m usic. s tanding w aves at the right frequencies a constrained wave will produce a standing wave...

MUSIC

STANDING WAVES

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

NODES AND ANTINODES

Nodes Wave doesn’t move Destructive

interference Antinodes

Wave moves Constructive

interference

HARMONICS

Fundamental frequency Two nodes Half a wavelength in

between ends Pattern of standing

waves is called the harmonic series

HARMONIC SERIES

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

INSTRUMENTS

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.

TIMBRE

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

BEATS 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

CONSONANCE AND DISSONANCE

Depends on the frequency difference between two tones

Varies between cultures and eras

Consonance Octave Perfect fourth Perfect fifth

Dissonance Minor second Major seventh