Physics 1251 The Science and Technology of Musical Sound Unit 1 Session 10 Fundamentals of Sound...

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 10Session 10

Fundamentals of Sound Fundamentals of Sound ReviewReview

Unit 1Unit 1

Session 10Session 10

Fundamentals of Sound Fundamentals of Sound ReviewReview

Physics 1251 Physics 1251 Unit 1 Session 10 Unit 1 Session 10 Fundamentals of Sound—Review Fundamentals of Sound—Review

Foolscap Quiz:Foolscap Quiz:Three students push a heavy box across the floor. Three students push a heavy box across the floor.

If together they exert a force of 1000 Newtons If together they exert a force of 1000 Newtons and they move it by 3.6 meters, how much work and they move it by 3.6 meters, how much work did they do? did they do? If they were able to move it that far in one If they were able to move it that far in one minute (60. seconds) what power did they minute (60. seconds) what power did they expend?expend?W=F W=F ‧ ‧ d = (1000. N)(3.6 m)= 3600 J = 3.6 d = (1000. N)(3.6 m)= 3600 J = 3.6

kJkJ;;Power = W/t = 3600 J/60 s = 60 W.Power = W/t = 3600 J/60 s = 60 W.

Physics 1251 Physics 1251 Unit 1 Session 10 Unit 1 Session 10 Fundamentals of Sound—ReviewFundamentals of Sound—Review

11′ Lecture: ′ Lecture: • Knowledge is of at least three (3) kinds:Knowledge is of at least three (3) kinds:

• Concepts—understand them.Concepts—understand them.• Facts—know them.Facts—know them.• Skills—practice them.Skills—practice them.

• Sound transmits energy through a Sound transmits energy through a material medium in the form of a material medium in the form of a pressure-displacement wave, originates pressure-displacement wave, originates from an oscillator or other disturbance, from an oscillator or other disturbance, and is characterized as a combination of and is characterized as a combination of sine waves of various frequencies. sine waves of various frequencies.


Concepts:Concepts:• Sound is a longitudinal pressure/Sound is a longitudinal pressure/

displacement wave that propagates displacement wave that propagates through a material medium in the range through a material medium in the range 20 to 20 kHz.20 to 20 kHz.

• Sound waves originate from oscillators.Sound waves originate from oscillators.• Complex repeating motion can be Complex repeating motion can be

analyzed as a combination of simple analyzed as a combination of simple harmonic motions.harmonic motions.

• A Simple Harmonic Oscillator oscillates A Simple Harmonic Oscillator oscillates in sinusoidal motion with a single well-in sinusoidal motion with a single well-defined frequency.defined frequency.


� � λ λ ��WavelengthWavelength

V V


Oscillating Hand DemonstrationOscillating Hand Demonstration

☞♫☞♫

CompressionCompression

RarefactioRarefactionn


Simple Harmonic OscillatorsSimple Harmonic Oscillators• Helmholtz ResonatorHelmholtz Resonator


Spring Spring ——————→→

Mass Mass ————→————→

Two Masses on Two Coupled Two Masses on Two Coupled SpringsSprings

Spring Spring ————→————→

Mass Mass ————→————→

Mode 1Mode 1 Mode 2Mode 2


80/20 80/20 A A Fourier AnalysisFourier Analysis is a is a representation of all the representation of all the components that comprise a components that comprise a waveform, waveform, amplitudeamplitude versus versus frequency and frequency and phasephase versus versus frequency.frequency.


Example: Synthesis of a Square wave-Example: Synthesis of a Square wave-

The Fourier SpectrumThe Fourier Spectrum

FrequencyFrequencyffoo 3f3f

oo

5f5f

oo

7f7f

oo

11stst Overtone – 3 Overtone – 3rdrd HarmonicHarmonic

22ndnd Overtone – 5 Overtone – 5thth HarmonicHarmonic

Fundamental – 1Fundamental – 1stst HarmonicHarmonic

Am

plitu

de

Am

plitu

de


Concepts:Concepts:• Sound transmits energy.Sound transmits energy.• The energy of an oscillator or of The energy of an oscillator or of

sound dissipates in an exponential sound dissipates in an exponential decay.decay.

