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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)
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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- (m) kilo- (k), mega- (M)
Wave velocity for a periodic vibrationLet the wavelength be λand the frequency of the vibration be f.The wave velocity v is just V=λ/T, orV= λf
More specifically, • we consider a force acting through a distance. • Work = Force x distance or W = F.d • Units - newtonsx 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= 0.738 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 )
2. POWER Watt Power = Work/time or P = W/t Units - J/s = W 550 ft.lb/s = 1 hp 1 hp = 746 J/s = 746 W 1 BTU/hr = 0.293 W 100 W bulb = 0.1341 hp 250 hp engine = 186,450 W
L overpressure
L Closed tubes(closed on one end) overpressure Closed end: antinode open end:node
We define the Sound Intensity Ias the Audio Power crossing a unit area,or I= P/AUnits- W/m2
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) I0 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 10-12 W/m2 and as high as 1 W/m2. 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.
Intervals 12-tone scale (chromatic) 8-tone scale (diatonic) Note span Interval Frequency ratio C - C unison 1/1 C - C# semitone 16/15 C - D whole tone (major second) 9/8 C - D# minor third 6/5 C - E major third 5/4 C - F perfect fourth 4/3 C - F# augmented fourth 45/32 C - G perfect fifth 3/2 C - G# minor sixth 8/5 C - A major sixth 5/3 C - A# minor seventh 16/9 (or 7/4) C - B major seventh 15/8 C3 - C4 octave 2/1 C3 - E4 octave+major third 5/2
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 5thDenote 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).
Beatsf1-f2 = beat frequencyAverage frequency “heard” = (f1+f2)/2
Modes • Ionian – Major Scale • Dorian – 2nd of Major Scale • Phrygian – 3rd of Major Scale • Lydian – 4th of Major Scale • Mixolydian – 5th of Major Scale • Aolian – 6th of Major Scale (Minor) • Locrian – 7th of Major Scale
