Transcript 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;