Musical Sounds Physical Science101 Chapter twenty Amanda Hyer.

Musical SoundsMusical SoundsMusical SoundsMusical Sounds

Physical Science101Chapter twenty

Amanda Hyer

Noise0.08839871 -0.2194841 0.42826439 0.77400521 -0.9591889 -0.99590410.94544515 0.04418245 -0.0882786 -0.1758679 -0.7732412 -2.02377220.6832397 0.3047532 -0.580513 -0.9453666 0.08947961 1.81188258-0.3878094 0.54397052 -0.912896 -0.745274 0.8738841 2.30358279-0.9997558 0.74507295 -0.993902 0.21918997 0.89342866 -1.233302-0.4281554 0.89396965 -0.8012248 0.95884728 0.13100707 1.586563990.65031074 0.98022773 -0.3879206 0.71508718 -0.7460774 0.334805190.95891572 0.99780327 0.13220235 -0.262084 -0.9701637 1.340707010.13232187 0.94546479 0.61592173 -0.9704553 -0.3451221 2.11569096-0.8509194 0.82687954 0.9300395 -0.6835038 0.58198476 2.49203002-0.8268117 0.65035654 0.98805951 0.30446608 0.99971424 2.67209930.17610529 0.42826439 0.77400521 0.98016804 0.54245198 2.838453010.97054255 0.17616464 0.3468191 0.65058549 -0.389587 4.699134680.61601671 -0.0882786 -0.1758679 -0.3462536 -0.9806431 -1.8560397-0.4677718 -0.3465364 -0.6501275 -0.9879664 -0.7133993 -2.7922646-0.9977953 -0.580513 -0.9453666 -0.6163966 0.17824135 -1.0536968-0.3465929 -0.7738143 -0.9802873 0.38736481 0.91387776 0.13318650.71491859 -0.912896 -0.745274 0.9938353 0.84965011 3.477560160.9300838 -0.988013 -0.3050403 0.5810038 0.04177313 1.003309690.04418245 -0.993902 0.21918997 -0.4277195 -0.8026654 -2.1659071-0.8940237 -0.9301502 0.68306359 -0.9977632 -0.9445776 -4.8163028-0.7738525 -0.8012248 0.95884728 -0.5444763 -0.2597559 1.209919190.26243303 -0.6161592 0.97060062 0.46723886 0.65241501 4.80134132

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MusicMusicMusicMusic50 100 2000 -0.2531828 -0.2619892 -0.515172

-0.9589243 -0.0221213 0.02651961 -0.954526-0.5440211 0.29030559 0.28363355 0.029918030.65028784 -0.465053 0.20497191 0.390206780.91294525 0.49011983 -0.1163428 1.28672225-0.1323518 -0.3574382 -0.2999268 -0.7897167-0.9880316 0.10971263 -0.1284466 -1.0067656-0.4281827 0.17332473 0.19509322 -0.05976470.74511316 -0.4005763 0.28767472 0.632211560.85090352 0.49889964 0.03969656 1.38949973-0.2623749 -0.4366486 -0.2552758 -0.9542993-0.9997552 0.23385926 -0.2480435 -1.0139394-0.3048106 0.04419936 0.05283159 -0.20777970.82682868 -0.3080321 0.29116276 0.809959340.77389068 0.47272258 0.18480501 1.43141827-0.3877816 -0.485264 -0.1403315 -1.0133772-0.9938887 0.34161985 -0.2993386 -0.9516074-0.1760756 -0.088023 -0.1039779 -0.36807650.89399666 -0.1939047 0.21447558 0.914567530.68326171 0.41342282 0.27902514 1.37570967-0.5063656 -0.4998779 0.01325473 -0.9929888-0.9705353 0.42544384 -0.2682071 -0.8132985-0.0442427 -0.2140777 -0.2321557 -0.4904761

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PitchPitchPitchPitch1 0 04 50 50

0 0 -0 -0 00.25 0.84147098 -0 -0 0.841470980.5 0.90929743 -0 -0 0.909297430.75 0.14112001 -0 -0 0.14112001

