M USIC

S TANDING W AVES At the right frequencies a constrained wave will produce a standing wave Standing waves appear stationary Result of constructive and destructive interference Have nodes and antinodes

N ODES AND A NTINODES Nodes Wave doesn’t move Destructive interference Antinodes Wave moves Constructive interference

H ARMONICS Fundamental frequency Two nodes Half a wavelength in between ends Pattern of standing waves is called the harmonic series

H ARMONIC S ERIES String or pipe open at both ends n = 1, 2, 3, 4, … String – both ends are nodes Open pipe – both ends are antinodes Pipe closed at one end n = 1, 3, 5, … Pipe open at one end – closed side in node, open side in antinode

I NSTRUMENTS Vibrating strings Violins, guitars, bass etc. Piano, harpsichord Pipe open at both ends Flute Pipe open at one end and closed at the other Saxophone, clarinet, trumpet, trombone, etc.

T IMBRE Different instruments playing the same note sound different because of harmonics The intensity of the harmonics varies between instruments Changes the timbre, or sound quality of each instrument

B EATS When two waves of different frequencies interfere the result is a complex interference pattern The result is areas of constructive interference and areas of destructive interference This amplitude variation are the beats And the frequency with which they vary is the beat frequency Beat frequency is the difference between the original two waves frequency

C ONSONANCE AND D ISSONANCE Depends on the frequency difference between two tones Varies between cultures and eras Consonance Octave Perfect fourth Perfect fifth Dissonance Minor second Major seventh