Lesson Plan 5.a
Sound and Digital Audio – Part 1
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Lesson Title |
Sound and Digital Audio - Part 1 |
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Duration |
1 class (1.5 hours) |
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Synopsis |
In this class we explore the mathematical properties of sine waves, the physical properties of sound and the biophysics of hearing. |
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Description of Class |
This class is divided into several lecture and demonstration sections.
In the first section the properties of waves, including amplitude, frequency, wavelength and speed are described. Sinusoidal waveforms are introduced as a way of describing a number of naturally occurring cyclic/harmonic phenomena, such as tides, moon phases, sunrise and sunset times. Finally waves are treated mathematically as sine functions and depicted as graphical plots.
In the second section the connection is made between vibrations, waves and sound. The properties of sound traveling through a transmission medium and the notion of longitudinal waves are introduced. The ideas of reflection and absorption and their role in producing complex waveforms are introduced.
The third section introduces the idea of synthesizing complex waveforms by combining fundamental sine waves. Examples of the waveforms of real musical instruments are presented. The notion that all wave forms can be decomposed into a series of sine waves (i.e. the Fourier series) is hinted at, but not formally introduced.
The principles behind the conversion (transduction) between pressure levels and electrical current (e.g. microphones and speakers) are introduced.
The last segment of this lesson describes the biophysics of sound perception. In this segment the anatomy of the human ear, from the pinna through the cochlea and into the auditory nerve, is described in some detail. The frequency decomposition by the cochlear hair-cells on the basilar membrane is related back to the composition of complex waves by fundamental sinusoidal components. Finally, binaural hearing and the process of sound localization is explained. |
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Primary Educational Objective |
Properties of waves, including amplitude, frequency, wavelength and speed. Sine and cosine functions. Vibration, sound, longitudinal waves and pressure levels. Anatomy of the human ear. Biophysics of hearing, including the signal (sound) transduction between the physiological components. |
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Additional Concepts and Skills |
Mathematical functions, function notation, graphs of functions. [Relationship between circles and sin/cos functions] Specialized cell structure (cell biology), esp. nerve cells. Communication between cells via electro-chemical reactions. |
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Assessment |
Classroom participation and homework assignment. |
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Classroom Activities |
This class is primarily a lecture using the referenced PowerPoint slides, along with several demonstrations. Demonstrations are given of the sounds produced by a number of different instruments. The relationship between thickness, length and tension is demonstrated for a stringed instrument (e.g. a guitar). Sound waves from a variety of sources are played and displayed as waveforms. |
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Homework Assignments |
The students compose complex sounds by combining fundamental frequencies and harmonics (additive sound synthesis) and with various sound envelopes (i.e. attack, sustain, decay). This could be done as a classroom exercise or a homework assignment. Software tools TBD. |
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Lecture Materials |
Lecture materials are available as a Power Point presentation |
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Reference Materials |
http://en.wikipedia.org/wiki/Waves http://arts.ucsc.edu/EMS/Music/tech_background/TE-13/teces_13.html http://www.cf.ac.uk/biosi/staff/jacob/teaching/sensory/ear.html http://147.162.36.50/cochlea/cochleapages/theory/main.htm http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/sound/u11l4b.html |
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Related Topics |
Mathematical functions of one variable. Circles and angles. Sine and cosine functions. Sound and waves. Vibrations (waves) passing through a medium |
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Technology Requirements |
Sound synthesizer software (TBD). |