1 -0.7568025 -0 -0 -0.75680251.25 -0.9589243 -0 -0 -0.95892431.5 -0.2794155 -0 -0 -0.27941551.75 0.6569866 -0 -0 0.6569866

2 0.98935825 -0 -0 0.989358252.25 0.41211849 -0 -0 0.412118492.5 -0.5440211 -0 -0 -0.54402112.75 -0.9999902 -0 -0 -0.9999902

3 -0.5365729 -0 -0 -0.53657293.25 0.42016704 -0 -0 0.420167043.5 0.99060736 -0 -0 0.990607363.75 0.65028784 -0 -0 0.65028784

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0.25 0.24740396 -0 -0 0.247403960.5 0.47942554 -0 -0 0.479425540.75 0.68163876 -0 -0 0.68163876

1 0.84147098 -0 -0 0.841470981.25 0.94898462 -0 -0 0.948984621.5 0.99749499 -0 -0 0.997494991.75 0.98398595 -0 -0 0.98398595

2 0.90929743 -0 -0 0.909297432.25 0.7780732 -0 -0 0.77807322.5 0.59847214 -0 -0 0.598472142.75 0.38166099 -0 -0 0.38166099

3 0.14112001 -0 -0 0.141120013.25 -0.1081951 -0 -0 -0.10819513.5 -0.3507832 -0 -0 -0.35078323.75 -0.5715613 -0 -0 -0.5715613

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High

Low

Intensity LoudnessIntensity LoudnessIntensity LoudnessIntensity Loudness0.25 0.24740396 -0 -0 0.247403960.5 0.47942554 -0 -0 0.479425540.75 0.68163876 -0 -0 0.68163876

1 0.84147098 -0 -0 0.841470981.25 0.94898462 -0 -0 0.948984621.5 0.99749499 -0 -0 0.997494991.75 0.98398595 -0 -0 0.98398595

2 0.90929743 -0 -0 0.909297432.25 0.7780732 -0 -0 0.77807322.5 0.59847214 -0 -0 0.598472142.75 0.38166099 -0 -0 0.38166099

3 0.14112001 -0 -0 0.141120013.25 -0.1081951 -0 -0 -0.1081951

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0.25 0.74221188 -0 -0 0.742211880.5 1.43827662 -0 -0 1.438276620.75 2.04491628 -0 -0 2.04491628

1 2.52441295 -0 -0 2.524412951.25 2.84695386 -0 -0 2.846953861.5 2.99248496 -0 -0 2.992484961.75 2.95195784 -0 -0 2.95195784

2 2.72789228 -0 -0 2.727892282.25 2.33421959 -0 -0 2.334219592.5 1.79541643 -0 -0 1.795416432.75 1.14498298 -0 -0 1.14498298

3 0.42336002 -0 -0 0.423360023.25 -0.3245854 -0 -0 -0.3245854

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Soft

Loud

Sound IntensitySound Intensity

I J / s / m2 J / (sm2) W / m2

I2 4R22 I14R1

2

I 1R2

Decibel Sound LevelDecibel Sound LevelDecibel Sound LevelDecibel Sound LevelSource of Sound Intensity (W/m^2) Sound Level dBJet at 30 m 1E+02 140

1E+00 120Disco Music 1E-01 110

1E-02 100Riveter 1E-03 90

1E-04 801E-05 70

Busy Street traffic 1E-06 601E-07 50

Quiet Radio 1E-08 401E-09 30

Whisper 1E-10 201E-11 10

Threshold of Hearing 1E-12 0

Decibel Sound LevelDecibel Sound LevelDecibel Sound LevelDecibel Sound Level

log10x x

decibel 10 logIntensity

10 12

ExerciseExerciseExerciseExercise What is decibel level of a sound that is 1000

times louder than the threshold of human hearing?

