Unit 7 of AP Physics 1: Waves and Sound.
This unit covers wave properties, interference, standing waves and sound — essential concepts for AP Physics 1. Use our interactive study games to test your understanding, or review questions in traditional format below.
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This unit covers wave properties, interference, standing waves and sound — essential concepts for AP Physics 1. Use our interactive study games to test your understanding, or review questions in traditional format below.
Key Concepts Breakdown
1 Wave Properties
Students must understand the relationships between wave speed, frequency, and wavelength (v = fλ) and how each property is determined. Wave speed depends on the medium, not the source. Transverse and longitudinal waves differ in the direction of particle displacement relative to wave propagation.
Key Points
- v = fλ; increasing frequency decreases wavelength if speed is constant
- Wave speed changes when the medium changes; frequency does not change at a boundary
- Amplitude determines energy carried by a wave, not speed or frequency
- Transverse: displacement perpendicular to propagation (e.g., string); Longitudinal: displacement parallel (e.g., sound)
A wave travels from shallow water (speed 2 m/s) to deep water (speed 4 m/s). If the frequency in shallow water is 5 Hz, find the wavelength in deep water.
Frequency stays constant across the boundary: f = 5 Hz. In deep water, λ = v/f = 4/5 = 0.8 m. The wavelength doubles because the speed doubled while frequency remained unchanged — a classic boundary-crossing question.
2 Wave Interference
When two waves occupy the same region, they superpose: the net displacement is the algebraic sum of individual displacements. Constructive interference occurs when crests align (path difference = nλ); destructive interference occurs when a crest meets a trough (path difference = (n + ½)λ). After passing through each other, waves continue unchanged.
Key Points
- Superposition principle: displacements add algebraically at every point
- Constructive interference: path difference = 0, λ, 2λ… → amplitude doubles
- Destructive interference: path difference = λ/2, 3λ/2… → amplitude cancels
- Interference is a property of waves; particles do not interfere this way
Two speakers emit sound at 340 Hz. A student stands 4.0 m from speaker A and 4.5 m from speaker B. Speed of sound = 340 m/s. Does the student hear constructive or destructive interference?
First find wavelength: λ = v/f = 340/340 = 1.0 m. The path difference is |4.5 − 4.0| = 0.5 m = λ/2. Since the path difference equals a half-wavelength, the waves arrive out of phase and destructive interference occurs — the student hears reduced or no sound.
3 Standing Waves
Standing waves form when a wave reflects back on itself in a bounded medium, creating fixed nodes (zero displacement) and antinodes (maximum displacement). For strings fixed at both ends and open pipes, harmonics follow fn = nf₁; for closed pipes (one closed end), only odd harmonics are present. Students must be able to sketch mode shapes and calculate frequencies.
Key Points
- String fixed at both ends: L = nλ/2, so f₁ = v/(2L); all harmonics present
- Open pipe (both ends open): same harmonic series as fixed string
- Closed pipe (one end closed): L = nλ/4 for odd n only; f₁ = v/(4L)
- Nodes are always at fixed/closed ends; antinodes are at open ends
A guitar string of length 0.65 m has a wave speed of 520 m/s. Find the fundamental frequency and the frequency of the third harmonic.
For a string fixed at both ends, f₁ = v/(2L) = 520/(2 × 0.65) = 400 Hz. The third harmonic is f₃ = 3f₁ = 1200 Hz. On the exam, always start with the fundamental formula and multiply by the harmonic number — do not re-derive from scratch each time.
4 Sound
Sound is a longitudinal mechanical wave that requires a medium; it cannot travel through a vacuum. The Doppler effect describes the shift in observed frequency when the source or observer is moving: when they approach each other the observed frequency is higher, when they recede it is lower. Students must qualitatively and semi-quantitatively reason about Doppler shifts on the exam.
Key Points
- Sound speed in air ≈ 343 m/s at 20°C; increases with temperature and in denser media (liquids > gases)
- Intensity decreases with distance squared (inverse square law for point sources)
- Doppler effect: approaching → higher observed frequency; receding → lower observed frequency
- Beats result from two slightly different frequencies; beat frequency = |f₁ − f₂|
A student plays two tuning forks simultaneously: one at 440 Hz and one at 444 Hz. What does the student hear, and at what rate?
The two sound waves interfere constructively and destructively periodically, producing beats. The beat frequency = |444 − 440| = 4 Hz, so the student hears the sound grow loud and soft 4 times per second. Beat problems on the exam often ask what happens when one fork is loaded with wax — if the beat frequency changes, you can infer the direction of the frequency shift.
Questions, answered.
What is Waves and Sound?
Waves and Sound is Unit 7 of AP Physics 1, covering wave properties, interference, standing waves and sound.
How to study for AP Physics 1 Unit 7?
Start with the Quick Summary above, review the Key Concepts, then test yourself with our interactive study games. Aim for 80%+ accuracy before moving on.
How many questions are in this unit?
This unit has 28+ review questions across 5 different game modes.