AP Physics 2: Unit 6 - Mechanical Waves and Acoustics

Mechanical wave

A disturbance that travels through a medium, transporting energy and momentum without transporting matter.

Transverse Waves

Waves where particle vibration is perpendicular to the direction of energy propagation.

Longitudinal Waves

Waves where particle vibration is parallel to the direction of energy propagation, consisting of compressions and rarefactions.

Period (T)

The time it takes for one complete cycle to pass a point, measured in seconds.

Frequency (f)

The number of cycles per second, measured in Hertz (Hz).

Wavelength (λ)

The distance between two consecutive identical points on a wave, measured in meters.

Amplitude (A)

The maximum displacement from the equilibrium position in a wave.

Wave Equation

The relationship between wave speed, frequency, and wavelength: v = λf.

Speed of a wave

Determined only by the physical properties of the medium, not by frequency or amplitude.

Frequency and medium

When a wave passes from one medium to another, its speed and wavelength change, but frequency remains constant.

Energy carried by a wave

Proportional to the square of its amplitude; doubling the amplitude quadruples the energy.

Constructive Interference

When waves meet in phase, leading to an increased amplitude.

Destructive Interference

When waves meet out of phase, leading to a decreased amplitude.

Sound

A longitudinal mechanical wave that travels as a pressure wave with compressions and rarefactions.

Speed of Sound

Generally increases with the density and stiffness of the medium, vsolids > vliquids > v_gases.

Beat Frequency

The frequency of variation in volume when two sound sources emit slightly different frequencies.

Doppler Effect

The apparent change in frequency of a wave detected by an observer due to relative motion.

Observer Frequency (f_obs)

The frequency heard by the observer, influenced by their motion relative to the source.

Closed Pipe Harmonics

In a closed pipe, only odd integer harmonics are allowed (n = 1, 3, 5,…).

Nodes

Points of zero amplitude in a standing wave where no displacement occurs.

Antinodes

Points of maximum amplitude in a standing wave where constructive interference occurs.

Boundary Rules for Strings

Nodes at both ends for strings or antinodes at both ends for open pipes.

Harmonics for Open Pipes

All integer harmonics are present, following the formula: λ_n = 2L/n.

Harmonics for Closed Pipes

Only odd integer harmonics are allowed, following the formula: λ_n = 4L/n.

Frequency vs. Speed Confusion

Misconception that increasing frequency makes a sound wave travel faster; speed is a property of the medium.

Changing Media Misconception

Belief that changing medium changes frequency; frequency is determined by the source.

Doppler Errors

Selecting the wrong signs in the Doppler equation; must assess motion to determine sign.