Given: Intensity/10-12=1000=103

Wanted: decibel level Solution: dB=10log(Intensity/10-12) dB=10log(103) = 30 dB

ExerciseExerciseExerciseExercise What is decibel level of a sound that is

10,000 times louder than a sound of 50 dB? Given: 50 dB=dB1 and Int2 =10,000 Int1 Wanted: dB2 Solution: Int1=100,000 (10-12) Int2=10,000*100,000 (10-12)= 109(10-12) dB2=10log(109) = 90 dB

it’s actually easyit’s actually easyit’s actually easyit’s actually easy intensity 10 (101) louder 10 dB higher intensity 100 (102) louder 20 dB higher intensity 1000 (103) louder 30 dB higher intensity 10,000 (104) louder 40 dB higher intensity 1,000,000 (106) louder 60 dB

higher

ExerciseExerciseExerciseExercise What is decibel level of a sound that is 1000

times louder than a sound of 70 dB? Given: 70 dB=dB1 and Int2 =1000 Int1 Wanted: dB2 Solution: dB2 is 30 dB higher dB2=70+30 dB=100 dB

QualityQuality

The quality of sound from a musical instrument depends on the number of higher harmonics included with the fundamental frequency.

Quality (a pure tone)Quality (a pure tone)

10 20 30 40 50 60 700 0 0 0 0 0 0 0

0.19866933 0 0 0 0 0 0 0.198669330.38941834 0 0 0 0 0 0 0.389418340.56464247 0 0 0 0 -0 -0 0.564642470.71735609 0 0 -0 -0 -0 -0 0.717356090.84147098 0 0 -0 -0 -0 0 0.841470980.93203909 0 -0 -0 -0 0 0 0.932039090.98544973 0 -0 -0 0 0 -0 0.985449730.9995736 -0 -0 0 0 -0 -0 0.99957360.97384763 -0 -0 0 0 -0 0 0.973847630.90929743 -0 -0 0 -0 -0 0 0.909297430.8084964 -0 0 0 -0 0 0 0.80849640.67546318 -0 0 -0 -0 0 -0 0.675463180.51550137 -0 0 -0 0 0 -0 0.515501370.33498815 -0 0 -0 0 -0 0 0.334988150.14112001 -0 0 -0 0 -0 0 0.14112001-0.0583741 0 -0 0 -0 0 -0 -0.0583741-0.2555411 0 -0 0 -0 0 -0 -0.2555411-0.4425204 0 -0 0 -0 0 0 -0.4425204-0.6118579 0 -0 0 0 -0 0 -0.6118579-0.7568025 0 -0 -0 0 -0 0 -0.7568025-0.8715758 0 0 -0 0 0 -0 -0.8715758

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Quality (1, .4, 0, .2)Quality (1, .4, 0, .2)0 0 0 0 0 0 0

0.02 0.19866933 0.15576734 0 0.14347122 0 00.04 0.38941834 0.28694244 0 0.19991472 0 00.06 0.56464247 0.37281563 0 0.13509264 0 -00.08 0.71735609 0.39982944 0 -0.0116748 -0 -00.1 0.84147098 0.36371897 0 -0.1513605 -0 -00.12 0.93203909 0.27018527 -0 -0.1992329 -0 00.14 0.98544973 0.13399526 -0 -0.1262533 0 00.16 0.9995736 -0.0233497 -0 0.02330984 0 -00.18 0.97384763 -0.1770082 -0 0.15873357 0 -00.2 0.90929743 -0.302721 -0 0.19787165 -0 -00.22 0.8084964 -0.3806408 0 0.11698344 -0 00.24 0.67546318 -0.3984658 0 -0.0348654 -0 00.26 0.51550137 -0.3533819 0 -0.1655653 0 00.28 0.33498815 -0.2525067 0 -0.1958355 0 -00.3 0.14112001 -0.1117662 0 -0.1073146 0 -00.32 -0.0583741 0.04661968 -0 0.04630197 -0 00.34 -0.2555411 0.19764534 -0 0.17183236 -0 00.36 -0.4425204 0.31746715 -0 0.19313156 -0 00.38 -0.6118579 0.38716787 -0 0.09727974 0 -00.4 -0.7568025 0.3957433 -0 -0.0575807 0 -00.42 -0.8715758 0.34183956 0 -0.1775134 0 00.44 -0.9516021 0.23396688 0 -0.1897689 -0 0

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Quality (1, 0, 0, .3, 0, 0, .5)Quality (1, 0, 0, .3, 0, 0, .5)

