Superposition and Standing Waves

Name: Superposition and Standing Waves
Author: StemPy Lab

The principle of superposition and the interference of two waves. Reflection at a fixed and at a free end. Standing waves and the normal modes of a string, and of pipes closed at one end or open at both.

3 lessons, about 1 h 30 min3 simulations12 problems6 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 30 min
Superposition and interference
When two waves meet, the displacement at each point is the sum of their displacements. This is the principle of superposition. Two waves of the same frequency with a phase difference $\phi$ add to a wave of amplitude $2a\cos(\phi/2)$ , so they can help each other or cancel.
1 simulation2 practice questions1 Python program4 problems1 Python lab
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Lesson 2about 30 min
Standing waves on a string
A wave reflected at a fixed end comes back inverted, and at a free end it comes back upright. The incident and reflected waves add to a standing wave $y = 2a\sin kx\cos\omega t$ , with nodes $\lambda/2$ apart. A string tied at both ends vibrates in normal modes $f_n = \dfrac{nv}{2L}$ .
1 simulation2 practice questions1 Python program4 problems
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Lesson 3about 30 min
Standing waves in air columns
Air in a pipe holds standing waves too. A closed end is a node and an open end an antinode. A pipe closed at one end has only odd harmonics, $f = \dfrac{(2n - 1)v}{4L}$ . A pipe open at both ends has every harmonic, $f = \dfrac{nv}{2L}$ .
1 simulation2 practice questions1 Python program4 problems1 Python lab1 question set1 note
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Superposition and Standing Waves: Timed Test

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Superposition and Standing Waves

Course outline (3 lessons)

Superposition and interference

Standing waves on a string

Standing waves in air columns

Test Your Learning

Your teacher

Discussion (0)