Beats, Resonance and the Doppler Effect

Name: Beats, Resonance and the Doppler Effect
Author: StemPy Lab

Beats from two close frequencies, and how a tuner uses them. The resonance tube with its end correction. The Doppler effect for a moving source, a moving observer and 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
Beats
Two sounds of close frequencies drift in and out of step. The sound swells and fades $f_b = |f_1 - f_2|$ times each second. You hear a pitch half way between them. Tuners use beats to match a note, and to find an unknown frequency.
1 simulation2 practice questions1 Python program4 problems1 Python lab
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Lesson 2about 30 min
The resonance tube
A fork over a tube of air closed by water makes the air boom when $l + e = \lambda/4$ , then $3\lambda/4$ . Two resonances give $\lambda = 2(l_2 - l_1)$ and the speed of sound, $v = 2f(l_2 - l_1)$ . The end correction is $e = (l_2 - 3l_1)/2$ , close to $0.3d$ .
1 simulation2 practice questions1 Python program4 problems1 Python lab
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Lesson 3about 30 min
The Doppler effect
When a source or a listener moves along the line between them, the frequency heard changes: $f' = f\,\dfrac{v \pm v_o}{v \mp v_s}$ , with the upper signs for moving towards. A source passing by drops in pitch. A moving reflector gives a change in two steps.
1 simulation2 practice questions1 Python program4 problems1 Python lab1 question set1 note
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Beats, Resonance and Doppler: Mock Exam

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