DP1 Physics Waves

Simple Harmonic Motion

- Oscillations around an equilibrium position

- Resisitive force F acting against displacement, in turn acceleration proportional to negative displacement

Amplitude

The maximum displacement of a particle in a wave from the equilibrium position.

Frequency

How many cycles occur in 1 second for a wave.

Wave (mechanical)

A wave which involves oscillating masses

Wave (electromagnetic)

A transverse wave composed of perpendicular electric and magnetic oscillating fields traveling at a speed of 3.0 × 10⁸ m s⁻¹ in free space.

Transverse wave

A wave in which the oscillations are perpendicular to the direction of transfer of energy. In other words, particles vibrate perpendicular to the direction of the wave's velocity.

Crest

The point of positive amplitude on a transverse wave

Trough

The point of negative amplitude on a transverse wave

Longitudinal wave

Waves in which the oscillations are parallel to the direction of transfer of energy. In other words, particles vibrate parallel to the direction of the wave's velocity.

Compressions

Places of increased density and pressure of a medium as a longitudinal wave passes through it.

Rarefactions

Places of reduced density and pressure of a medium as a longitudinal wave passes through it.

Wavelength, λ

The distance between two adjacent crests of a wave; the shortest distance between two points moving in phase.

Time period, T

The time taken for one complete wave to pass a point.

Wave speed, v

The speed at which energy is transferred by a wave.

Pulse (wave)

A traveling wave of short duration.

Sound

Longitudinal waves in air or other media that are audible to humans.

Principle of superposition

The resultant of two or more waves arriving at the same point can be determined by the vector addition of their individual displacements.

Constructive interference

Two waves combine in order to create a wave with a stronger amplitude.

Destructive interference

Two waves cancel each other out, creating a wave with less or zero amplitude.

Coherent waves

Waves that have the same frequency and a constant phase difference.

Interference

Superposition effect that may be produced when similar waves meet. Most important for waves of the same frequency and similar amplitude.

Standing wave

A wave formed by two similar traveling waves moving in opposite directions. Most commonly formed when waves are reflected back upon themselves. The wave pattern does not move, and the waves do not transfer energy.

Nodes

The positions in a standing wave where the amplitude is zero.

Antinodes

The positions in a standing wave where the amplitude is greatest.

Boundary conditions

The conditions at the ends of a system. These conditions affect, in standing waves, whether there are nodes or antinodes at the ends. In travelling waves, it affects the phase and direction of travel.

Open end

Standing: An antinode is formed. Travelling: Wave axis orientation remains and there is no phase difference.

Closed/fixed end

Standing: A node is formed. Traveling: Wave flips over the x-axis and its phase shifts by π.

Reflection (waves)

Change of direction that occurs when travelling waves meet a boundary such that the waves return into the medium from which they came.

Harmonics

Different frequencies (modes) of standing wave vibrations of a given system. The frequencies are all multiples of the frequency of the first harmonic.

Modes of vibration

The different ways in which a standing wave can arise in a given system. (Eg. with a node, antinode)

Natural frequency

The frequency at which a system oscillates when it is disturbed and then left to oscillate on its own, without influence from outside.

Fundamental frequency, f₀

The first harmonic of a standing wave; the lowest possible frequency.

In phase

Particles that

- In travelling waves: have the same displacement at the same time

- In standing waves: are in the same point of their cycle at the same time

Out of phase

Particles that

- In travelling waves: have different displacements at the same time

- In standing waves: are in different points in their cycle at the same point in time

Phase difference

Difference in phase, represented with π.

Resonance

An increase to maximum amplitude that occurs when the driving frequency of an external oscillator in phase matches the natural frequency of a system.

Damping

A decrease in amplitude and dissipation of energy that occurs when resistive forces act on an oscillating system.

Light damping

The system continues to oscillate, but its amplitude decreases at an exponential rate as time goes on. The resonant frequency also decreases.

Heavy damping

The system quickly and gradually dissipates all of its energy. It no longer oscillates and instead returns slowly to its equilibrium position.

Critical damping

The system returns to equilibrium as quickly as possible, with minimal or no oscillation.

Travelling wave

A wave that transfers energy away from a

source. Sometimes called a progressive wave.

Phase

A relative measurement of the difference in position within the wave cycle between two points on a wave