Science of Sound
Chapter 6

Decibel scales are used to compare two quantities (levels)
ΔL = L
2
- L
1
= 10 log W
2
/W
1 or to compare a level with a reference level
L
W
= 10 log W/W
0
L
W
= Sound power level (in dB)
W = Sound power (in W/m 2 )
Example: What is the sound power level of a loudspeaker with W = 0.1 W?
L
W
= 10 log 0.1/10 -12 = 110 dB
What is the dB gain of an amplifier when the power gain is 400?
400 = 2x2x100, so the dB gain is 3+3+20 = 26 dB
4 The decibel scale (Tracks 8,9,10)

I
I
0
0
-12
2
Example: What is L
I
L
I when I = 10 -4 W/m
= 10 log 10 -4 /10 -12 = 10(8) = 80 dB
2 ?

)
I = W/4πr 2 at r = 1 m:
L
I
= 10 log I/10 -12
= 10 log W/10 -12 – 10 log 4 p
= L
W
- 11

HEMISPHERICAL
FIELD
I = W/2 p r 2 at r = l m
L
I
= L
W
- 8
Note that the intensity I 1/r 2 for both free and hemispherical fields; therefore, L
I decreases 6 dB for each doubling of distance
4 Decibel scale (free-field speech) Track 11

Our ears respond to extremely small pressure fluctuations p
Intensity of a sound wave is proportional to the sound
Pressure squared:
I = p 2 /ρc ρ = density
ρc ≈ 400 c = speed of sound
We define sound pressure level:
L p
= 20 log p/p
(or SPL)
0 p
0
= 2 x 10 -5 Pa (or N/m 2 )

TYPICAL SOUND LEVELS

Example:Two uncorrelated sources of 80 dB each will produce a sound level of
83dB
(Not 160 dB)

MULTIPLE SOURCES
What we really want to add are mean-square average pressures (average values of p 2 )
This is equivalent to adding intensities
Example: 3 sources of 50 dB each
Lp = 10 log [(P
1
2 +P
2
2 +P
3
2 )/P
0
2 ] = 10 log ( I
1
+ I
2
+ I
3
)/ I
0
)
= 10 log I
1
/ I
0
+ 10 log 3 = 50 + 4.8 = 54.8 dB

SOUND PRESSURE and INTENSITY
Sound pressure level is measured with a sound level meter (SLM)
Sound intensity level is more difficult to measure, and it requires more than one microphone
In a free field, however, L
I
≈ L
P

FOUR ATTRIBUTES USED TO DESCRIBE A SOUND:
• Loudness
• Pitch
• Timbre
• Duration
EACH OF THESE DEPENDS ON ONE OR MORE PHYSICAL
PARAMETERS THAT CAN BE MEASURED:
• Sound pressure
• Frequency
• Spectrum
• Duration (measured)
• Envelope
Relating the SUBJECTIVE QUALITIES to the PHYSICAL
PARAMETERS that we can MEASURE OBJECTIVELY
Is an important problem in PSYCHOACOUSTICS

DEPENDENCE OF SUBJECTIVE QUALITIES OF
SOUND ON PHYSICAL PARAMETERS

LOUDNESS LEVEL
Contours of equal loudness are labeled phons
At 1000 Hz, Loudness Level = L p

www.phys.unsw.edu.au/~jw/hearing.html

HOW DOES
LOUDNESS
DEPEND ON
FREQUENCY?
Don’t confuse loudness level
Expressed in phons) with loudness
(expressed in sons)

7 Loudness scaling
(Tracks 19-20)
The reference tone plus the strongest and weakest noise samples
Twenty noise samples
Write down the loudness on a scale where the reference sound is 100

7 Loudness scaling
(Tracks 19-20)
The reference tone plus the strongest and weakest noise samples
Twenty noise samples
Write down the loudness on a scale where the reference sound is 100
Test tone levels were +15,-5,-20, 0,
-10,+20,+5,+10,-15, 0,-10,+15,+20,
-5,+10,-15,-5,-20,+5,+15 dB

LOUDNESS SCALING
7 Loudness scaling (Track 19,20)

LOUDNESS RESPONSE OF THE EAR

DEPENDENCE OF LOUDNESS ON BANDWIDTH
CRITICAL BANDS
3 Critical bands by loudness comparison Track 7
The bandwidth of the test band is increased each time while the amplitude is decreased to keep the power constant. Note when the loudness begins to increase.

DEPENDENCE
OF
LOUDNESS
ON
BANDWIDTH
CRITICAL
BANDS
3 Critical bands by loudness comparison Track 7

LOUDNESS OF COMBINED SOUNDS

JUST NOTICEABLE LEVEL DIFFERENCE

LEVEL INCREMENT NEEDED TO DOUBLE LOUDNESS

RANGE OF FREQUENCY AND INTENSITY
OF THE EAR

MUSICAL DYNAMICS AND LOUDNESS

Count how many steps of the test tone can be heard in each case
9 Asymmetry of masking (Track 22)

Count how many steps of the test tone can be heard in each case
Mpst people hear more steps when the masker is higher in frequency
9 Asymmetry of masking (Track 22)
10 Backward an d forward masking (Tracks 23-25)

HOW DOES
LOUDNESS
DEPEND ON
PARTIAL
MASKING?

HOW DOES LOUDNESS DEPEND ON DURATION?
8 Temporal integration (Track 21)
Noise bands of 1000,300,100,
30,10 , 3 and 1 ms are presented in 8 decreasing steps. Count the number you hear for each duration.

UNUSUALLY RAPID GROWTH OF LOUDNESS
ABOVE A CERTAIN THRESHOLD
GENERALLY ASSOCIATED WITH HEARING LOSS,
BUT NORMAL LISTENERS EXPERIENCE IT FOR
TONES OF VERY HIGH OR VERY LOW FREQUENCY

FOR SOFT SOUNDS (~20dB) BINAURAL
LOUDNESS EXCEEDS MONAURAL LOUDNESS
BY A FACTOR OF 2
( CORRESPONDS TO ΔL = 8dB)
FOR LOUD SOUNDS (~80dB) BINAURAL
LOUDNESS EXCEEDS MONAURAL
LOUDNESS BY A FACTOR ~/.4
( CORRESPONDS TO ΔL = 6dB)
Zwicker & Fastl (1990)

AT LOW LEVELS, INTENSITY CHANGES CAN BE
SIGNALLED BOTH BY CHANGES IN FIRING RATES OF
NEURONS AT THE CENTER OF THE EXCITATION
PATTERN AND BY THE SPREADING OF THE EXCITATION
PATTERN (TO INCLUDE MORE NEURONS)
AT HIGH LEVELS, MOST NEURONS AT THE CENTER OF
THE EXCITATION PATTERN ARE SATURATED, BUT
INTENSITY CHANGES ARE SIGNALLED BY CHANGES
IN FIRING RATES AT THE EDGES.
AN INCREASE IN LEVEL ALSO MAY BE SIGNALLED
BY INCREASED PHASE LOCKING TO THE TONE WHICH
RESULTS IN TEMPORAL REGULARITY OF
NEURAL FIRINGS

ASSIGNMENT FOR WEDESDAY
Exercises 2,4,5,6 (p. 119)
Plot loudness scaling curve (log of loudness rating
vs sound level)
Re-read Chapter 7