Physics / Unit 7: Waves and Sound
7.5 Superposition and Interference
Notes
When two waves meet, their displacements add. This is the principle of superposition.
- Constructive interference: crest meets crest; the combined amplitude is larger.
- Destructive interference: crest meets trough; the waves partly or fully cancel.
- From two sources in step, a path difference of a whole number of wavelengths gives constructive interference; a half-wavelength path difference gives destructive interference.
- Beats: two close frequencies make the loudness pulse at the beat frequency $f_{\text{beat}} = |f_1 - f_2|$.
- Noise-canceling headphones use destructive interference.
Practice
Two waves of amplitude 3 cm meet crest to crest. What is the amplitude where they overlap?
Constructive interference adds the amplitudes: $3 + 3 = 6 \text{ cm}$.
A tuning fork of 440 Hz and a guitar string of 444 Hz sound together. How many beats per second are heard?
$f_{\text{beat}} = |444 - 440| = 4 \text{ Hz}$.
Two speakers play the same tone in step. At a point, the sound from one speaker travels half a wavelength farther than from the other. What is heard there?
A half-wavelength path difference lines up crests with troughs.
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