Standing waves

1. 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;