AP PHYSICS 1 — physicsMedium3 min read

Mechanical Waves & Sound

AP Physics 1 study guide for mechanical waves and sound: wave properties, standing waves, interference, resonance, and the Doppler effect.

Tutor AI Team2026-02-26T00:08:45.359Z

# Mechanical Waves & Sound — AP Physics 1

Waves transfer energy without transferring matter. AP Physics 1 covers the properties of mechanical waves (including sound), superposition, standing waves, and resonance. Understanding wave behavior is important for both the multiple-choice and free-response sections.

Key Concepts

Wave Properties

Wavelength ( $\lambda$ ): distance between successive crests (or any two equivalent points).
Frequency ( $f$ ): number of complete cycles per second (Hz).
Period ( $T = 1/f$ ): time for one complete cycle.
Amplitude ( $A$ ): maximum displacement from equilibrium.
Wave speed: $v = f\lambda$

Transverse vs. Longitudinal Waves

Transverse: oscillation is perpendicular to wave travel (e.g., waves on a string).
Longitudinal: oscillation is parallel to wave travel (e.g., sound waves).

Wave Speed on a String

$v = \sqrt{\frac{F_T}{\mu}}$ where $F_T$ is tension and $\mu = m/L$ is linear mass density.

Superposition and Interference

Constructive interference: waves add (crest + crest).
Destructive interference: waves cancel (crest + trough).
The resultant displacement is the sum of individual displacements.

Standing Waves

Formed by superposition of two waves traveling in opposite directions.

On a string fixed at both ends:

Wavelengths: $\lambda_n = \frac{2L}{n}$ for $n = 1, 2, 3, \ldots$
Frequencies: $f_n = \frac{nv}{2L}$
$n = 1$ : fundamental (first harmonic)

In an open pipe (open at both ends):

Same as string: $f_n = \frac{nv}{2L}$ , all harmonics.

In a closed pipe (closed at one end):

$f_n = \frac{nv}{4L}$ , odd harmonics only ( $n = 1, 3, 5, \ldots$ ).

Sound

Sound is a longitudinal mechanical wave.
Speed of sound in air: $\approx 343\ \text{m/s}$ at $20°\text{C}$ .
Intensity relates to amplitude squared; loudness is measured in decibels.

Doppler Effect (Conceptual)

Source moving toward observer: frequency increases (higher pitch).
Source moving away: frequency decreases (lower pitch).

Worked Example

Problem: A guitar string of length $0.65\ \text{m}$ has a fundamental frequency of $330\ \text{Hz}$ . What is the wave speed on the string?

Solution:

Fundamental: $f_1 = v/(2L)$

$v = 2Lf_1 = 2(0.65)(330) = 429\ \text{m/s}$

Practice Questions

1. A wave has frequency $500\ \text{Hz}$ and wavelength $0.68\ \text{m}$ . What is the wave speed?

$v = f\lambda = 500 \times 0.68 = 340\ \text{m/s}$ .

2. A string vibrates in its third harmonic with $L = 1.2\ \text{m}$ . What is the wavelength?

$\lambda_3 = 2L/3 = 2(1.2)/3 = 0.8\ \text{m}$ .

3. A closed pipe is $0.5\ \text{m}$ long. What is the fundamental frequency? (Use $v = 340\ \text{m/s}$ .)

$f_1 = v/(4L) = 340/(4 \times 0.5) = 170\ \text{Hz}$ .

4. Two speakers emit the same frequency in phase. At a point equidistant from both, is the interference constructive or destructive?

Constructive — the path difference is zero, so the waves arrive in phase.

Want to check your answers and get step-by-step solutions?

Summary

Wave speed: $v = f\lambda$ .
Standing waves form at specific resonance frequencies determined by boundary conditions.
Open pipes support all harmonics; closed pipes support only odd harmonics.
Sound is a longitudinal wave; the Doppler effect shifts frequency based on relative motion.

Tags:

#ap#physics#waves

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