analysis of of sound

1. MUSICAL ACOUSTICS
SOUND
PRESSURE,
POWER AND
LOUDNESS
Science of Sound
Chapter 6

4. FREE FIELD
I = W/4πr2
at r = 1 m:
LI = 10 log I/10-12
= 10 log W/10-12 – 10 log 4p
= LW - 11

5. HEMISPHERICAL
FIELD
I = W/2pr2
at r = l m
LI = LW - 8
Note that the intensity I α 1/r2 for both free and
hemispherical fields;
therefore, LI decreases 6 dB for each doubling of distance

6. SOUND PRESSURE LEVEL
Our ears respond to extremely small pressure
fluctuations p
Intensity of a sound wave is proportional to the sound
Pressure squared:
ρc ≈ 400
I = p2 /ρc ρ = density (1.21kg/m3)
c = speed of sound (343 m/s)
We define sound pressure level:
Lp = 20 log p/p0 p0 = 2 x 10-5 Pa (or N/m2)
(or SPL)

7. TYPICAL SOUND LEVELS

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

9. MULTIPLE SOURCES
What we really want to add are mean-square
average pressures (average values of p2)
This is equivalent to adding intensities
Example: 3 sources of 50 dB each
Lp = 10 log [(P12+P22+P32)/P02] = 10 log (I1 + I2 + I3)/ I0)
= 10 log I1/I0 + 10 log 3 = 50 + 4.8 = 54.8 dB

10. 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, LI ≈ LP

11. 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

12. DEPENDENCE OF SUBJECTIVE QUALITIES OF
SOUND ON PHYSICAL PARAMETERS

13. LOUDNESS LEVEL
Contours of equal loudness are labeled phons
At 1000 Hz, Loudness Level = Lp

14. PLOT YOUR OWN FREQUENCY RESPONSE
ASSIGNMENT: Plot your own frequency
response curves by using
www.phys.unsw.edu.au/~jw/hearing.html

16. HOW DOES
LOUDNESS
DEPEND ON
FREQUENCY?

17. LOUDNESS SCALING

18. LOUDNESS RESPONSE OF THE EAR

19. LOUDNESS OF COMPLEX TONES
Loudness depends mainly on
SOUND PRESSURE.
but it also depends on FREQUENCY,
SPECTRUM and DURATION

20. DEPENDENCE
OF
LOUDNESS
ON
BANDWIDTH
CRITICAL
BANDS

21. LOUDNESS OF COMBINED SOUNDS

22. JUST NOTICEABLE LEVEL DIFFERENCE

23. LEVEL INCREMENT NEEDED TO DOUBLE LOUDNESS

24. RANGE OF FREQUENCY AND INTENSITY
OF THE EAR

25. MUSICAL DYNAMICS AND LOUDNESS

27. HOW DOES
LOUDNESS
DEPEND ON
PARTIAL
MASKING?

28. HOW DOES LOUDNESS DEPEND ON DURATION?

29. LOUDNESS RECRUITMENT
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

30. MONAURAL vs BINAURAL LOUDNESS
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)

31. INTENSITY DISCRIMINATION AND CODING
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