Physics 1251 The Science and Technology of Musical Sound Unit 1 Session 9 Transients and Resonances 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. P =5.0 ms = sec; f = 1/P = 200. Hz; A = 2.0 mPa; Phase = +25% (90⁰)

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

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

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

Physics 1251 Unit 1 Session 9 Transients and Resonances The Simple Harmonic Oscillator of Doom

Physics 1251 Unit 1 Session 9 Transients and Resonances Why doesn’t the bowling ball return to the same height? Why doesn’t the bowling ball return to the same height? (1)Energy is conversed, i.e. total energy is constant. (2) The bowling ball does work (a little) moving the air out of the way. { Recall: W = F‧d } (3) Therefore, the bowling ball has less energy to make it up the “hill.”

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

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.

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

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

Physics 1251 Unit 1 Session 9 Transients and Resonances Where does the “lost energy” go? Where does the “lost energy” go? (1)Energy is conversed, i.e. total energy is constant. (2) The SHO does work (a little each cycle) moving the air or water out of the way. { Recall: W = F‧d } (3) Therefore, the SHO slows down a little each cycle. It has less energy. (4) Ultimately, the energy goes into heat (random motion of air molecules).

Physics 1251 Unit 1 Session 9 Transients and Resonances “Dr. M’s Energy Conservation Furnace” 1.Rub your hands together briskly. 2.What do you feel? 3.Why?

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

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

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

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

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

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

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

Physics 1251 Unit 1 Session 9 Transients and Resonances Summary: Transients occur because radiation and friction damp the various harmonics differently. 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. 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. Sound transmits energy since pressure = force/area and a displacement occurs as a sound wave passes.