AQA Physics A Unit 2 Chapters 12 and 13 Waves and Optics Dr K. Newson TGSG Physics Dept.
Waves and their properties Chapter 12 AQA PHY 2
Section 1 Wave Types and Polarisation Objectives: • Know the differences between transverse and longitudinal waves • Be able to describe a plane-polarised wave • Know the physical test that can distinguish between transverse and longitudinal waves.
Types of wave • There are two types: • Longitudinal waves • Transverse waves • Waves can also be categorized in terms of their origins, i.e. either: • Electromagnetic e.g. light, UV • Mechanical e.g. sound or seismic
Longitudinal Waves 1) Longitudinal Wave: The vibration of particles is parallel to the direction of the wave. • E.g. sound waves, some seismic waves.
Longitudinal waves in springs Transverse Wave: The vibration (red arrow) is parallel to the wave’s direction (black arrow). • E.g. sound waves.
Transverse Waves Transverse Wave: The vibration (red arrow) is perpendicular to the wave’s direction (black arrow). • E.g. light waves (or any electromagnetic waves).
End-on view Polarisation • In reality, unpolarised transverse waves have displacements in every plane, but all the directions are at right angles to the direction of the wave. Direction of wave Wave vibrations are in more than one plane
Wave vibrations are in just one plane End-on view Polarisation contd. • Transverse waves that are plane polarised have vibrations that are in one plane only. Note: Longitudinal waves cannot be polarised as the vibration is parallel to the wave’s direction of motion.
Polarising filters • A polarising filter is a sheet of plastic material. The sheet allows vibrations to pass through in one plane only. • The molecules that make up polarising filters are aligned so that they act like billions of slits. The slits will only allow the component of light that is in the same direction as the slit to pass through. Wave passes through Wave doesn’t pass through
Polarising filters Filter will polarise the light in the vertical plane If rotated by 90o the light will be polarised in the horizontal plane
Polarisation of light Unpolarised light Polarizing filter Plane polarised light
Polarisation of light A second filter will stop the light if it is at right angles to the first filter. Light is stopped by two filters at right-angles
Polarisation of light If the second filter is in the same orientation as the first then the light will still only be polarised in the same plane.
Section 2 Measuring Waves Objectives: • Know what amplitude of a wave is • Know between which two points a wavelength can be measured • Know how to calculate frequency from time period
Waves – Key terms All waves can be characterised in terms of their: • Displacement: The distance and direction of a particle from its equilibrium position. • Amplitude: The maximum displacement of a vibrating particle. • Cycle: this refers to one full wave passing. • Frequencyf : The number of complete cycles (vibrations) of a particle per unit time. This measured in Hertz (Hz). • Wavelengthλ: The distance between two neighbouring points on a wave that are vibrating in phase e.g. two successive peaks or troughs. • Period T: The time for one complete cycle of a wave.
λ Representing waves Amplitude λ Length/m
T Representing waves Amplitude T Time
Wave speed (c) • The time taken for one cycle = 1/f • Since frequency = number of waves per second, and the wavelength = length of each wave, then: • Frequency × wavelength = total length per second = speed • In symbols: c = fλ
Phase angle and phase difference • The Phase angle is a measure of how far through a cycle an oscillation is. • Note: 1 complete cycle = 360o in degrees, this is equal to 2π radians. • We can use degrees, radians or wavelength as a measure of phase difference. • Remember:
Phase difference These oscillations are in step, they are said to be in phase. Their phase difference is zero.
Phase difference • These oscillations are a ¼ of a cycle out of phase. Their phase difference is π/2 radians (90o), or λ/4
Phase difference These oscillations are ½ of a cycle out of phase. They are said to be in anti-phase. Their phase difference is π radians (180o) = λ/2.
Section 3 Reflection, Refraction and Diffraction Objectives: • Know what causes waves to refract when they pass across a boundary • Know which way light waves refract when passing from glass into air • Be able to define diffraction
Wavefronts • Wavefronts are lines joining points of a wave that are in phase • In the diagrams below line PP, QQ, and RR represent wavefronts • The distance between wavefronts is equal to the wavelength Circular wavefronts Plain wavefronts R P Q R Q P λ λ λλλλ λ P Q R P Q R
Wavefronts contd. • The expanding circles in the wave train are called wave fronts.
Reflection • Straight waves that hit a hard flat surface reflect off at the same angle. • That means that: the angle of incidence = the angle of reflection • This effect occurs when light strikes a plane mirror. • More later in the Optics work.