• The timbre of an instrument changes The timbre of an instrument changes with time because of the transients.with time because of the transients.

• An oscillator can be caused to vibrate An oscillator can be caused to vibrate in “sympathy” when the driving in “sympathy” when the driving frequency is close to that of a natural frequency is close to that of a natural mode of oscillation.mode of oscillation.


““Exponential Decay”Exponential Decay”

E = EE = Eoo/2 /2 t /tt /t1/21/2


Time Dependent Fourier Spectrum:Time Dependent Fourier Spectrum:

Observe TransientsObserve Transients

Piano Transient Frequency Piano Transient Frequency SpectrumSpectrum

FrequencyFrequency

Am

plitu

de o

f A

mp

litu

de o

f C

om

pon

en

tC

om

pon

en

t


ADSR:ADSR:Attack, Decay, Sustain, ReleaseAttack, Decay, Sustain, Release

The “envelop” of the amplitude of all musical The “envelop” of the amplitude of all musical soundsound

Is described by ADSR .Is described by ADSR .

AttackAttackDecayDecay SustainSustainReleaseRelease


““Resonantly Driven”Resonantly Driven”Simple Harmonic OscillatorSimple Harmonic Oscillator


Facts:Facts:Definitions:Definitions:• SoundSound• Longitudinal waveLongitudinal wave• Transverse waveTransverse wave• PressurePressure• DisplacementDisplacement• PeriodPeriod• FrequencyFrequency• WavelengthWavelength• Non-dispersiveNon-dispersive


Facts:Facts:Definitions:Definitions:• Simple Harmonic OscillatorSimple Harmonic Oscillator• Spring constant Spring constant • Helmholtz ResonatorHelmholtz Resonator• Normal Mode of oscillationNormal Mode of oscillation• DegeneracyDegeneracy• Fourier Analysis and SynthesisFourier Analysis and Synthesis• Harmonic seriesHarmonic series• FundamentalFundamental• OvertoneOvertone• MicrophoneMicrophone• OscilloscopeOscilloscope


Facts:Facts:Definitions:Definitions:• Sine waveSine wave• SinusoidalSinusoidal• AmplitudeAmplitude• PhasePhase• Ohm’s LawOhm’s Law• IntervalInterval• TimbreTimbre• WaveformWaveform• TransientTransient


Facts:Facts:• Definitions:Definitions:

• WorkWork• EnergyEnergy• PowerPower• IntensityIntensity• TransientTransient• ResonanceResonance• PrecisionPrecision• AccuracyAccuracy• Significant figureSignificant figure• Logical InductionLogical Induction


Facts:Facts:

Important Prefixes:Important Prefixes:

Mega- ( M) = 1 000 000= Mega- ( M) = 1 000 000= 10 10 66

kilo- ( k) = 1 000 = 10kilo- ( k) = 1 000 = 10 3 3

centi- ( c) = 1/100 = 10centi- ( c) = 1/100 = 10 -2 -2

milli- ( m) = 1/1 000 = 10milli- ( m) = 1/1 000 = 10 -3 -3

micro- (micro- (μμ) = 1/1 000 000 = ) = 1/1 000 000 = 1010 -6 -6


Scientific NotationScientific NotationA number can be written as the product of A number can be written as the product of

two numbers: the first (mantissa) is a two numbers: the first (mantissa) is a number 1 or more but less than 10; the number 1 or more but less than 10; the second is 10 to a power (the exponent) second is 10 to a power (the exponent) that puts the decimal in the correct that puts the decimal in the correct place. Negative powers mean 1/10 to the place. Negative powers mean 1/10 to the power (e.g. 10 power (e.g. 10 - 3- 3 = 1/10 = 1/10 33).).

