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Physics 1251 The Science and Technology of Musical Sound

Physics 1251 The Science and Technology of Musical Sound. Unit 1 Session 9 Transients and Resonances. Physics 1251 Unit 1 Session 9 Transients and Resonances. Foolscap Quiz: What are the following quantities for the waveform below? Period, Frequency, Amplitude and Phase.

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Physics 1251 The Science and Technology of Musical Sound

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  1. Physics 1251The Science and Technology of Musical Sound Unit 1 Session 9 Transients and Resonances

  2. Physics 1251 Unit 1 Session 9 Transients and Resonances Foolscap Quiz: What are the following quantities for the waveform below? Period, Frequency, Amplitude and Phase. P =5.0 ms =0.0050 sec; f = 1/P = 200. Hz; A = 2.0 mPa; Phase = +25% (90⁰)

  3. Physics 1251 Unit 1 Session 9 Transients and Resonances 80/20Period is the time from one point on a wave to a corresponding point on the next. 80/20Frequency (in Hz)= 1/Period (in seconds). 80/20Amplitude is the maximum excursion from equilibrium for a wave. 80/20Phase is the shift (measured in fraction of a cycle) for a wave relative to a time standard.

  4. Physics 1251 Unit 1 Session 9 Transients and Resonances 1′ Lecture: • Sound carries mechanical energy. • Frequency spectra can change with time producing transients as energy is dissipated by radiation and frictional forces. • Resonance is the strongly driven oscillation, occurring at natural frequencies of the natural modes of oscillation.

  5. Physics 1251 Unit 1 Session 9 Transients and Resonances 80/20Work=Force x distance movedW =F‧d . 80/20Energy is the work performed or stored. E = W; [W]= Joule = N∙m 80/20Energy is conserved; it changes form but is never really lost . 80/20Heat is a form of energy.

  6. Physics 1251 Unit 1 Session 9 Transients and Resonances TheSimple Harmonic Oscillator of Doom

  7. Physics 1251 Unit 1 Session 9 Transients and Resonances Why doesn’t the bowling ball return to the same height? • Energy is conversed, i.e. total energy is constant. • The bowling ball does work (a little) moving the air out of the way. { Recall: W = F‧d } • Therefore, the bowling ball has less energy to make it up the “hill.”

  8. Physics 1251 Unit 1 Session 9 Transients and Resonances 80/20Sound waves carry energy. 80/20Power is the rate of energy dissipation or radiation.ℙ = W/t; [ℙ]= Watt = Joule/sec 80/20Intensity is the power/square meter. I = ℙ/A ; [I ] =Watt/m 2 .

  9. Physics 1251 Unit 1 Session 9 Transients and Resonances Energy Dissipation: If a constant fraction of the energy is dissipated every second, the amplitude of an oscillator “decays” exponentially.

  10. Physics 1251 Unit 1 Session 9 Transients and Resonances “Damped” Simple Harmonic Oscillator

  11. Physics 1251 Unit 1 Session 9 Transients and Resonances Transients are due to work done by the SHO. Energy of SHO Heat

  12. Physics 1251 Unit 1 Session 9 Transients and Resonances Where does the “lost energy” go? • Energy is conversed, i.e. total energy is constant. • The SHO does work (a little each cycle) moving the air or water out of the way. { Recall: W = F‧d } • Therefore, the SHO slows down a little each cycle. It has less energy. • Ultimately, the energy goes into heat (random motion of air molecules).

  13. Physics 1251 Unit 1 Session 9 Transients and Resonances “Dr. M’s Energy Conservation Furnace” • Rub your hands together briskly. • What do you feel? • Why?

  14. Physics 1251 Unit 1 Session 9 Transients and Resonances 80/20Higher frequencies tend to “damp” more rapidly than do lower frequencies. Why? ΔE = Energy dissipated in each cycle = (damping) force x distance. Energy dissipated per second = Energy dissipated per cycle x cycles per second = ΔE ∙ f.

  15. Physics 1251 Unit 1 Session 9 Transients and Resonances Time Dependent Fourier Spectrum: Observe Transients

  16. Physics 1251 Unit 1 Session 9 Transients and Resonances Time Dependent Fourier Spectrum: Observe Transients Piano Transient Frequency Spectrum Amplitude of Component Frequency

  17. Physics 1251 Unit 1 Session 9 Transients and Resonances Resonantly Driven Simple Harmonic Oscillator

  18. Push Physics 1251 Unit 1 Session 9 Transients and Resonances Resonantly Driven Simple Harmonic Oscillator Wait 1 period

  19. Physics 1251 Unit 1 Session 9 Transients and Resonances Resonance: An oscillator will absorb energy and grow in amplitude when the energy is supplied at a frequency near that of a natural mode. Helmholtz Resonator Video Demonstration

  20. Physics 1251 Unit 1 Session 9 Transients and Resonances “Resonantly Driven” Simple Harmonic Oscillator

  21. 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.

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