SOUND PRESSURE,

POWER AND LOUDNESS

MUSICAL ACOUSTICS

Science of SoundChapter 6

DECIBEL SCALES

Decibel scales are used to compare two quantities (levels) ΔL = L 2 - L 1 = 10 log W2/W1

or to compare a level with a reference level LW = 10 log W/W0 LW = Sound power level (in dB) W = Sound power (in W/m2)

Example: What is the sound power level of a loudspeaker with W = 0.1 W? LW= 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)

Sound intensity level (LI or SIL)

LI = 10 log I/I0 where I0 = 10 -12 W/m2

Example: What is LI when I = 10-4 W/m2 ? LI = 10 log 10-4/10-12 = 10(8) = 80 dB

FREE FIELDI = W/4πr2

at r = 1 m:

LI = 10 log I/10-12

= 10 log W/10-12 – 10 log 4

= LW - 11

)

HEMISPHERICALFIELD

I = W/2r2

at r = l m LI = LW - 8

Note that the intensity I 1/r2 for both free and

hemispherical fields; therefore, LI decreases 6 dB for each doubling of distance

4 Decibel scale (free-field speech) Track 11

SOUND PRESSURE LEVEL

Our ears respond to extremely small pressure fluctuations p

Intensity of a sound wave is proportional to the sound Pressure squared: I = p2 /ρc ρ = density ρc ≈ 400 c = speed of sound

We define sound pressure level:

Lp = 20 log p/p0 p0 = 2 x 10-5 Pa (or N/m2)(or SPL)

TYPICAL SOUND LEVELS

MULTIPLE SOURCES

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-squareaverage pressures (average values of p2)This is equivalent to adding intensities

Example: 3 sources of 50 dB each

Lp = 10 log [(P12+P2

2+P32)/P0

2] = 10 log (I1 + I2 + I3)/ I0)= 10 log I1/I0 + 10 log 3 = 50 + 4.8 = 54.8 dB

SOUND PRESSURE and INTENSITYSound pressure level is measured with a sound level meter (SLM)Sound intensity level is more difficult to measure, and it requiresmore than one microphoneIn a free field, however, LI ≈ LP

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 OBJECTIVELYIs 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 = Lp

PLOT YOUR OWN FREQUENCY RESPONSE

ASSIGNMENT: Plot your own frequency response curves by using

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

HOW DOES LOUDNESS DEPEND ON

FREQUENCY?

Don’t confuse loudness levelExpressed 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 samplesWrite 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 samplesWrite 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

LOUDNESS OF COMPLEX TONES

Loudness depends mainly on SOUND PRESSURE.

but it also depends on FREQUENCY, SPECTRUM and DURATION

DEPENDENCE OF LOUDNESS ON BANDWIDTHCRITICAL 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

9 Asymmetry of masking (Track 22)

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

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.

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

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) BINAURALLOUDNESS EXCEEDS MONAURAL

LOUDNESS BY A FACTOR ~/.4

(CORRESPONDS TO ΔL = 6dB)

Zwicker & Fastl (1990)

INTENSITY DISCRIMINATION AND CODING

AT LOW LEVELS, INTENSITY CHANGES CAN BESIGNALLED BOTH BY CHANGES IN FIRING RATES OF

NEURONS AT THE CENTER OF THE EXCITATIONPATTERN 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 CHANGESIN 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