physics 1251 the science and technology of musical sound unit 1 session 8 harmonic series unit 1...

Physics 1251Physics 1251The Science and The Science and

Technology of Musical Technology of Musical SoundSound

Physics 1251Physics 1251The Science and The Science and

Technology of Musical Technology of Musical SoundSound

Unit 1Unit 1

Session 8Session 8

Harmonic SeriesHarmonic Series

Unit 1Unit 1

Session 8Session 8

Harmonic SeriesHarmonic Series

Physics 1251 Physics 1251 Unit 1 Session 8 Unit 1 Session 8 Harmonic SeriesHarmonic Series

Foolscap Quiz:Foolscap Quiz:What is the lowest frequency component of the What is the lowest frequency component of the

following waveform?following waveform?

Repeat period P =10 ms =0.010 sec; Repeat period P =10 ms =0.010 sec; f f = 1/P = 1/P = 100. Hz= 100. Hz


Recall:Recall: 80/2080/20The The lowest (or fundamental) lowest (or fundamental) frequencyfrequency ff11 of the components of a of the components of a waveform is equal to 1/Pwaveform is equal to 1/Prepeatrepeat..


11′ Lecture: ′ Lecture: • A A harmonic seriesharmonic series is is

a Fourier Frequency Spectrum a Fourier Frequency Spectrum in which the frequency of each of the in which the frequency of each of the components is an components is an integral multipleintegral multiple of of the fundamental frequency: the fundamental frequency:

ff11 = 1= 1 f f1 1 , , ff22 = 2= 2 f f1 1 , , ff33 = 3= 3 f f1 1 , , ff44 = 4= 4 f f1 1 etc.etc.


““Harmonic” implies an Harmonic” implies an integerinteger ratioratioof frequency.of frequency.

ff11 = 1= 1 f f1 1 , , ff22 = 2= 2 f f1 1 , , ff33 = 3= 3 f f1 1 , , ff44 = 4= 4 f f1 1 etc.etc.

e.g. 100 Hz, 200 Hz, 300 Hz, 400 Hz…e.g. 100 Hz, 200 Hz, 300 Hz, 400 Hz…

Peregrination in Existential Peregrination in Existential PhysicsPhysics::

• Move you hand up and down in Move you hand up and down in sinusoidal motion.sinusoidal motion.

• Now diminish the range of motion.Now diminish the range of motion.• Now increase the range of motion.Now increase the range of motion.• You have changed the You have changed the amplitudeamplitude of of

the oscillation.the oscillation.


Peregrination in Existential PhysicsPeregrination in Existential Physics::• Move you hand up and down in Move you hand up and down in

sinusoidal motion.sinusoidal motion.• Now move you hand faster but keep the Now move you hand faster but keep the

same range of motion.same range of motion.• Now move you rhand more slowly.Now move you rhand more slowly.• You have changed the fYou have changed the frequency requency of the of the

oscillation.oscillation.


Peregrination in Existential Peregrination in Existential PhysicsPhysics::

• Move both of your hands up and Move both of your hands up and down in sinusoidal motion, starting down in sinusoidal motion, starting them at the same time.them at the same time.

• Now let one hand precede the other.Now let one hand precede the other.• You have changed the You have changed the phasephase of the of the

oscillation.oscillation.



80/2080/20Important terms:Important terms:• AmplitudeAmplitude A: amount or size of a A: amount or size of a

component wave.component wave.• FrequencyFrequency ff: number of oscillations : number of oscillations

per second.per second.• PhasePhase φφ : the relative starting point : the relative starting point

of a component wave.of a component wave.


Amplitude:Amplitude:

the size of the excursion from the the size of the excursion from the average.average.

AmplitudeAmplitude


Frequency, Amplitude, and Phase of a Frequency, Amplitude, and Phase of a sine wave:sine wave:

• AmplitudeAmplitude


FrequencyFrequency

the number of oscillations per the number of oscillations per secondsecond

Higher Higher frequencyfrequency

Lower frequencyLower frequency



• FrequencyFrequency


Phase:Phase:

the relative starting point of an the relative starting point of an oscillation.oscillation.

PhasePhase



• PhasePhase


80/2080/20Important terms:Important terms:• AmplitudeAmplitude A: amount or size of a A: amount or size of a

component wave.component wave.• FrequencyFrequency ff: number of oscillations : number of oscillations

per second.per second.• PhasePhase φφ : the relative starting point : the relative starting point

of a component wave.of a component wave.

p = Ap = A1 1 sin( 2sin( 2π π ff11 t + t + φφ1 1 ) + ) + AA2 2 sin( 2sin( 2π π ff22 t + t + φφ2 2 ) )

+ + AA3 3 sin( 2sin( 2π π ff33 t + t + φφ3 3 ) + ) + AA4 4 sin( 2sin( 2π π ff44 t t + + φφ4 4 ) …) …

AmplitudeAmplitudeFrequencyFrequency PhasePhase


How does a square wave sound?How does a square wave sound?

What about a different waveform with What about a different waveform with the same harmonic series but different the same harmonic series but different

phases?phases?

FrequencFrequencyy

PhasePhase


The waveform is determined by the The waveform is determined by the frequency spectrum frequency spectrum andand phase phase

spectrum.spectrum.

FrequencyFrequency

PhasePhase WaveformWaveform


80/2080/20Ohms’ Law for acoustics: Ohms’ Law for acoustics: Humans cannot directly sense the Humans cannot directly sense the

phase of a sound wave.phase of a sound wave.

Different waveforms with the same Different waveforms with the same frequency spectra (but different phase frequency spectra (but different phase

spectra) sound the same to us.spectra) sound the same to us.


♬☺♬☺ Listen to difference in Listen to difference in

• AmplitudeAmplitude• FrequencyFrequency

• (Phase)(Phase)• WaveformWaveform


Correlation of physical with musicalCorrelation of physical with musicalcharacteristics:characteristics:

• Amplitude—Intensity (AAmplitude—Intensity (A22))

• FrequencyFrequency

• WaveformWaveform(phase + harmonic series)(phase + harmonic series)

♫♫ LoudnessLoudness♫ ♫ PitchPitch

♫♫ TimbreTimbre


80/2080/20Pitch is based on the Pitch is based on the ratioratio of of frequencies.frequencies.

80/2080/20A given frequency ratio is called an A given frequency ratio is called an intervalinterval..

80/2080/20An An octaveoctave is the pitch interval that is the pitch interval that corresponds to a ratio of corresponds to a ratio of ff22 / / ff11 =2 / =2 / 1.1.


Summary:Summary:

• AA harmonic seriesharmonic series is the sum of sine wave is the sum of sine wave components each frequency of which is an components each frequency of which is an integral multipleintegral multiple of the fundamental frequency. of the fundamental frequency.

• Ohm’s LawOhm’s Law : : humans do not sense the phase of humans do not sense the phase of sound directly.sound directly.

• IntensityIntensity determines determines loudnessloudness..• FrequencyFrequency determines determines pitchpitch..• WaveformWaveform (harmonic series) determines (harmonic series) determines

timbretimbre..• An An ooctavectave interval corresponds to a frequency interval corresponds to a frequency

ratio of ratio of 2 : 12 : 1..

physics 1251 the science and technology of musical sound unit 1 session 8 harmonic series unit 1...

Documents

harmonic series harmonic

fundamental frequency

harmonic series frequency

harmonic series unit

harmonic series amplitude

harmonic series recall

amplitude amplitude

hz slide