Lecture 12 - Standing Waves

what are standing waves

waves formed due to superposition of two waves of same A-amplitude, f-frequency and wavelength travelling in opposite directions in the same medium

why are standing waves called standing waves

doesn’t appear to be travelling, the cord appears to have segments that oscillate up and down in a fixed position

stand waves can occur in….

strings = transverse waves

air columns = longitudinal waves

frequency of harmonics: string fixed at both ends

fn = n(v/2L) where n = 1, 2, 3…

speed of wave on string

v = root(F/(m/L))

standing waves in air columns: types

open pipes = flute

closed pipes = clarinet

harmonics for flutes

fn = nf1 where n = 1, 2, 3…

closed pipes (clarinets) only produce … harmonics

odd

the shorter the length of a clarinet the … the frequency

higher

interference of waves: what are they and types

superposition of two travelling waves in the same medium

constructive = waves are in phase

restructure = when waves are out of phase

beats - interference in time

when two sound waves of slightly different frequencies f1 and f2 superimpose the loudness of the resulting sound rises and falls periodically = beats

2 successive overtones of vibrating string are 280 Hz and 350 Hz, frequency of fundamental?

f2 - f1 = 350 - 280 = 70 Hz