0 0 0 0 0 0 00.02 0.19866933 0 0 0.21520683 0 00.04 0.38941834 0 0 0.29987208 0 00.06 0.56464247 0 0 0.20263895 0 -00.08 0.71735609 0 0 -0.0175122 -0 -00.1 0.84147098 0 0 -0.2270407 -0 -00.12 0.93203909 0 -0 -0.2988494 -0 00.14 0.98544973 0 -0 -0.18938 0 00.16 0.9995736 -0 -0 0.03496476 0 -00.18 0.97384763 -0 -0 0.23810036 0 -00.2 0.90929743 -0 -0 0.29680747 -0 -00.22 0.8084964 -0 0 0.17547516 -0 00.24 0.67546318 -0 0 -0.052298 -0 00.26 0.51550137 -0 0 -0.2483479 0 00.28 0.33498815 -0 0 -0.2937533 0 -00.3 0.14112001 -0 0 -0.1609719 0 -00.32 -0.0583741 0 -0 0.06945295 -0 00.34 -0.2555411 0 -0 0.25774854 -0 00.36 -0.4425204 0 -0 0.28969733 -0 00.38 -0.6118579 0 -0 0.14591961 0 -00.4 -0.7568025 0 -0 -0.086371 0 -00.42 -0.8715758 0 0 -0.2662701 0 00.44 -0.9516021 0 0 -0.2846533 -0 0

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FourierFourier

10 20 30 40 50 60 700 0 0 0 0 0 0 0

0.19866933 0 0 0 0 0 0 0.198669330.38941834 0 0 0 0 0 0 0.389418340.56464247 0 0 0 0 -0 -0 0.564642470.71735609 0 0 -0 -0 -0 -0 0.717356090.84147098 0 0 -0 -0 -0 0 0.841470980.93203909 0 -0 -0 -0 0 0 0.932039090.98544973 0 -0 -0 0 0 -0 0.985449730.9995736 -0 -0 0 0 -0 -0 0.99957360.97384763 -0 -0 0 0 -0 0 0.973847630.90929743 -0 -0 0 -0 -0 0 0.909297430.8084964 -0 0 0 -0 0 0 0.80849640.67546318 -0 0 -0 -0 0 -0 0.675463180.51550137 -0 0 -0 0 0 -0 0.515501370.33498815 -0 0 -0 0 -0 0 0.334988150.14112001 -0 0 -0 0 -0 0 0.14112001-0.0583741 0 -0 0 -0 0 -0 -0.0583741-0.2555411 0 -0 0 -0 0 -0 -0.2555411-0.4425204 0 -0 0 -0 0 0 -0.4425204-0.6118579 0 -0 0 0 -0 0 -0.6118579-0.7568025 0 -0 -0 0 -0 0 -0.7568025-0.8715758 0 0 -0 0 0 -0 -0.8715758

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Any periodic signal can be made up from a sum of harmonic waves (sine waves).

Fourier (1, 0, -(1/9))Fourier (1, 0, -(1/9))Any periodic signal can be made up from a sum of harmonic waves (sine waves).

0 0 0 -0 0 0 00.02 0.19866933 0 -0.0627381 0 0 00.04 0.38941834 0 -0.1035599 0 0 00.06 0.56464247 0 -0.1082053 0 0 -00.08 0.71735609 0 -0.0750515 -0 -0 -00.1 0.84147098 0 -0.01568 -0 -0 -00.12 0.93203909 0 0.04916894 -0 -0 00.14 0.98544973 0 0.09684175 -0 0 00.16 0.9995736 -0 0.11068496 0 0 -00.18 0.97384763 -0 0.08586272 0 0 -00.2 0.90929743 -0 0.03104617 0 -0 -00.22 0.8084964 -0 -0.0346157 0 -0 00.24 0.67546318 -0 -0.0881853 -0 -0 00.26 0.51550137 -0 -0.1109493 -0 0 00.28 0.33498815 -0 -0.0949554 -0 0 -00.3 0.14112001 -0 -0.0457909 -0 0 -00.32 -0.0583741 0 0.01936964 0 -0 00.34 -0.2555411 0 0.07776385 0 -0 00.36 -0.4425204 0 0.10899291 0 -0 00.38 -0.6118579 0 0.10214761 0 0 -00.4 -0.7568025 0 0.05961921 -0 0 -00.42 -0.8715758 0 -0.0037359 -0 0 00.44 -0.9516021 0 -0.0657859 -0 -0 0

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Fourier (1, 0, -(1/9), 0, +(1/25))Fourier (1, 0, -(1/9), 0, +(1/25))Any periodic signal can be made up from a sum of harmonic waves (sine waves).

