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Musical Sounds Physical Science101 Chapter twenty Amanda Hyer

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Noise

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MusicMusic

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PitchPitch High Low

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Intensity Loudness Soft Loud

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Sound Intensity

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Decibel Sound Level

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ExerciseExercise What is decibel level of a sound that is 1000 times louder than the threshold of human hearing? Given: Intensity/10 -12 =1000=10 3 Wanted: decibel level Solution: dB=10log(Intensity/10 -12 ) dB=10log(10 3 ) = 30 dB

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ExerciseExercise 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 )= 10 9 (10 -12 ) dB2=10log(10 9 ) = 90 dB

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its actually easy intensity 10 (10 1 ) louder 10 dB higher intensity 100 (10 2 ) louder 20 dB higher intensity 1000 (10 3 ) louder 30 dB higher intensity 10,000 (10 4 ) louder 40 dB higher intensity 1,000,000 (10 6 ) louder 60 dB higher

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ExerciseExercise 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

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

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Quality (a pure tone)

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

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

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

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

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

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

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

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

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

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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).

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Compact Discs binary numbers 00 0 01 1 10 2 11 3 100 4=2 2 101 5 10000 16=2 4 11111111 255

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Compact Discs Sample rate of 44,100 bytes per second This gives 0 to 10,000 Hz frequencies

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