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SOUND 1
Michael Drolet -- 2005
Home PHYSICS OF SOUND




Our aim is to attain a basic understanding of:
Sound
  • What is sound? 
  • How is it generated?
  • How does it propagate? 
Acoustics
  • effects of boundaries (theatre walls,floor, ceiling) on:
  • propagation 
  • perception (psychoacoustics) 
Audio
  • sound in its electronic form 
  • transducers 
  • processing 
  • transmission 
  • recording 
  • editing 
  • system design 




For our purposes:
Sound is the transmission of vibrations in air  as perceived by the human ear.
Theatre
  • speech 
  • music 
  • sound effects 

Sources of Sound

How is sound generated?
Sound   is generated by a vibrating source as waves of changing pressure.
Human
  • vocal chords 
Musical instruments
  • strings
  • guitar
  • violin
  • membrane
  • gong
  • drum skin
Electro-mechanical
  • loudspeaker diaphragm

How does sound propagate?


Sound travels at a finite speed, dependent on the density of the medium.
Speed of Sound
Medium
Speed (m./sec.)
Speed (ft./sec.)
Speed Factor
air
344
1,130
1
water
1,480
4,854
4.3
concrete
3,400
11,152
9.8
dry wall
6,600 22,304 19.6

Sound  takes a finite time to travel from one point to another.
Travel Time
Distance
Time
1 mile
5 sec.
1 km.
3 sec.
1 foot
.88 msec.
1 metre
3 msec.
1 inch
73 µsec.
1 cm.
30 µsec.

A sound wave has certain properties which define it.
Properties of a Sound Wave
 Property Sound Wave Properties
Frequency
  • number of cycles per second
  • measured in:
    • hertz (Hz)
Period
  • inverse of frequency ( 1 / frequency )
  • measured in:
    • number of seconds (or milliseconds) per cycle
Wavelength
  • distance to complete one cycle ( speed / frequency )
  • measured in:
    • metres or feet
Amplitude
  • intensity of wave
  • measured in:
  • Pascals (pressure)
  • dB-SPL (Sound Pressure Level)
  • volts (electrical)

Range of Human Hearing
Amplitude
Frequency
20µPascals - 20 Pascals
20 Hz to 20 kHz
1,000,000:1
1000:1

Amplitude vs. Frequency
These two waveforms have the same amplitude, but the one on the right has 4 times the period (hence 1/4 the frequency).
Amplitude 2.3 div. p-p
These two waveforms have the same period (hence the same frequency), but the one on the right is 2 times the amplitude.
Period 1.5 div.

The musical equivalent of frequency is pitch.  A higher frequency has a higher pitch. A above middle C has a frequency of 440 Hz.  A doubling of frequency is called and octave.
Frequency and Musical Pitch
Frequency and Pitch


Frequency Ranges of  Musical Instruments
Frequnecy Range of Instruments

 


Lower frequencies have longer wavelengths and periods.
Frequency vs. Period and Wavelength
Frequency
Period
Wavelength
Wavelength
20 Hz
50 msec.
56.4 ft.
 17.2 m.
200 Hz
5 msec.
5 ft. 6 in
1.72 m.
2 kHz
0.5 msec.
6.67 in
17.2 cm.
20 kHz
0.05 msec
.67 in
17.2 mm.

If we made a measuring device for intensity where the smallest division was 1 mm. ;  it would have to be 100 metres wide to accomodate the loudest sound  we can hear.
Sound Pressure
Source
Pressure
(µPascals)
Distance
Threshold of Hearing
20
0.0 mm.
Sound Stage
200
1.0 mm.
Cinema Audience
2,000
10 mm.
Conversation
20,000
10.0 cm.
Noisy Factory
200,000
 1.0 m.
Niagara Falls
2,000,000
 10.0 m.
Threshold of Pain
20,000,000
100.0 m.

We use a logarithmic scale to represent relative intensities.  Each increase of 10 times in intensity is represented by an increase of 20 decibels(dB)  in Sound Pressure Level (SPL).
Sound Pressure Level
 Source
Pressure
(µPascals)
dB - SPL
Threshold of Hearing
20
0
Sound Stage
200
20
Cinema Audience
2,000
40
Conversation
20,000
60
Noisy Factory
200,000
80
Niagara Falls
2,000,000
100
Threshold of Pain
20,000,000
120

Range of Human Hearing
Amplitude
Frequency
µPascals - 20 Pascals
20 Hz to 20 kHz
1,000,000:1
1000:1
120 dB
~10 octaves
 

Steps of 10.
Decibel Scale
Ratio
Log (Ratio)
20 x Log (Ratio)
decibels (dB)
1
0
0
10
1
20
100
2
40
1,000
3
60
10,000
4
80
100,000
5
100
1,000,000
6
120

Smaller steps.
Decibel Scale
Ratio
Log (Ratio)
20 x Log (Ratio)
decibels (dB)
1
0
0
2
.3
6
3
.5
9.5
4
.6
12
5
.7
14
6
.8
16
7
.85
17
8
.9
18
9
.95
19
10
1
20

The ear is not equally sensitive to all frequencies at all levels of intensity.  At low intensities, low frequencies are perceived as being less loud.
Frequency Sensitivity vs. Loudness
Equal Loudness Curves