6.6 Signal Superposition, Beats, and Interference of Sound Waves

Superposition of Sound Waves

When two or more sound waves overlap, their displacements add algebraically — this is superposition. If crests align with crests (in phase), you get constructive interference (louder sound). If crests align with troughs (out of phase), you get destructive interference (quieter or silent). The result depends on the path difference between the waves relative to their wavelength.

Beats: Interference in Time

When two sound waves of slightly different frequencies overlap, they produce beats — periodic rises and falls in loudness heard as the waves alternately reinforce and cancel. The beat frequency equals the absolute difference between the two source frequencies: f_beat = |f₁ − f₂|. Beats are a useful way to tune instruments by listening for the beats to slow and disappear.

Constructive vs. Destructive Interference Conditions

For two coherent sound sources, constructive interference occurs when the path difference is a whole number of wavelengths (Δ = nλ), producing loud spots. Destructive interference occurs when the path difference is a half-integer number of wavelengths (Δ = (n + ½)λ), producing quiet spots. This creates a pattern of loud and quiet regions in space.

Key terms

Superposition

The principle that overlapping waves combine by adding their displacements at each point in space and time.

Constructive interference

Occurs when waves are in phase (path difference = nλ), resulting in a larger amplitude/louder sound.

Destructive interference

Occurs when waves are out of phase (path difference = (n + ½)λ), resulting in reduced amplitude/quieter sound.

Beats

Periodic loudness variations produced when two sound waves of slightly different frequencies interfere.

Beat frequency formula

f_beat = |f₁ − f₂|, the absolute difference between two interfering wave frequencies.

Try an AP-style question

Two tuning forks of 440 Hz and 444 Hz sound together. What beat frequency is heard?

1. 4 Hz
2. 884 Hz
3. 442 Hz
4. 2 Hz