richter scale for earthquakes (example of a logarithmic scale)

Description Richter Effects

value

Light 4 Noticeable shaking of indoor items. Significant damage unlikely.

Moderate 5 Major damage to poorly constructed buildings

Strong 6 Can be destructive in areas up to 100 miles across.

A 1 unit increase corresponds to about 32 times the energy released

The Richter scale is thus a logarithmic scale

Sound pressure levels of common noises

dBA

THRESHOLD OF PAIN 120

Disco noise 105

Full orchestra, loud passage 95

Working environment without ear defenders (8-hour day)

Sound pressure levels of common noises

dBA

THRESHOLD OF PAIN 120

Disco noise 105

Full orchestra, loud passage 95

Working environment without ear defenders (8-hour day)

The decibel can be used as an absolute measure of how loud sound is,

with values between 0 and 120 dB

It can also be used as a relative measure, say for a car silencer

Silencer

Acoustic efficiency

15 dB

Note: a doubling of intensity (energy) = +3 dB

Threshold of hearing and frequency

Music and speech: frequency and level

Preliminary conclusions

The major acoustic variables are frequency and sound level

The audible frequency range is 20 20,000 Hz. The ear uses a fundamental

interval of an octave, a doubling of frequency, which implies that it hears

frequency logarithmically

Hearing of amplitude is also logarithmic, hence the decibel

The decibel can be used as an absolute measure of how loud sound is,

with values between 0 and 120 dB

It can also be used as a relative measure, say for a car silencer, or insulation

provided by a wall

Our ears do NOT hear different frequencies with the same sensitivity