Compute the gravitational and Coulomb force betweentwo protons in 3He. Assume the distance between theprotons is equal to the nuclear radius. The average nuclearpotential energy is an attractive 40 MeV effectiveover a distance of 3.0 fm. Compare that energy with thepotential energies associated with the gravitational andCoulomb forces at the same distance.
Musical Scales First Instrument – human voice 100,000 yrs ago Libya – simple 1note whistle was made Oldest known song – a religious hymn in Ugarit 3400 yrs ago. Pythagoras of Crotona – first studied how music was made monochord – box with 1 string and a bridge. An equal ratio of frequencies sounds like an equal difference or interval of pitch. Scale – progression of tones ascending from a fundamental frequency known as the tonic. Chromatic scale: 12 tone scale with all semitone steps Diatone scale: 7 tone scale that includes five wholetone steps and two semitone steps To find a certain key in a scale, say a 5 , multiply the tonic by the corresponding ratio. With Just Temperament it is impossible to tune all notes or tones of the chromatic scale. Equal Temperament Developed to allow musicians to play in any key without retuning All semitones are the same size Can transpose the notes to change the scale. A semitone is 1/12 of an octave A cent (¢) is 1/100 of a semitone or 1/1200 of an octave 1 octave = 1200¢ Pitch interval corresponding to f1 and f2 H:f1 = (1200¢/log2)log(f2/f1) Individual notes in Just and Equal temperament are close enough to sound the same. The difference is in the chords. Equal temperament is best for piano Just temperament is best for strings On the standard keyboard, the sharps # and flats b are enharmonic (same frequency) Strings Musical Instrument Components 1) Mechanical energy source – to create the sound 2) Frequency generator – to change the sound 3) Frequency