For example:For example:

Big Numbers: Big Numbers: 1.234567 x 10 1.234567 x 10 33 = 1234.567 = 1234.567Small Numbers: Small Numbers: 1.234567 x 10 1.234567 x 10 –2–2 = =

0.012345670.01234567


Know your calculator:Know your calculator:

Enter: “Enter: “1.234567 EXP” or “EE” “03” 1.234567 EXP” or “EE” “03”

You will read “1.234567 You will read “1.234567 0303” or” or

““1.234567E03”1.234567E03”

Enter: “Enter: “1.234567 EXP 03 +/- or (-)” 1.234567 EXP 03 +/- or (-)”

You will read “1.234567You will read “1.234567-03-03” or ” or “1.234567E-03”“1.234567E-03”


Vademecum Vademecum (take with me)(take with me)::• v = d /tv = d /t (also d = v(also d = v∙t and t = d /v )∙t and t = d /v )• p = F /Ap = F /A• ρ = m/Vρ = m/V• P = 1/ P = 1/ ff• v = v = λλ ⋅ ⋅ ff• v = 343 +0.6v = 343 +0.6(T - 20 C) m/s(T - 20 C) m/s• F = - k F = - k ‧ ‧ xx f = 1/(2f = 1/(2π) π) ‧ √ (k/m)‧ √ (k/m)• ff1 1 =1/P=1/Prepeat repeat • W =FW =F‧d; ‧d; E = W E = W • ℙℙ = W/t;= W/t; I = I = ℙℙ/A /A • E = EE = Eoo/2 /2 t /tt /t1/21/2


Skills:Skills:Word ProblemWord ProblemA sonar operator sends out a “ping” into the A sonar operator sends out a “ping” into the

sea. He hears an echo from another sea. He hears an echo from another submarine 4.50 seconds later. How far submarine 4.50 seconds later. How far away is the second sub?away is the second sub?

(Essential data: the speed of sound in sea (Essential data: the speed of sound in sea water is 1500. m/s)water is 1500. m/s)

4.50/2 4.50/2 secondsseconds

4.50/2 4.50/2 secondsseconds

d = v td = v td =1500 d =1500 m/s(2.25 s)m/s(2.25 s)d= 3.38 kmd= 3.38 km

λλ


Skills:Skills:Word ProblemWord ProblemA sound wave is emitted by a large pipe of an A sound wave is emitted by a large pipe of an

organ. If its frequency is approximately organ. If its frequency is approximately 65.5 Hz and the air temperature in the 65.5 Hz and the air temperature in the church is a chilly 15C, what is the church is a chilly 15C, what is the wavelength of the sound wave?wavelength of the sound wave?

λλ = v / f, v =? = v / f, v =?v =343. +0.6( T-20)v =343. +0.6( T-20)v = 343 + 0.6( 15-v = 343 + 0.6( 15-20)20)v = 343 – 3.0 = 340 v = 343 – 3.0 = 340 m/sm/s

λλ = v / f = v / fλλ = 340 / 65.5 = 340 / 65.5 mmλλ = 5.19 m = 5.19 m

F =2.0 nF =2.0 nx= -.02 mx= -.02 m


Skills:Skills:Word ProblemWord ProblemA 1.2 kg mass is mounted on a thin steel rod. A 1.2 kg mass is mounted on a thin steel rod.

If when I press on the rod with a force of If when I press on the rod with a force of about 2.0 N is deflects to the side by about about 2.0 N is deflects to the side by about 2.0 cm, at what frequency will the mass 2.0 cm, at what frequency will the mass oscillate if I pluck it? oscillate if I pluck it?

ff = (1/2 = (1/2π)π)√(k/m), k =?√(k/m), k =?k = -F/x = 2.0 N/0.02 m = 100 k = -F/x = 2.0 N/0.02 m = 100 N/mN/m

ff = (1/2 = (1/2π)π)√(k/m)√(k/m) = = (1/2(1/2π)π)√(100/1.2)√(100/1.2) f = (.1592)f = (.1592)√(83.3)= 1.45 Hz√(83.3)= 1.45 Hz


Skills:Skills:AnalysisAnalysisWhen John fills a jug with water he notices When John fills a jug with water he notices

that the pitch of the splashing noise that he that the pitch of the splashing noise that he hears rises as the jugs fills. Why is thathears rises as the jugs fills. Why is that??

(1)(1) Higher pitch means higher frequency.Higher pitch means higher frequency.

