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This is PHYS 1240 - Sound and Music Lecture 11 Professor Patricia Rankin Cell Phones silent Clickers on Remember - Learning Team – you can email/skype/facetime/zoom in virtual office hours Graduate student Teaching Assistant Tyler C Mcmaken - online 10-11am Friday Undergraduate Learning Assistants Madeline Karr Online 6-7pm Monday Rishi Mayekar Online 11-12noon Thur Miles Warnke Online 3-4pm Wed Professor Patricia Rankin Online 2-3pm Wed Physics 1240 Lecture 11 Today: Timbre, Fourier, Sound Spectra, Sampling Size Next time: Sound Intensity, Intervals, Scales physicscourses.colorado.edu/phys1240 Canvas Site: assignments, administration, grades Homework – HW5 Due Wed February 19th 5pm Homelabs – Hlab3 Due Monday Feb 24th 5pm Debrief – Last Class(es) Waves in pipes Open-open n=1,2,3,4 Closed-open n = 1,3,5 Pressure nodes at open ends, pressure antinodes at closed ends Displacement nodes/antinodes opposite to pressure ones. Open-open 푓푛=푛∙푣푠/2퐿 So, fundamental doesn’t depend just on length of pipe Closed-open 푓푛=푛∙푣푠/4퐿 Homework hints Check your units You can use yx key to find 2n Be aware – you may need to do some manipulation e.g. Suppose question asks you to find the mass/unit length of a string given velocity, tension…. You know F 2 퐹 , 퐹 v 푠표, 푣푡 = 휇 = 2 t 휇 푣푡 Timbre – the tone color/voice of an instrument Timbre is why we can recognize different instruments from steady tones. Perception Physics Pitch Frequency Consonance Frequencies are ratios of small integers Loudness Overall amplitude Timbre Amplitudes of a harmonic series of notes Superposition We can add/superimpose sine waves to get a more complex wave profile Overall shape (Timbre) depends on the frequency spectra (the frequencies of waves added together), and the amplitudes of the waves Ohm's acoustic law, sometimes called the acoustic phase law or simply Ohm's law (but another Ohm’s law in Electricity and Magnetism), states that a musical sound is perceived by the ear as the fundamental note of a set of a number of constituent pure harmonic tones. The law was proposed by physicist Georg Ohm in 1843. Fourier Theorem – for any periodic waveform Suppose a waveform is periodic with period T. We say it has fundamental frequency f1=1/T Any periodic waveform with period T can be expressed as a superposition of sinusoidal waves with multiples of fundamental frequency (Fourier Synthesis) f1=1·f1 , f2=2·f1 , f3=3·f1 , f4=4·f1 , f5=5·f1 , f6=6·f1 , … This is a harmonic series. Some of the wave amplitudes can be zero. The timbre is determined by the amplitudes of the sinusoidal waves in the harmonic series. Ohm’s Law: you can hear the frequencies and amplitudes but not the phases. All of the harmonics meet each other at the fundamental frequency! (This is the pitch that you hear) 1st Harmonic 3rd Harmonic 5th Harmonic Sum Not all sounds are periodic! Periodic: steady tones from musical instruments, pattern of sound repeats multiple times Not Periodic: Most transient and percussion sounds. Chaotic sounds. Superposition/Decomposition We add/superimpose sine waves to get a more complex wave profile E.g. 100Hz, 200 Hz, 300 Hz (100 Hz base) E.g. 400 Hz, 600 Hz (200 Hz base, 600 not an integer multiple of 400) We can also take a complex periodic wave form and break it down into components Decomposition Fourier Analysis There is a mathematical process you can use to do this – basically looking for amplitudes of component sine waves Clicker 11.1 Which statement is false: A) Some complex periodic waveforms do not have a harmonic series B) A steady tone produces a harmonic series C) A pure tone produces only the fundamental frequency D) The pitch is determined by the fundamental frequency Clicker 11.1 Which statement is false: A) Some complex periodic waveforms do not have a harmonic series B) A steady tone produces a harmonic series C) A pure tone produces only the fundamental frequency D) The pitch is determined by the fundamental frequency Clicker 11.2 3 sine waves are added together to produce a sound. Which set of frequencies would produce the sensation of a distinct pitch? a) 105, 205, 305 Hz b) 100, 200, 300 Hz c) 113, 217, 323 Hz d) All of the above Clicker 11.2 B 3 sine waves are added together to produce a sound. Which set of frequencies would produce the sensation of a distinct pitch? a) 105, 205, 305 Hz b) 100, 200, 300 Hz Want group of frequencies that are low n multiples of a fundamental frequency c) 113, 217, 323 Hz d) All of the above Clicker 11.3 In this superposition waveform periodic? A) Yes B) No Clicker 11.3 A In this superposition waveform periodic? A) Yes B) No Clicker 11.4 If sine waves of frequency 200, 300, 500 Hz are added together, what is the repetition frequency of the resulting complex waveform? a) 100 Hz b) 200 Hz c) 300 Hz d) 500 Hz e) None of the above Clicker 11.4 A If sine waves of frequency 200, 300, 500 Hz are added together, what is the repetition frequency of the resulting complex waveform? a) 100 Hz b) 200 Hz c) 300 Hz d) 500 Hz e) None of the above Fourier Synthesis • Goal: recreate any periodic sound by combining harmonics with set amplitudes (“additive synthesis”) • Spectrum: list of relative amplitudes of harmonics present in a sound • Simplest examples: Sine Sawtooth Square Fourier Synthesis and the Harmonic Series f1 fundamental 2nd harmonic 2f1 3rd harmonic 3f1 overtones • • • sum Sum of pure tones gives a complex waveform The more waveforms you add in – the smoother it gets… - sum an infinite series… • Noise: waveforms have no periodicity, inharmonic spectrum • Tones: periodic waveforms, harmonic spectrum Compare “time domain” to “frequency domain” (i.e. look at “frequency spectrum”) Individual waves (one low-freq., one high-freq.) Summed waves Frequency Spectrum Fourier Synthesis • Instruments: usually have harmonics and noise components • Timbre can change on the same instrument playing different pitches or volumes Flute spectrum https://www.youtube.com/watch?v=VRAXK4QKJ1Q Types of Noise • White: flat spectrum; cymbals/snare/“sh”, acoustics EQ test • Pink: equal energy per octave, testing speakers, background • Violet: acoustic thermal noise of water • Brownian: random walk Types of Noise (ctd.) • Grey: equal loudness at all frequencies.
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