L 20 Course Review

W= mg, where g=9.8 m/s 2 In Previous slide W (=F G ) = F N

Simple Harmonic Motion Position x vs. time t Definition of period T Definition of amplitude A

Frequency and Period f = 1/T or T = 1/f or f T =1 T period, in seconds (s) f = frequency in Hertz (Hz) Metric prefixes: centi- (c), milli- (m), micro- (  kilo- (k), mega- (M)

Wave velocity for a periodic vibration Let the wavelength be λ and the frequency of the vibration be f. The wave velocity v is just V=λ/T, or V= λf

More specifically,  we consider a force acting through a distance.  Work = Force x distance or W = F. d  Units - newtons x meters = joules (J), or  pounds x feet (foot pounds, ft.lbs)  BTU = 778 ft.lbs (energy of one wooden kitchen match)  Pushing on a wall and wall doesn’t move (no work done on the wall) Conversion: 1J= ft.lb

Potential Energy  Energy of position or configuration Other examples - Springs, bow, sling shot, chemical energy, and gravitational potential energy  The latter is GPE = mgh (the force required to lift at constant speed times the distance )

W Power = Work/time or P = W/t Units - J/s = Watt 2.POWER 550 ft. lb/s = 1 hp 1 hp = 746 J/s = 746 W 1 BTU/hr = W 100 W bulb = hp 250 hp engine = 186,450 W

Conditions for standing waves

overpressure L

Closed tubes (closed on one end) overpressure Closed end: antinode open end:node L

We define the Sound Intensity I as the Audio Power crossing a unit area, or I = P/A Units- W/m 2

12-2 Intensity of Sound: Decibels An increase in sound level of 3 dB, which is a doubling in intensity, is a very small change in loudness. In open areas, the intensity of sound diminishes with distance: However, in enclosed spaces this is complicated by reflections, and if sound travels through air the higher frequencies get preferentially absorbed.

12-2 Intensity of Sound: Decibels The loudness of a sound is much more closely related to the logarithm of the intensity. Sound level is measured in decibels (dB) and is defined: (12-1) I 0 is taken to be the threshold of hearing:

12-2 Intensity of Sound: Decibels The intensity of a wave is the energy transported per unit time across a unit area. The human ear can detect sounds with an intensity as low as W/m 2 and as high as 1 W/m 2. Perceived loudness, however, is not proportional to the intensity.

12-3 The Ear and its Response; Loudness The ear’s sensitivity varies with frequency. These curves translate the intensity into sound level at different frequencies.

Note spanInterval Frequency ratio C - Cunison 1/1 C - C#semitone 16/15 C - Dwhole tone (major second) 9/8 C - D#minor third 6/5 C - Emajor third 5/4 C - Fperfect fourth 4/3 C - F#augmented fourth 45/32 C - Gperfect fifth 3/2 C - G#minor sixth 8/5 C - Amajor sixth 5/3 C - A#minor seventh 16/9 (or 7/4) C - Bmajor seventh 15/8 C 3 - C 4 octave 2/1 C 3 - E 4 octave+major third 5/2 Intervals 12-tone scale (chromatic) 8-tone scale (diatonic)

Pythagorean Scale Built on 5ths

A pleasant consonance was observed playing strings whose lengths were related by the ratio of 3/2 to 1 (demo). Let’s call the longer string C, and the shorter G, and the interval between G and C a 5 th Denote the frequency of C simply by the name C, etc.

The major triad is the basis for the just scale, which we now develop in a way similar to that of the Pythagorean scale.

We wish to make a chromatic scale- 12 tones including both octaves- and we want all the intervals (ratios of adjacent notes to all be the same).

Beats f 1 -f 2 = beat frequency Average frequency “heard” = (f 1 +f 2 )/2

Modes Ionian – Major Scale Dorian – 2 nd of Major Scale Phrygian – 3 rd of Major Scale Lydian – 4 th of Major Scale Mixolydian – 5 th of Major Scale Aolian – 6 th of Major Scale (Minor) Locrian – 7 th of Major Scale

Non-Western Scales

Resonance

Fourier Synthesis Demo- PhET (Physics,Fourier)

String Instruments

The Vocal Tract epiglottis

Vocal Formants “had”

To calculate T, consider a room with a hole in one wall of area A. Call the reverberation time T. T ˜ volume V, 1/A T= K V/A It has been worked out that, for V in m 3, A in m 2 T= 0.16 V/A

Let us now replace the open window area with an absorbing material of area S and absorption coefficient a. Then A= Sa. If there is more than one type of absorbing material, the A= S 1 a 1 +s 2 a 2 +S 3 a 3 +…

Basic Analog Electronics Ohm’s Law Links: Bob Holtzworth part 1 slides 1- 11,12,16

Ohm’s Law The current (charge per unit time) flowing through a circuit element is equal to the potential drop across this element divided by the resistance of the element. I= V/R

Digital Electronics Introduction to Binary Numbers

We can write the number 752 as 2x x x10 2 Similarly We could use the base 2, e.g. 3 = 1x x2 1, which we represent as 11. Hence 01 is 2 These are 2-binary digit (bit) numbers.

Digital Sampling

Calculating Bit-rates (CD quality) Sampling Rate xResolutionx # of Channels =Bit-rate 44,100x16x2=1,411,200 Calculating File Sizes (one minute of CD audio) Sampling Rate xResolutionx Number of Channels x Time in Seconds / Bits / Byte = File Size (in Bytes) 44,100x16x2x60/8=10,584,000 MP3 compression at 128 kbps compresses this by a factor of 11

MP 3 Compression

The most important principle in MP3 compression is the psychoacustic selection of sound signals to cut away. Those signals, we are unable to hear are removed. These include weaker sounds that are present but are not heard because they are drowned out (masked) by louder instruments/sounds. Many encoders use the fact that the human ear is most sensitive to midrange sound frequencies (1 to 4 KHz). Hence sound data within this range is left unchanged. An other compression used is to reduce the stereo signal into mono, when the sound waves are so deep, that the human ear cannot register the direction. Also the contents of common information in the two stereo channels is compressed. The Huffman algorithm reduces the file size by optimizing the data code for the most often used signals. This is a lossless compression working within the MP3 system.

More on CDs 750 Mbytes 75 minutes of audio Link: “how Edison got his groove back”

The elongated bumps that make up the track are each 0.5 microns wide, a minimum of 0.83 microns, they look something like this: