Standing waves
A fixed pattern of nodes and antinodes made by two waves moving in opposite directions. Only certain frequencies fit.
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Analogy
A guitar string vibrating in one big loop.
Example
f1 = v / (2L)f1 = 260 / 1.3f1 = 200 Hzf2 = 400 Hz
In practice
A 0.65 m string with wave speed 260 m/s has a lowest note of 200 Hz.
Practice
Flashcards
- What is a node?A point on a standing wave that never moves.
Interview questions
- Explain how a standing wave forms on a guitar string and find the first three frequencies for a 0.65 m string with wave speed 260 m/s.
- Two waves moving opposite ways superpose
- Ends are nodes
- f_n = n v / 2L gives 200, 400, 600 Hz
Questions people ask
What are nodes and antinodes?
Nodes are points on a standing wave that stay still, where the two waves always cancel. Antinodes are points halfway between nodes where the movement is largest. The distance between two neighbouring nodes is half a wavelength, which helps when measuring wavelength on a string.
Why do different instruments sound different at the same note?
Each instrument produces the main frequency plus a particular mix of higher harmonics. The mix gives the sound its timbre. A violin and a flute may both play 440 Hz, but the strengths of their overtones differ, so you can tell them apart.