1. Music, Superposition and Chords Physics 11Adv

2. Comprehension Check 1. What beat frequency would you expect if two trumpets play the same note but one sounds 440Hz and the other 438Hz? 2. Complete the superposition (analytically) if x = 0, amplitude is unity and ω 1 = 3 and ω 2 = 6. Simplify as much as possible.

3. Comprehension Check 1. 2.0Hz 2. Complete the superposition:

4. Chromatic Scale The chromatic scale (A, A#, B, C, C#, D, D#, E, F, F#, G, G#) has been around for centuries and the note frequencies can be determined mathematically Each semitone is represented by 100 cents and provided a root frequency, the remaining frequencies can be determined

5. Chromatic Scale Determine the notes of one full octave of the chromatic scale, using f 0 =440Hz and c=0, 100, 200, …, 1200 Assuming the speed of sound to be 343m/s, determine the angular frequency and wavenumber for each frequency

6. Chromatic Scale Note Frequency (Hz)c Wavelength (m) Omega (rad/s) Wavenumber (m^-1) A44000.78027658.06 A#4661000.73629298.54 B4942000.69431039.05 C5233000.65632889.59 C#5544000.619348310.16 D5875000.584369010.76 D#6226000.551391011.40 E6597000.520414212.08 F6988000.491438912.79 F#7409000.464464913.56 G78410000.438492614.36 G#83111000.413521915.22 A88012000.390552916.12

7. Basic Music Theory A major chord is constructed with a root note (c = 0), major third (c = 400) and perfect fifth (c = 700) A minor chord is constructed with a root note (c = 0), minor third (c = 300) and perfect fifth (c = 700) The difference between the major third and minor third results in more destructive interference

8. Major Chord

9. Minor Chord