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Standing waves . standing waves on a string: reflection of wave at end of string, interference of outgoing with reflected wave  “ standing wave ” nodes: string fixed at ends  displacement at end must be = 0  “( displacement) nodes” at ends of string  not all wavelengths possible;

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standing waves
Standing waves
  • standing waves on a string:
    • reflection of wave at end of string, interference of outgoing with reflected wave “standing wave”
    • nodes: string fixed at ends  displacement at end must be = 0  “(displacement) nodes” at ends of string  not all wavelengths possible;
    • length must be an integer multiple of half-wavelengths: L = n /2, n = 1,2,3,…
    • possible wavelengths are: n = 2L/n, n=1,2,3,…
    • possible frequencies: fn = n  v/(2L), n=1,2,3,….called “characteristic” or “natural” frequencies of the string; f1 = v/(2L)is the “fundamental frequency; the others are called “harmonics” or “overtones”
  • RESONANCE:
    • when a system is excited by a periodic disturbance whose frequency equals one of its characteristic frequencies, a standing wave develops in the system, with large amplitudes; at resonance, energy transfer to the system is maximal
    • examples:
      • pushing a swing;
      • shape of throat and nasal cavity  overtones  sound of voice;
      • musical instruments;
      • Tacoma Narrows Bridge;
      • oscillator circuits in radio and TV;