Physics 1251 The Science and Technology of Musical Sound

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

2. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review Foolscap Quiz: Three students push a heavy box across the floor. If together they exert a force of 1000 Newtons and they move it by 3.6 meters, how much work did they do? If they were able to move it that far in one minute (60. seconds) what power did they expend? W=F ‧ d = (1000. N)(3.6 m)= 3600 J = 3.6 kJ;Power = W/t = 3600 J/60 s = 60 W.

3. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review 1′ Lecture: • Knowledge is of at least three (3) kinds: • Concepts—understand them. • Facts—know them. • Skills—practice them. • Sound transmits energy through a material medium in the form of a pressure-displacement wave, originates from an oscillator or other disturbance, and is characterized as a combination of sine waves of various frequencies.

4. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review Concepts: • Sound is a longitudinal pressure/displacement wave that propagates through a material medium in the range 20 to 20 kHz. • Sound waves originate from oscillators. • Complex repeating motion can be analyzed as a combination of simple harmonic motions. • A Simple Harmonic Oscillator oscillates in sinusoidal motion with a single well-defined frequency.

5. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review Wavelength ⃒⃖ λ ⃒⃗ ⃗ ⃖ ⃖ ⃗ V ⃗ ⃗ ⃗

6. Compression Rarefaction Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review Oscillating Hand Demonstration ☞♫

7. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review Simple Harmonic Oscillators • Helmholtz Resonator

8. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review Two Masses on Two Coupled Springs Spring ———→ Mass ————→ Spring ————→ Mass ————→ Mode 1 Mode 2

9. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review 80/20 A Fourier Analysis is a representation of all the components that comprise a waveform, amplitude versus frequency and phase versus frequency.

10. Fundamental – 1st Harmonic 1st Overtone – 3rd Harmonic 2nd Overtone – 5th Harmonic Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review Example: Synthesis of a Square wave- The Fourier Spectrum Amplitude fo 3fo 5fo 7fo Frequency

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

12. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review Concepts: • Sound transmits energy. • The energy of an oscillator or of sound dissipates in an exponential decay. • The timbre of an instrument changes with time because of the transients. • An oscillator can be caused to vibrate in “sympathy” when the driving frequency is close to that of a natural mode of oscillation.

13. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review “Exponential Decay” E = Eo/2 t /t1/2

14. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review Time Dependent Fourier Spectrum: Observe Transients Piano Transient Frequency Spectrum Amplitude of Component Frequency

15. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review ADSR: Attack, Decay, Sustain, Release The “envelop” of the amplitude of all musical sound Is described by ADSR . Attack Decay Sustain Release

16. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review “Resonantly Driven” Simple Harmonic Oscillator

17. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review Facts:Definitions: • Sound • Longitudinal wave • Transverse wave • Pressure • Displacement • Period • Frequency • Wavelength • Non-dispersive

18. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review Facts:Definitions: • Simple Harmonic Oscillator • Spring constant • Helmholtz Resonator • Normal Mode of oscillation • Degeneracy • Fourier Analysis and Synthesis • Harmonic series • Fundamental • Overtone • Microphone • Oscilloscope

19. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review Facts:Definitions: • Sine wave • Sinusoidal • Amplitude • Phase • Ohm’s Law • Interval • Timbre • Waveform • Transient

20. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review Facts: • Definitions: • Work • Energy • Power • Intensity • Transient • Resonance • Precision • Accuracy • Significant figure • Logical Induction

21. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review Facts: Important Prefixes: Mega- ( M) = 1 000 000= 10 6 kilo- ( k) = 1 000 = 10 3 centi- ( c) = 1/100 = 10 -2 milli- ( m) = 1/1 000 = 10 -3 micro- (μ) = 1/1 000 000 = 10 -6

22. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review Scientific Notation A number can be written as the product of two numbers: the first (mantissa) is a number 1 or more but less than 10; the second is 10 to a power (the exponent) that puts the decimal in the correct place. Negative powers mean 1/10 to the power (e.g. 10 - 3 = 1/10 3). For example: Big Numbers: 1.234567 x 10 3 = 1234.567 Small Numbers: 1.234567 x 10 –2 = 0.01234567

23. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review Know your calculator: Enter: “1.234567 EXP” or “EE” “03” You will read “1.234567 03” or “1.234567E03” Enter: “1.234567 EXP 03 +/- or (-)” You will read “1.234567-03” or “1.234567E-03”

24. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review Vademecum (take with me): • v = d /t (also d = v∙t and t = d /v ) • p = F /A • ρ = m/V • P = 1/ f • v = λ⋅ f • v = 343 +0.6(T - 20 C) m/s • F = - k ‧ x f = 1/(2π) ‧ √ (k/m) • f1 =1/Prepeat • W =F‧d; E = W • ℙ= W/t; I = ℙ/A • E = Eo/2 t /t1/2

25. 4.50/2 seconds 4.50/2 seconds Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review Skills: Word Problem A sonar operator sends out a “ping” into the sea. He hears an echo from another submarine 4.50 seconds later. How far away is the second sub? (Essential data: the speed of sound in sea water is 1500. m/s) d = v td =1500 m/s(2.25 s)d= 3.38 km

26. λ Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review Skills: Word Problem A sound wave is emitted by a large pipe of an organ. If its frequency is approximately 65.5 Hz and the air temperature in the church is a chilly 15C, what is the wavelength of the sound wave? λ = v / fλ = 340 / 65.5 mλ = 5.19 m λ = v / f, v =?v =343. +0.6( T-20)v = 343 + 0.6( 15-20)v = 343 – 3.0 = 340 m/s

27. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review Skills: Word Problem A 1.2 kg mass is mounted on a thin steel rod. If when I press on the rod with a force of about 2.0 N is deflects to the side by about 2.0 cm, at what frequency will the mass oscillate if I pluck it? f = (1/2π)√(k/m), k =?k = -F/x = 2.0 N/0.02 m = 100 N/m f = (1/2π)√(k/m) = (1/2π)√(100/1.2)f = (.1592)√(83.3)= 1.45 Hz F =2.0 n x= -.02 m

28. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review Skills: Analysis When John fills a jug with water he notices that the pitch of the splashing noise that he hears rises as the jugs fills. Why is that? • Higher pitch means higher frequency. • The jug is a Helmholtz resonator (a SHO). • The air “spring” gets stiffer as the volume gets smaller, i.e. k get larger. • Therefore, since f ∝ √k for a SHO, f gets higher.

29. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review Skills:AnalysisHow can you know that the speed of sound in air is non-dispersive? • “Non-dispersive” means that the speed does not depend on frequency. • When a person speaks, his voice contains many frequencies. • If the speed depended on frequency, the timbre of the voice would change as you got farther away from a person. It doesn’t. • Therefore, sound must be non-dispersive.

30. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review Skills:AnalysisDr. M bought an acoustic ruler. How do you think it works? And what sources of error do you anticipate will affect the reading? • The acoustic ruler uses timing of an echo, similar to sonar, to determine the distance from the source to the reflecting surface. • Temperature can affect the speed of sound. But 10 C changes the speed only about 1.7%. (6/343)

31. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review Skills:AnalysisListen to the sound bite. How do you know that the sound has been modified? • The transients are not correct. The sound has been played backward. • Now listen to sound forward.

32. Physics 1251 Unit 1 Session 10 Fundamentals of Sound—Review Summary of Summaries & The Cavalcade of Concepts

33. Physics 1251 Unit 1 Session 1 Introductions Summary: • To get the most out of this course use 80/20 thinking. • The key to success is “ Attend!” • Learn how you learn and do it! • Know your learning style(s). • Study • Concepts –Facts –Skills • Then take practice test

34. Physics 1251 Unit 1 Session 2 Fundamentals of Sound Summary: • Sound is a longitudinal mechanical wave that originates from a mechanical vibration and propagates in a material medium with a frequency of 20 Hz to 20 kHz. • Radio waves are E-M waves. • Sound is non-dispersive. • The velocity of sound is 343 m/s at 20 C.

35. Physics 1251 Unit 1 Session 3 Sound Waves Summary: • Pressure: p = F / A • Standard atmospheric pressure = 101 kPa • Frequency = number of cycles per second • Hz = Hertz = cycle/second • Period: P = 1/ f • v = λ⋅ f • v = 343 + 0.6 (T – 20 C) m/s

36. Physics 1251 Unit 1 Session 4 Thinking as a Physicist Summary: • Observe—see what is there. • Abstract—ideate the significant. • Measure—compare to standard. • Model—use math. • Predict—risk a prognostication. • Compare—check it out.

37. Physics 1251 Unit 1 Session 4 Thinking as a Physicist Summary (cont’d.): • Units: fundamental—second, meter, kilogram; derived—Hz, N, Pa • Scale Prefixes: M, k, c, m, μ • Scientific notation: 1.234 x 103 [1.234 E03 or 1.234 03 ] • Experimental error • Significant figures • Insufficiency of induction

38. Physics 1251 Unit 1 Session 5 Simple Harmonic Oscillators Summary: • A Simple Harmonic Oscillator is a device that oscillates at one frequency, determined by the spring constant k and the mass m of the system. • The natural frequency of an SHO moving in sinusoidal motion is related to these quantities by the equation: f = 1/(2π) ‧ √ (k/m)

39. Physics 1251 Unit 1 Session 6 Helmholtz Resonators and Vibration Modes Summary: • A Helmholtz Oscillator is a SHO comprised of an enclosed air volume and a narrow neck and has a single frequency. • A normal or natural mode of vibration or oscillation is one of the fundamental ways that a device can move. • The number of modes is equal to the number of simple harmonic oscillators in the system. • Degeneracy means two or more normal modes have the same frequency.

40. Physics 1251 Unit 1 Session 7 Good Vibrations Summary: • Waveforms can be broken down into simple sine waves, called Fourier Analysis. • Waveforms can be built up from simple sine waves, called Fourier Synthesis. • The lowest frequency needed is 1/Prepeat. • A Fourier Spectrum is the recipe for building the waveform.

41. Physics 1251 Unit 1 Session 8 Harmonic Series Summary: • Aharmonic seriesis the sum of sine wave components each frequency of which is an integral multiple of the fundamental frequency. • Ohm’s Law : humans do not sense the phase of sound directly. • Intensity determines loudness • Frequencydetermines pitch. • Waveform (harmonic series) determines timbre. • An octave interval corresponds to a frequency ratio of 2 : 1.

42. Physics 1251 Unit 1 Session 9 Transients and Resonances Summary: • Transients occur because radiation and friction damp the various harmonics differently. • Resonance is the phenomenon of sympathetic vibration at a natural frequency with energy supplied by an outside source. • Sound transmits energy since pressure = force/area and a displacement occurs as a sound wave passes.