Standing Waves Flashcards
(6 cards)
Standing Waves
When identical waves travelling in opposite directions overlap, they produce stationery points of constructive and destructive interference. This can occur when a single wave is reflected back on itself.
Nodes - destructive interference and 180˚ out of phase
Antinodes - constructive interference and in phase
String Harmonics
When a string is vibrated, multiple standing wave patterns are formed simultaneously atop each other. These patterns are called harmonics. Each has a different wavelength and frequency. A string fixed at both ends has nodes at both. The λ for the first harmonic is 2L (L being the length of the string) because L is the length of half a wavelength, therefore a whole λ will be two times L.
Open Pipe Harmonics
An open pipe has antinodes at both ends.
Closed Pipe Harmonics
The open end of a closed pipe is always an antinode. As waves travelling down the pipe they reflect off the closed end and experience a 180˚ phase change. As the incident and reflected wave are exactly out of phase at the closed end, a node is always formed there.
Only odd harmonics are possible. Closed pipes cannot form even harmonics because they require an antinode at one end and a node at the other. Therefore, as you add 1/4 of a λ with each harmonic, you can’t have even-numbered harmonics.
Timbre
Notes played on musical instruments consist of all the frequencies of the excited harmonics, superimposed. The physical structure of an instrument affects how much each of these harmonic frequencies are emphasised. This gives every instrument a unique sound signature, called timbre.
Beating
When waves are observed from two sources at different frequencies, the waves alternate between in phase and out of phase. This results in moments of high amplitude with constructive interference (in phase) and of low amplitude with destructive interference (out of phase). These are beats.