0 0 0 -0 0 0 00.02 0.19866933 0 -0.0627381 0 0.03365884 00.04 0.38941834 0 -0.1035599 0 0.0363719 00.06 0.56464247 0 -0.1082053 0 0.0056448 -00.08 0.71735609 0 -0.0750515 -0 -0.0302721 -00.1 0.84147098 0 -0.01568 -0 -0.038357 -00.12 0.93203909 0 0.04916894 -0 -0.0111766 00.14 0.98544973 0 0.09684175 -0 0.02627946 00.16 0.9995736 -0 0.11068496 0 0.03957433 -00.18 0.97384763 -0 0.08586272 0 0.01648474 -00.2 0.90929743 -0 0.03104617 0 -0.0217608 -00.22 0.8084964 -0 -0.0346157 0 -0.0399996 00.24 0.67546318 -0 -0.0881853 -0 -0.0214629 00.26 0.51550137 -0 -0.1109493 -0 0.01680668 00.28 0.33498815 -0 -0.0949554 -0 0.03962429 -00.3 0.14112001 -0 -0.0457909 -0 0.02601151 -00.32 -0.0583741 0 0.01936964 0 -0.0115161 00.34 -0.2555411 0 0.07776385 0 -0.0384559 00.36 -0.4425204 0 0.10899291 0 -0.0300395 00.38 -0.6118579 0 0.10214761 0 0.00599509 -00.4 -0.7568025 0 0.05961921 -0 0.03651781 -00.42 -0.8715758 0 -0.0037359 -0 0.03346623 00.44 -0.9516021 0 -0.0657859 -0 -0.0003541 0

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Fourier (1, 0, -(1/9), 0, 1/25,0,-(1/49),0)

Fourier (1, 0, -(1/9), 0, 1/25,0,-(1/49),0)

0 0 0 -0 0 0 00.02 0.19866933 0 -0.0627381 0 0.03365884 00.04 0.38941834 0 -0.1035599 0 0.0363719 00.06 0.56464247 0 -0.1082053 0 0.0056448 -00.08 0.71735609 0 -0.0750515 -0 -0.0302721 -00.1 0.84147098 0 -0.01568 -0 -0.038357 -00.12 0.93203909 0 0.04916894 -0 -0.0111766 00.14 0.98544973 0 0.09684175 -0 0.02627946 00.16 0.9995736 -0 0.11068496 0 0.03957433 -00.18 0.97384763 -0 0.08586272 0 0.01648474 -00.2 0.90929743 -0 0.03104617 0 -0.0217608 -00.22 0.8084964 -0 -0.0346157 0 -0.0399996 00.24 0.67546318 -0 -0.0881853 -0 -0.0214629 00.26 0.51550137 -0 -0.1109493 -0 0.01680668 00.28 0.33498815 -0 -0.0949554 -0 0.03962429 -00.3 0.14112001 -0 -0.0457909 -0 0.02601151 -00.32 -0.0583741 0 0.01936964 0 -0.0115161 00.34 -0.2555411 0 0.07776385 0 -0.0384559 00.36 -0.4425204 0 0.10899291 0 -0.0300395 00.38 -0.6118579 0 0.10214761 0 0.00599509 -00.4 -0.7568025 0 0.05961921 -0 0.03651781 -00.42 -0.8715758 0 -0.0037359 -0 0.03346623 00.44 -0.9516021 0 -0.0657859 -0 -0.0003541 0

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Fourier (1,0)Fourier (1,0)Any periodic signal can be made up from a sum of harmonic waves (sine waves).

