21/04/23

WavesWaves

W Richards

The Weald School

21/04/23

Simple Harmonic MotionSimple Harmonic Motion

Definition: simple harmonic motion is when acceleration is proportional to displacement and is always directed towards equilibrium.

21/04/23

Simple Harmonic MotionSimple Harmonic MotionConsider a pendulum bob:

Let’s draw a graph of displacement against time:

Displacement

Time

Equilibrium position “Sinusoidal”

21/04/23

SHM GraphsSHM Graphs

Time

Displacement

Velocity

Acceleration

Time

Time

21/04/23Waves revisionWaves revision

Watch a “Mexican Wave”

21/04/23Some definitions…Some definitions…

1) Amplitude – this is “how high” the wave is:

2) Wavelength () – this is the distance between two corresponding points on the wave and is measured in metres:

3) Frequency – this is how many waves pass by every second and is measured in Hertz (Hz)

21/04/23Transverse vs. longitudinal Transverse vs. longitudinal waveswaves

Transverse waves are when the displacement is at right angles to the direction of the wave…

Longitudinal waves are when the displacement is parallel to the direction of the wave…

Dis

pla

cem

en

tDirection

Direction

Displacement

21/04/23

The Wave EquationThe Wave Equation

The wave equation relates the speed of the wave to its frequency and wavelength:

Wave speed (v) = frequency (f) x wavelength ()

in m/s in Hz in m

V

f

21/04/23

1) A water wave has a frequency of 2Hz and a wavelength of 0.3m. How fast is it moving?

2) A water wave travels through a pond with a speed of 1m/s and a frequency of 5Hz. What is the wavelength of the waves?

3) The speed of sound is 330m/s (in air). When Dave hears this sound his ear vibrates 660 times a second. What was the wavelength of the sound?

4) Purple light has a wavelength of around 6x10-7m and a frequency of 5x1014Hz. What is the speed of purple light?

Some example wave equation Some example wave equation questionsquestions

0.2m

0.5m

0.6m/s

3x108m/s

21/04/23Refraction RevisionRefraction Revision

21/04/23Refraction through a glass Refraction through a glass

block:block:

Wave slows down and bends towards the normal due to

entering a more dense medium

Wave speeds up and bends away from the normal due to entering a less dense

medium

Wave slows down but is not bent, due to

entering along the normal

21/04/23Finding the Critical Angle…Finding the Critical Angle…

1) Ray gets refracted

4) Ray gets internally reflected3) Ray still gets refracted (just!)

2) Ray still gets refracted

THE CRITICAL ANGLE

21/04/23Uses of Total Internal Uses of Total Internal ReflectionReflection

Optical fibres:

An optical fibre is a long, thin, _______ rod made of glass or plastic. Light is _______ reflected from one end to the other, making it possible to send ____ chunks of information

Optical fibres can be used for _________ by sending electrical signals through the cable. The main advantage of this is a reduced ______ loss.

Words – communications, internally, large, transparent, signal

21/04/23

Wave diagramsWave diagrams1) Reflection

4) Diffraction3) Refraction

2) Refraction

21/04/23DiffractionDiffraction

More diffraction if the size of the gap is similar to the wavelength

More diffraction if wavelength is increased (or frequency decreased)

21/04/23Sound can also be diffracted…Sound can also be diffracted…

The explosion can’t be seen over the hill, but it can be heard. We know sound travels as waves

because sound can be refracted, reflected (echo) and diffracted.

21/04/23Diffraction depends on Diffraction depends on frequency…frequency…

A high frequency (short wavelength) wave doesn’t get diffracted much – the house won’t be able to receive

it…

21/04/23Diffraction depends on Diffraction depends on frequency…frequency…

A low frequency (long wavelength) wave will get diffracted more, so the

house can receive it…

21/04/23

Phase DifferencePhase DifferencePhase difference means when waves have the same frequency but oscillate differently to each other. For example:

These two waves have different amplitudes but the same frequency and hit their peaks at the same time – they are “in phase”

These two waves start opposite to each other – they are “in antiphase” or “out of phase by π radians”

21/04/23

Phase DifferencePhase Difference

What is the phase difference between each of these waves?