# Oscillatory Motion and Waves

## Connection for AP® Courses

In this chapter, students are introduced to oscillation, the regular variation in the position of a system about a central point accompanied by transfer of energy and momentum, and to waves. A child’s swing, a pendulum, a spring, and a vibrating string are all examples of oscillations. This chapter will address simple harmonic motion and periods of vibration, aspects of oscillation that produce waves, a common phenomenon in everyday life. Waves carry energy from one place to another.” This chapter will show how harmonic oscillations produce waves that transport energy across space and through time. The information and examples presented support Big Ideas 1, 2, and 3 of the AP® Physics Curriculum Framework.
The chapter opens by discussing the forces that govern oscillations and waves. It goes on to discuss important concepts such as simple harmonic motion, uniform harmonic motion, and damped harmonic motion. You will also learn about energy in simple harmonic motion and how it changes from kinetic to potential, and how the total sum, which would be the mechanical energy of the oscillator, remains constant or conserved at all times. The chapter also discusses characteristics of waves, such as their frequency, period of oscillation, and the forms in which they can exist, i.e., transverse or longitudinal. The chapter ends by discussing what happens when two or more waves overlap and how the amplitude of the resultant wave changes, leading to the phenomena of superposition and interference.
The concepts in this chapter support:
Big Idea 3 The interactions of an object with other objects can be described by forces.
Enduring Understanding 3.B Classically, the acceleration of an object interacting with other objects can be predicted by using 
  .
Essential Knowledge 3.B.3 Restoring forces can result in oscillatory motion. When a linear restoring force is exerted on an object displaced from an equilibrium position, the object will undergo a special type of motion called simple harmonic motion. Examples should include gravitational force exerted by the Earth on a simple pendulum and a mass-spring oscillator.
Big Idea 4 Interactions between systems can result in changes in those systems.
Enduring Understanding 4.C Interactions with other objects or systems can change the total energy of a system.
Essential Knowledge 4.C.1 The energy of a system includes its kinetic energy, potential energy, and microscopic internal energy. Examples should include gravitational potential energy, elastic potential energy, and kinetic energy.
Essential Knowledge 4.C.2 Mechanical energy (the sum of kinetic and potential energy) is transferred into or out of a system when an external force is exerted on a system such that a component of the force is parallel to its displacement. The process through which the energy is transferred is called work.
Big Idea 5 Changes that occur as a result of interactions are constrained by conservation laws.
Enduring Understanding 5.B The energy of a system is conserved.
Essential Knowledge 5.B.2 A system with internal structure can have internal energy, and changes in a system’s internal structure can result in changes in internal energy. [Physics 1: includes mass-spring oscillators and simple pendulums. Physics 2: includes charged object in electric ﬁelds and examining changes in internal energy with changes in conﬁguration.]
Big Idea 6 Waves can transfer energy and momentum from one location to another without the permanent transfer of mass and serve as a mathematical model for the description of other phenomena.
Enduring Understanding 6.A A wave is a traveling disturbance that transfers energy and momentum.
Essential Knowledge 6.A.1 Waves can propagate via different oscillation modes such as transverse and longitudinal.
Essential Knowledge 6.A.2 For propagation, mechanical waves require a medium, while electromagnetic waves do not require a physical medium. Examples should include light traveling through a vacuum and sound not traveling through a vacuum.
Essential Knowledge 6.A.3 The amplitude is the maximum displacement of a wave from its equilibrium value.
Essential Knowledge 6.A.4 Classically, the energy carried by a wave depends on and increases with amplitude. Examples should include sound waves.
Enduring Understanding 6.B A periodic wave is one that repeats as a function of both time and position and can be described by its amplitude, frequency, wavelength, speed, and energy.
Essential Knowledge 6.B.1 The period is the repeat time of the wave. The frequency is the number of repetitions over a period of time.
Essential Knowledge 6.B.2 The wavelength is the repeat distance of the wave.
Essential Knowledge 6.B.3 A simple wave can be described by an equation involving one sine or cosine function involving the wavelength, amplitude, and frequency of the wave.
Essential Knowledge 6.B.4 The wavelength is the ratio of speed over frequency.
Enduring Understanding 6.C Only waves exhibit interference and diffraction.
Essential Knowledge 6.C.1 When two waves cross, they travel through each other; they do not bounce off each other. Where the waves overlap, the resulting displacement can be determined by adding the displacements of the two waves. This is called superposition.
Enduring Understanding 6.D Interference and superposition lead to standing waves and beats.
Essential Knowledge 6.D.1 Two or more wave pulses can interact in such a way as to produce amplitude variations in the resultant wave. When two pulses cross, they travel through each other; they do not bounce off each other. Where the pulses overlap, the resulting displacement can be determined by adding the displacements of the two pulses. This is called superposition.
Essential Knowledge 6.D.2 Two or more traveling waves can interact in such a way as to produce amplitude variations in the resultant wave.
Essential Knowledge 6.D.3 Standing waves are the result of the addition of incident and reﬂected waves that are conﬁned to a region and have nodes and antinodes. Examples should include waves on a ﬁxed length of string, and sound waves in both closed and open tubes.
Essential Knowledge 6.D.4 The possible wavelengths of a standing wave are determined by the size of the region to which it is conﬁned.
Essential Knowledge 6.D.5 Beats arise from the addition of waves of slightly different frequency.