Refraction • When waves pass a boundary where their wave speed changes, the wavelength also changes. For EM waves this occurs where there is a change in density of the medium. • If the wave fronts cross the boundary at an angle that is not aligned with the normal, then they change direction as well as speed. This is called refraction. • More later in the Optics work.
Diffraction • Diffraction is the spreading of waves after passing a gap or around the edge of an obstacle. • Diffraction is at a maximum when: • The wavelength is large. • The gap is the same size as the wavelength of the wave. • The wavelength is approximately the same size as the obstacle.
Diffraction Strong diffraction as gap width ≈ λ
Diffraction If the wavelength does not match the size of the gap, then only a little diffraction will occur (at the edge of the wave).
Section 4 Superposition Objectives: • Know what causes reinforcement • Be able to explain phase difference • Know the phase difference that produces maximum cancellation • Be able to explain why maximum cancellation is difficult to achieve
Travelling waves • Water, sound and electromagnetic waves convey energy from the source that produces them. For this reason they are known as travelling or progressive waves.
Superposition • When two or more waves meet, their displacements superpose. • The Principle of superposition states that when two waves overlap, the resultant displacement at a given instant is equal to the vector sum of the individual displacements.
Constructive superposition = Two waves of the same wavelength that are in phase add constructively. This is also known as constructive interference. The end result is an increase in amplitude, with no change in λ
Destructive superposition • If the two waves are in antiphase, they cancel each other. The resulting amplitude will be zero. This is also known as destructive interference.
Coherence Coherence is an essential condition for the interference of waves. Two sources of waves are described as coherent if: • The waves have the same wavelength. • The waves are in phase or have a constant phase difference. • Lasers are an example of a coherent source of light. Light from a normal filament bulb is not coherent since the light is emitted randomly from the individual atoms in the filament
Sections 5&6 Stationary and Progressive Waves Objectives: • Describe what’s needed to form a stationary wave • Know if stationary waves are formed by superposition • Explain why nodes are in fixed positions • Know how frequencies of overtones compare to the fundamental
Experiments • Three demonstrations of stationary waves • Melde’s apparatus (string) using sheet wv6
Stationary waves (a.k.a. standing waves) If two waves of equal frequency and amplitude, travelling along the same line with the same speed, but in opposite directions meet, they undergo superposition to produce a wave pattern in which the positions of the crests and troughs do not move. This pattern is called a stationary wave.
Nodes and Antinodes N N N N N N A A A λ/2 A = antinode N = node
Nodes and Antinodes • The places labelled N are called nodes, the amplitude at nodes is zero. Nodes are caused by destructive superposition. • The places labelled A are called antinodes, the amplitude is at a maximum at the antinodes. Antinodes are caused by constructive superposition. • The distance between adjacent nodes (or adjacent antinodes) is half a wavelength.
N A N X Y Stationary wave patterns • Different stationary wave patterns are obtained at certain resonant frequencies. • The simplest standing wave pattern consists of a single loop • If the string has a length L, then L= λ/2 • This simplest mode of oscillation is called the fundamental and occurs at the fundamental frequency.
Harmonics • If the frequency is doubled, the next stationary wave pattern is formed. This is called the first harmonic. A A N N N If the string has a length L, then λ= L
Harmonics • The trend continues for the other resonant frequencies, remember each single loop has a length of λ/2. Each subsequent harmonic adds one single loop • The frequencies only occur at certain values because the length of string (or air column or other) must equal a whole number of half wavelengths i.e. L = nλ/2. • This effect is often used in music written for violins.
Stationary Waves on a Vibrating String • Carry out the experiment described on p.184 • Setting for the fundamental, 1st and 2nd overtones. • Fundamentals have nodes at either end and an antinode in the middle, so λ0=2L. Hence f0=c/λ0=c/2L • The next stationary wave pattern is the first overtone this has a node in the middle, so the string has two loops, so λ1=L. Hence f1=c/λ1=c/L=2f0 • The next stationary wave pattern is the first overtone this has a node in the middle, so the string has two loops, so λ2=2/3L. Hence f2=c/λ2=3c/2L=3f0 • Stationary waves occur at f0, 2f0, 3f0, 4f0, etc.
Energy and stationary waves • A travelling wave carries energy in its direction of travel. • A stationary wave consists of two identical travelling waves acting in opposite directions. Therefore, the two waves convey equal energies in opposite directions. • The net effect of this is that NO energy is transferred by a stationary wave.
Y Thick rubber cord X Signal generator Vibration generator Demonstration of stationary waves 1) On a string/cord The cord is fixed at positions X and Y.
Simulation of Stationary waves • http://www.walter-fendt.de/ph14e/stwaverefl.htm