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?