IB HL Physics (2023) - Wave Behaviour

Angular Frequency

Radians turned per second (Rad s^-1)

displacement

how far away in m a pendulum or particle of a wave is from the equilibrium

Simple Harmonic Motion

Motion of a Simple pendulum or Mass spring where the restoring force / acceleration is directly proportional to the extension in the opposite direction

One Cycle of SHM

One full cycle of SHM is:

• one time period

• one oscillation

• 2π rad

Time Period of a Pendulum

• does not depend on mass or displacement'

  • when L is greater the period is longer

Natural (Resonant) Frequency

The frequency an oscillator vibrates at freely after an initial disturbance

Forced Vibrations

it’s possible to force an object to vibrate using a periodic driving force. The frequency of this force is called the driving frequency

Resonance

Occours when the driving frequency matches the natural frequency which leads to maximum the amplitude being achieved

Damping

The way a system performing SHM loses energy to its surroundings. The heavier the damping the faster the amplitude decrease

Types of Damping

• Over Damping - the displaced object returns very slowly to the equilibrium position

• Critical Damping - The displaced object returns to equilibrium as fast as possible

Standing Wave

A wave that does not transfer energy or matter, and has nodes which dont move and antinodes which do move

Travelling Wave

A wave which transfers energy but not matter

Transverse Wave

A Travelling Wave in which the particles oscillate perpendicular to the direction of energy transfer

Longitudinal Waves

A Travelling Wave in which the particles oscillate parallel to te direction of energy transfer

Mechanical Waves

• A wave that involves the movement of particles

• a transverse mechanical wave would be water ripples

  • a longitudinal mechanical wave would be sound waves

EM Waves

• Transverse waves that can travel through a vaccum or through a medium

• made of a pair of oscillating magnetic and electric fields

• travel at 3 ×10⁸ ms^-1 in a vaccum

Key Wave Features

• Amplitude - maximum displacement of the wave from the equilibrium (m)

• Wavelength - shortest distance between two points in phase (m)

• Time Period - Time it takes for one complete Oscillations (s)

• Frequency - The number of Oscillations per second (Hz = s^-1)

• Wavespeed - The distance a wave travels in a second (ms^-1)

Displacement - Distance Graph

can be used to determine amplitude and wavelength

Displacement - Time Graph

can be used to determine ampiltude and period

Phase Difference

The amount in metres degrees or radians that one wave lags behind another

waves in phase have an even Phase Difference (2π, 4π, 6π). Waves out of phase have an odd Phase Difference (π, 3π, 5π)

Law of Reflection

when a wave is reflected off a boundary the angle of incidence is equal to the angle of reflection

Wavefronts

parts of a wave that are in phase with eachother

Rays

Lines perpendicular to the wavefronts that show direction of energy transfer

Waves at Boundaries

waves can undergo:

• Reflection

• Refraction

• Transmission

• Diffraction

• Absorption

• Scattering

Waves in different materials

• in a more dense medium waves slow down and bend towards the normal

• in a less dense medium wave speed up and bend away from the normal

Refraction

The change of a wave’s wavelength speed or direction as it enters a new medium

Refractive index

The ratio of the speed of light to the speed of light in a medium

Total Internal reflection

Reflection of a wave within an object.

Occurs when the angleof incidence is in the more dense subject and the angle of incidence is greater than the critical angle

Critical angle

Sinθ_c= n1/n2 OR v1/v2

Principle of Superposition

When two or more waves cross, the resultant displacement equals the vector sum of the individual displacements

Interference

• The result of superposition of two waves

• can be:

  • constructive (Phase difference = n*λ)

  • or destructive (Phase difference = [n+1/2]*λ)

Diffraction

the spreading of waves through an aperture/slit or around an obstacle

diffraction is greatest when the wavelength is similar to the slit size

Young’s Double slit

• Two slits act as coherent sources

• curved wavefronts overlap and interfere

• an interference pattern of light and dark fringes is produced on the screen

Double slit intensity graphy

• all fringes are equal width

• central fringe (order of maximum = 0) has maximum intensity, decreasing for subsequent fringes

Huygens’ Principle

The wavefront of a travelling wave consists of circular wavelets created by every point on the previous wavefront.

Single Slit Diffraction

• a wave will diffract through a single slit

• the greatest diffraction happens when λ≈b

• each part of the wave can act as its own source

• each point of the wave can interfere and superpose with another part of the wave

Single Slit intensity graph

• Central maximum is double the width of the secondary maxima on either side

• secondary maxima greatly reduce in intensit

Double slit modulation

when light passes through the slits both single slit and double slit intereference occour, leading to a double slit pattern modulated by the single slit envelope

Multi-Slit interference

As the number of slits increases:

• the intensity of primary maxima increases

• the primary maxima become shaper

• the secondary maxima become less bright

Multi-Slit intensity pattern

the number ofsecondary maxima between each primary maxima is equal to the number of slits -2

Diffraction grating

an optical element with many parallel slits which produces bright maxima at discrete points along the sceen

Reflection off an end

When a rave reflects off a closed end the reflected wave inverts and is pi radians out of phase withthe incidence wave

When a wave reflects off an open end the wave doesnt invert and stays in phase

Coherent waves

Waves with a constant phase difference between them

Standing wave formation

When two coherent waves with the same amplitude, travelling in opposite directions, interfere with each other, superposition occurs and a standing wave is formed.

Nodes and Antinodes

• Nodes are point of no displacement

• antinodes are points of displacement

• allparticles in an antinode are in phase with eachother

• adjacent antinodes are out of phase by pi radians

harmonics

• the harmonic number refers to the number of antinodes that form in a standing wave

• the wavelength and frequency of a wave are different in each harmonic

• There will always be a node at a fixed end and an antinode at an open end

Two fixed/open ends

For two closed or open ends the frequency that forms the ‘n’th harmonic is always

f_n = nc/2L (when n = the harmonic number)

One closed and One open end

The harmonic number refers to the number of quarter waves visible. Therfore there can only be odd harmonic numbers because one end must always be an antinode

f_n =nc/4L (when n = the harmonic number)

Doppler effect

the apparent change in frequency of a wave due to relative motion between the source and the observer.

Moving source

When the source is moving the wavefronts are compressed or expanded and so the percieved wavelength changes

Moving Observer

The wavelength is constant but the observers experience of the frequency changes

Double Doppler

The double doppler effect occours when the observer and source are moving in opposite directions either towards or away from eachother

Uses of Dopper Effect

• Determining the distance to a galaxy

• Determining the speed of things like blood or cars