0 0 0 0 0 0 00.02 0.19866933 0 0 0 0 00.04 0.38941834 0 0 0 0 00.06 0.56464247 0 0 0 0 -00.08 0.71735609 0 0 -0 -0 -00.1 0.84147098 0 0 -0 -0 -00.12 0.93203909 0 -0 -0 -0 00.14 0.98544973 0 -0 -0 0 00.16 0.9995736 -0 -0 0 0 -00.18 0.97384763 -0 -0 0 0 -00.2 0.90929743 -0 -0 0 -0 -00.22 0.8084964 -0 0 0 -0 00.24 0.67546318 -0 0 -0 -0 00.26 0.51550137 -0 0 -0 0 00.28 0.33498815 -0 0 -0 0 -00.3 0.14112001 -0 0 -0 0 -00.32 -0.0583741 0 -0 0 -0 00.34 -0.2555411 0 -0 0 -0 00.36 -0.4425204 0 -0 0 -0 00.38 -0.6118579 0 -0 0 0 -00.4 -0.7568025 0 -0 -0 0 -00.42 -0.8715758 0 0 -0 0 00.44 -0.9516021 0 0 -0 -0 0

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Fourier (1,0, (1/3))Fourier (1,0, (1/3))Any periodic signal can be made up from a sum of harmonic waves (sine waves).

0 0 0 0 0 0 00.02 0.19866933 0 0.18821416 0 0 00.04 0.38941834 0 0.3106797 0 0 00.06 0.56464247 0 0.32461588 0 0 -00.08 0.71735609 0 0.22515439 -0 -0 -00.1 0.84147098 0 0.04704 -0 -0 -00.12 0.93203909 0 -0.1475068 -0 -0 00.14 0.98544973 0 -0.2905253 -0 0 00.16 0.9995736 -0 -0.3320549 0 0 -00.18 0.97384763 -0 -0.2575882 0 0 -00.2 0.90929743 -0 -0.0931385 0 -0 -00.22 0.8084964 -0 0.10384712 0 -0 00.24 0.67546318 -0 0.26455595 -0 -0 00.26 0.51550137 -0 0.33284778 -0 0 00.28 0.33498815 -0 0.2848663 -0 0 -00.3 0.14112001 -0 0.13737283 -0 0 -00.32 -0.0583741 0 -0.0581089 0 -0 00.34 -0.2555411 0 -0.2332916 0 -0 00.36 -0.4425204 0 -0.3269787 0 -0 00.38 -0.6118579 0 -0.3064428 0 0 -00.4 -0.7568025 0 -0.1788576 -0 0 -00.42 -0.8715758 0 0.01120768 -0 0 00.44 -0.9516021 0 0.19735784 -0 -0 0

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Fourier (1,0,1/3,0,1/5)Fourier (1,0,1/3,0,1/5)Any periodic signal can be made up from a sum of harmonic waves (sine waves).

0 0 0 0 0 0 00.02 0.19866933 0 0.18821416 0 0.1682942 00.04 0.38941834 0 0.3106797 0 0.18185949 00.06 0.56464247 0 0.32461588 0 0.028224 -00.08 0.71735609 0 0.22515439 -0 -0.1513605 -00.1 0.84147098 0 0.04704 -0 -0.1917849 -00.12 0.93203909 0 -0.1475068 -0 -0.0558831 00.14 0.98544973 0 -0.2905253 -0 0.13139732 00.16 0.9995736 -0 -0.3320549 0 0.19787165 -00.18 0.97384763 -0 -0.2575882 0 0.0824237 -00.2 0.90929743 -0 -0.0931385 0 -0.1088042 -00.22 0.8084964 -0 0.10384712 0 -0.199998 00.24 0.67546318 -0 0.26455595 -0 -0.1073146 00.26 0.51550137 -0 0.33284778 -0 0.08403341 00.28 0.33498815 -0 0.2848663 -0 0.19812147 -00.3 0.14112001 -0 0.13737283 -0 0.13005757 -00.32 -0.0583741 0 -0.0581089 0 -0.0575807 00.34 -0.2555411 0 -0.2332916 0 -0.1922795 00.36 -0.4425204 0 -0.3269787 0 -0.1501974 00.38 -0.6118579 0 -0.3064428 0 0.02997544 -00.4 -0.7568025 0 -0.1788576 -0 0.18258905 -00.42 -0.8715758 0 0.01120768 -0 0.16733113 00.44 -0.9516021 0 0.19735784 -0 -0.0017703 0

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0 0.5 1 1.5 2 2.5

Fourier (1,0,1/3,0,1/5,0,1/7)Fourier (1,0,1/3,0,1/5,0,1/7)Any periodic signal can be made up from a sum of harmonic waves (sine waves).