(2)(2) The jug is a Helmholtz resonator (a SHO).The jug is a Helmholtz resonator (a SHO).

(3)(3) The air “spring” gets stiffer as the volume The air “spring” gets stiffer as the volume gets smaller, i.e. k get larger.gets smaller, i.e. k get larger.

(4)(4) Therefore, since f Therefore, since f ∝ √k for a SHO, f gets ∝ √k for a SHO, f gets higher.higher.


Skills:Skills:AnalysisAnalysisHow can you know that the speed of sound How can you know that the speed of sound in air is non-dispersive?in air is non-dispersive?

(1)(1) “ “Non-dispersive” means that the speed Non-dispersive” means that the speed does not depend on frequency.does not depend on frequency.

(2)(2) When a person speaks, his voice contains When a person speaks, his voice contains many frequencies.many frequencies.

(3)(3) If the speed depended on frequency, the If the speed depended on frequency, the timbre of the voice would change as you got timbre of the voice would change as you got farther away from a person. It doesn’t.farther away from a person. It doesn’t.

(4)(4) Therefore, sound must be non-dispersive.Therefore, sound must be non-dispersive.


Skills:Skills:AnalysisAnalysisDr. M bought an acoustic ruler. How do you Dr. M bought an acoustic ruler. How do you think it works? And what sources of error do think it works? And what sources of error do you anticipate will affect the reading?you anticipate will affect the reading?

(1)(1) The acoustic ruler uses timing of an echo, The acoustic ruler uses timing of an echo, similar to sonar, to determine the distance similar to sonar, to determine the distance from the source to the reflecting surface.from the source to the reflecting surface.

(2)(2) Temperature can affect the speed of sound. Temperature can affect the speed of sound. But 10 C changes the speed only about 1.7%. But 10 C changes the speed only about 1.7%. (6/343)(6/343)


Skills:Skills:AnalysisAnalysisListen to the sound bite. How do you know Listen to the sound bite. How do you know that the sound has been modified?that the sound has been modified?

(1)(1)The transients are not correct. The The transients are not correct. The sound has been played backward.sound has been played backward.

(2)(2)Now listen to sound forward.Now listen to sound forward.


Summary of SummariesSummary of Summaries

&&

The Cavalcade of ConceptsThe Cavalcade of Concepts

Physics 1251Physics 1251 Unit 1 Session 1Unit 1 Session 1IntroductionsIntroductions

Summary:Summary:• To get the most out of this course use To get the most out of this course use

80/20 thinking.80/20 thinking.• The key to success is “ The key to success is “ Attend!Attend!””• Learn how you learn and do it!Learn how you learn and do it!• Know Know youryour learning style(s). learning style(s).

StudyStudy• Concepts –Facts –SkillsConcepts –Facts –Skills

• Then take practice test

Physics 1251Physics 1251 Unit 1 Session 2Unit 1 Session 2Fundamentals of SoundFundamentals of Sound

Summary:Summary:• Sound is a longitudinal mechanical Sound is a longitudinal mechanical

wave that originates from a wave that originates from a mechanical vibration and mechanical vibration and propagates in a material medium propagates in a material medium with a frequency of 20 Hz to 20 kHz.with a frequency of 20 Hz to 20 kHz.

• Radio waves are E-M waves.Radio waves are E-M waves.• Sound is non-dispersive.Sound is non-dispersive.• The velocity of sound is 343 m/s The velocity of sound is 343 m/s

at 20 C.at 20 C.

Physics 1251 Unit 1 Session 3Physics 1251 Unit 1 Session 3 Sound Waves Sound Waves

Summary:Summary:• Pressure: p = F / APressure: p = F / A• Standard atmospheric pressure = 101 Standard atmospheric pressure = 101

kPakPa• Frequency = number of cycles per Frequency = number of cycles per

secondsecond• Hz = Hertz = cycle/secondHz = Hertz = cycle/second• Period: P = 1/ Period: P = 1/ ff• v = v = λλ ⋅ ⋅ ff • v = 343 + 0.6 (T – 20 C) m/sv = 343 + 0.6 (T – 20 C) m/s

Physics 1251 Physics 1251 Unit 1 Session 4 Unit 1 Session 4 Thinking as a Physicist Thinking as a Physicist

Summary:Summary:• Observe—see what is there.Observe—see what is there.• Abstract—ideate the significant.Abstract—ideate the significant.• Measure—compare to standard.Measure—compare to standard.• Model—use math.Model—use math.• Predict—risk a prognostication.Predict—risk a prognostication.• Compare—check it out.Compare—check it out.

