example: pluck string at 1/4 point from end.

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Presentation transcript:

example: pluck string at 1/4 point from end. Plucked String example: pluck string at 1/4 point from end. which harmonics will be strong? which harmonics will be absent? Answer: 2nd harmonic has belly where string is plucked: STRONGEST 4th harmonic has NODE where string is plucked: ABSENT 8th harmonic …. ABSENT other harmonics: more or less present, depending how much amplitude they have at pt. where plucked.

Pipes (woodwinds, brass, organ pipes) an “open” pipe PH 109 Lecture 8 10/1/2001 Pipes (woodwinds, brass, organ pipes) an “open” pipe (open at both ends) L at open end, no pressure build-up because air is free to escape: OPEN END is always a PRESSURE NODE

Fundamental Oscillation: fundamental freq: air press. L (T = round trip travel time) Example:find length of flute of frequency C = 260 Hz demo: 1.25 m long pipe

How change pitch of pipe? f = v/2L air flow half a period later: air press. L air press. L How change pitch of pipe? f = v/2L can ONLY change L (fingerholes on flute) can’t change speed of sound v! diameter has (almost) no effect!

pan pipe Pan and Nymph

Higher modes of flute: example f1 first mode (fundamental) 260Hz f2 = 2f1 second mode (first overtone) 520Hz f3 = 3f1 third mode (second overtone) 780Hz fn = nf1 MODES ARE HARMONICS demo: modes of pipe - plastic tube graphs of pressure and air velocity on blackboard at pressure node air speed has antinode at pressure antinode air speed had node why?

Closed Pipe Pipe closed at ONE end: closed end pressure antinode L air press. L = l/4

fundamental frequency of closed pipe: note: this is half the frequency of an open pipe of same length (octave below) open end: pressure NODE (motion antinode) closed end: pressure antinode (motion node)