0 0 0 0 0 0 00.02 0.19866933 0 0.18821416 0 0.1682942 00.04 0.38941834 0 0.3106797 0 0.18185949 00.06 0.56464247 0 0.32461588 0 0.028224 -00.08 0.71735609 0 0.22515439 -0 -0.1513605 -00.1 0.84147098 0 0.04704 -0 -0.1917849 -00.12 0.93203909 0 -0.1475068 -0 -0.0558831 00.14 0.98544973 0 -0.2905253 -0 0.13139732 00.16 0.9995736 -0 -0.3320549 0 0.19787165 -00.18 0.97384763 -0 -0.2575882 0 0.0824237 -00.2 0.90929743 -0 -0.0931385 0 -0.1088042 -00.22 0.8084964 -0 0.10384712 0 -0.199998 00.24 0.67546318 -0 0.26455595 -0 -0.1073146 00.26 0.51550137 -0 0.33284778 -0 0.08403341 00.28 0.33498815 -0 0.2848663 -0 0.19812147 -00.3 0.14112001 -0 0.13737283 -0 0.13005757 -00.32 -0.0583741 0 -0.0581089 0 -0.0575807 00.34 -0.2555411 0 -0.2332916 0 -0.1922795 00.36 -0.4425204 0 -0.3269787 0 -0.1501974 00.38 -0.6118579 0 -0.3064428 0 0.02997544 -00.4 -0.7568025 0 -0.1788576 -0 0.18258905 -00.42 -0.8715758 0 0.01120768 -0 0.16733113 00.44 -0.9516021 0 0.19735784 -0 -0.0017703 0

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Compact DiscsCompact Discsbinary numbers 00 001 110 211 3100 4=22

101 510000 16=24

11111111 255

Compact DiscsCompact Discs0 0 0 0 0 0 0

0.02 0.19866933 0.15576734 0.22585699 0.07173561 0 00.04 0.38941834 0.28694244 0.37281563 0.09995736 0 00.06 0.56464247 0.37281563 0.38953905 0.06754632 0 -00.08 0.71735609 0.39982944 0.27018527 -0.0058374 -0 -00.1 0.84147098 0.36371897 0.056448 -0.0756802 -0 -00.12 0.93203909 0.27018527 -0.1770082 -0.0996165 -0 00.14 0.98544973 0.13399526 -0.3486303 -0.0631267 0 00.16 0.9995736 -0.0233497 -0.3984658 0.01165492 0 -00.18 0.97384763 -0.1770082 -0.3091058 0.07936679 0 -00.2 0.90929743 -0.302721 -0.1117662 0.09893582 -0 -00.22 0.8084964 -0.3806408 0.12461655 0.05849172 -0 00.24 0.67546318 -0.3984658 0.31746715 -0.0174327 -0 00.26 0.51550137 -0.3533819 0.39941734 -0.0827826 0 00.28 0.33498815 -0.2525067 0.34183956 -0.0979178 0 -00.3 0.14112001 -0.1117662 0.16484739 -0.0536573 0 -00.32 -0.0583741 0.04661968 -0.0697307 0.02315098 -0 00.34 -0.2555411 0.19764534 -0.2799499 0.08591618 -0 00.36 -0.4425204 0.31746715 -0.3923745 0.09656578 -0 00.38 -0.6118579 0.38716787 -0.3677314 0.04863987 0 -00.4 -0.7568025 0.3957433 -0.2146292 -0.0287903 0 -00.42 -0.8715758 0.34183956 0.01344922 -0.0887567 0 00.44 -0.9516021 0.23396688 0.23682941 -0.0948844 -0 0

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Sample rate of 44,100 bytes per secondThis gives 0 to 10,000 Hz frequencies