Physics 1251 Physics 1251 Unit 1 Session 4 Unit 1 Session 4 Thinking as a Physicist Thinking as a Physicist

Summary (cont’d.):Summary (cont’d.):• UnitsUnits: fundamental—second, meter, : fundamental—second, meter,

kilogram; derived—Hz, N, Pakilogram; derived—Hz, N, Pa• Scale PrefixesScale Prefixes: M, k, c, m, : M, k, c, m, μμ• Scientific notationScientific notation: 1.234 x 10: 1.234 x 1033

[1.234 E03 or 1.234 [1.234 E03 or 1.234 0303 ] ]• Experimental errorExperimental error• Significant figuresSignificant figures• Insufficiency of inductionInsufficiency of induction

Physics 1251 Physics 1251 Unit 1 Session 5 Unit 1 Session 5 Simple Harmonic Oscillators Simple Harmonic Oscillators

Summary:Summary:• A A Simple Harmonic OscillatorSimple Harmonic Oscillator is a is a

device that oscillates at one device that oscillates at one frequency, determined by the spring frequency, determined by the spring constant k and the mass m of the constant k and the mass m of the system.system.

• The natural frequency of an SHO The natural frequency of an SHO moving in sinusoidal motion is moving in sinusoidal motion is related to these quantities by the related to these quantities by the equation:equation:

f = 1/(2f = 1/(2π) π) ‧ √ (k/m)‧ √ (k/m)

Physics 1251 Physics 1251 Unit 1 Session 6 Unit 1 Session 6 Helmholtz Resonators and Vibration Modes Helmholtz Resonators and Vibration Modes

Summary:Summary:• A Helmholtz Oscillator is a SHO comprised A Helmholtz Oscillator is a SHO comprised

of an enclosed air volume and a narrow of an enclosed air volume and a narrow neck and has a single frequency.neck and has a single frequency.

• A normal or natural mode of vibration or A normal or natural mode of vibration or oscillation is one of the fundamental oscillation is one of the fundamental ways that a device can move.ways that a device can move.

• The number of modes is equal to the The number of modes is equal to the number of simple harmonic oscillators in number of simple harmonic oscillators in the system.the system.

• Degeneracy means two or more normal Degeneracy means two or more normal modes have the same frequency.modes have the same frequency.

Physics 1251 Physics 1251 Unit 1 Session 7 Unit 1 Session 7 Good VibrationsGood Vibrations

Summary:Summary:

• Waveforms can be broken down into Waveforms can be broken down into simple sine waves, called simple sine waves, called Fourier Fourier Analysis.Analysis.

• Waveforms can be built up from simple Waveforms can be built up from simple sine waves, called sine waves, called Fourier Synthesis.Fourier Synthesis.

• The lowest frequency needed is 1/PThe lowest frequency needed is 1/Prepeatrepeat..

• A A Fourier SpectrumFourier Spectrum is the recipe for is the recipe for building the waveform.building the waveform.

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

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 Physics 1251 Unit 1 Session 9 Unit 1 Session 9 Transients and ResonancesTransients and Resonances

Summary:Summary:• TransientsTransients occur because radiation and occur because radiation and

friction damp the various harmonics friction damp the various harmonics differently.differently.

• ResonanceResonance is the phenomenon of is the phenomenon of sympathetic vibration at a natural sympathetic vibration at a natural frequency with energy supplied by an frequency with energy supplied by an outside source.outside source.

• Sound transmits energySound transmits energy since pressure since pressure = force/area and a displacement occurs = force/area and a displacement occurs as a sound wave passes.as a sound wave passes.

Physics 1251 The Science and Technology of Musical Sound Unit 1 Session 10 Fundamentals of Sound...

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