4.5 Standing Waves

Question 1

Standing Wave

Answer 1

Phenomena within which a wave exhibits a pattern where it seems it is fixed in space, and only its amplitude changes over time

Question 2

Standing Waves Occur When

Answer 2

Two waves:

• Of same frequency
• Of same amplitude
• Travelling in opposite directions

Question 3

Nodes

Answer 3

Points on the wave which are always at rest

Question 4

Antinodes

Answer 4

Points on the wave at which the maximum movement takes place

Question 5

Boundary Conditions

Answer 5

The conditions that must be met at the edges (boundaries) of the system when standing waves are taking place. When these are met by a standing wave, it will be a possible resonant mode of the system

Question 6

Steps for Standing Transverse Wave on a String

Answer 6

1. Take string of length L
2. Keep both ends fixed, one attached to an oscillator
3. Travelling wave created towards fixed end
4. Waves reflect at fixed end, so two waves created travelling in opposite directions at once
5. Standing wave formed

Question 7

First Harmonic

Answer 7

The standing wave with the longest wavelength and lowest frequency

Question 8

Harmonic Wavelength Formula

Answer 8

λ = 2L/n where n = number of harmonic

Question 9

Harmonic Frequency Formula

Answer 9

f = n(v/2L) where n = number of harmonic

Question 10

Longitudonal Sound Waves in a Pipe

Answer 10

• Can be set up in a column of air in a pipe from reflections that take place at both ends
• Closed end must be node, open end must be antinode

Question 11

Wavelength of Pipe with One End Open/Closed

Answer 11

λ = 4L/n where n = number of harmonics (odd only)

Question 12

Frequency of Pipe with One End Open/Closed

Answer 12

f = n(v/4L) where n = number of harmonics (odd only)