Waves by Computer: Adding and Fitting

Name: Waves by Computer: Adding and Fitting
Author: StemPy Lab

Draw travelling waves and standing waves from their equations, add two waves to see beats and interference, build a complex sound from harmonics, and fit a sine curve to noisy measurements.

3 lessons, about 1 h 40 min3 simulations10 problems4 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
Drawing a wave from its equation
A travelling wave is $y = A\sin(kx - \omega t)$ . In numpy, $x$ is an array of positions, so one line gives the wave at one time. Here $k = 2\pi/\lambda$ and $\omega = 2\pi f$ , and the speed is $v = f\lambda$ . Plotting at several times shows a crest moving.
1 simulation1 practice question2 Python programs3 problems1 Python lab
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Lesson 2about 35 min
Adding waves: beats and standing waves
Waves add point by point: $y = y_1 + y_2$ . Two close frequencies give beats at $|f_1 - f_2|$ . Two equal waves running opposite ways give a standing wave $2A\sin(kx)\cos(\omega t)$ with nodes half a wavelength apart. Odd harmonics build a square wave.
1 simulation1 practice question4 Python programs4 problems
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Lesson 3about 40 min
Fitting a sine curve to data
Real readings are noisy. The FFT in numpy shows which frequencies a signal holds and gives a first guess. Then scipy's curve_fit finds the amplitude, frequency and phase of the best sine, with an error for each. Read too slowly and a fast wave looks slow.
1 simulation2 practice questions4 Python programs3 problems1 Python lab1 question set1 note
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Waves by Computer: Adding and Fitting

Course outline (3 lessons)

Drawing a wave from its equation

Adding waves: beats and standing waves

Fitting a sine curve to data

Test Your Learning

Your teacher

Discussion (0)