Module 4- Waves

Module 4- Waves

1. 4.1 Oscillations

   • Oscillations
     • Oscillations are vibrations that repeat themselves
     • Maximum displacement is the amplitude
     • Point of zero displacement is the equilibrium position
     • Period is the time it takes for the mass to make one full oscillation
     • Frequency is how many cycles occur per second
     • f=1/T
     • The wavelength is the distance from crest to crest or trough to trough
     • The speed at which the crest moves is the wave speed- rate at which disturbance can travel through the medium
       • v=lambda/T
       • v=f lambda
   • Simple Harmonic Motion
     • a is proportional to -x
     • Any force that is proportional to the opposite of the displacement is called a restoring force
       • F is proportional to -x
     • As potential energy increases, kinetic energy decreases
       • Ek+Ep=Et

2. 4.2 Travelling Waves

   • Energy Transfer
     • When a wave pulse reaches the end of a rope it does work against gravity
     • The material through which the wave propagates is called the medium
   • Transverse and Longitudinal Waves
     • Vibrations travelling perpendicular to the direction of the wave velocity is called a transverse wave
     • Vibrations travelling parallel to the direction of wave velocity is called a longitudinal wave
     • In a transverse wave, each particle has the same period and are slightly out of phase
     • Longitudinal waves have rarefactions and compressions instead of crests and troughs
   • Wavefronts and Rays
     • The wavefronts are located at compressions
     • Rays are drawn from the source outward and show the direction of the wave speed or velocity
     • Wavefronts and rays are perpendicular
     • Wavefronts can be bent by obstacles
   • Electromagnetic Waves
     • All EM waves travel at 3x10^8 ms^-1
       • c= lambda f
     • Red has the largest wavelength out of visible light
     • Light can propagate through a vacuum but sound can't as the medium through which it travels has been removed

3. 4.3 Wave Characteristics

   • Intensity
     • Intensity is the rate energy is being transmitted
       • I=power/area
     • Intensity against distance
       • I=power/4*pi*r^2
       • I is proportional to x^-2
     • I is proportional to A^2
   • Reflection and Refraction
     • Wave reflection occurs when a wave meets a boundary or a change in medium and is at least partially diverted backwards
     • Angles are always measured with respect to the normal
       • Angle of Incidence=Angle of Reflection
     • The frequency and wavelength of the wave do not change for reflection
     • Wave refraction occurs when a wave meets a boundary or a change in medium and is at least partially allowed through the boundary
     • The frequency and period do not change for refraction
   • Interference
     • Wave superposition is the addition of two or more waves passing simultaneously through a medium
   • Polarisation
     • Transverse waves can have infinitely many modes of oscillation, each of which is perpendicular to the propagation whereas longitudinal can only have a single mode
       • The phenomenon of polarisation only applies to transverse waves
     • Light is a transverse wave that has two types of oscillation perpendicular to the direction of propagation
       • Mutually oscillating electric and magnetic fields
     • Random orientations of electric fields in a light source constitute unpolarised light
     • A manmade film called Polaroid can take unpolarised light and absorb all rays of light whose electric fields are not orientated in a certain line
       • The electric fields are all orientated in a single direction and the light is said to be polarised
       • When there are two polarisers, the first is a polariser and the second is an analyser
       • Malus' Law- I=I0cos^2(theta)
       • Brewster's Law= If theta(reflected)+theta(refracted) = 90 then the reflected way will be completely plane polarised
     • Linear-polarised light is called plane-polarised
     • Polarisation occurs parallel to the surface between two media and varies with angle of incidence
     • A substance is termed optically active if the plane of polarised light rotates as it passes through a substance

4. 4.4 Wave Behaviour

   • Snell's Law
     • Snell's Law relates the wave velocities in two mediums to their angles
       • n1/n2 =v2/v1=sin(theta1)/sin(theta2)
       • A refractive index is where the speed of the light is related to the medium
         • Nm=c/Vm n1sin(theta1)=n2sin(theta2)
     • The critical angle is where the angle of refraction = 90 degrees
       • sin(critical angle)=n2/n1

5. 4.5 Standing Waves

   • Nodes and Anti-Nodes
     • It does not travel to the left or the right
     • Its lobes grow and shrink but do not go to the left or right
     • No displacement- Node
     • Grow and shrink- Anti-Node
   • Sketching and Interpreting
     • Fundamental Frequency- lowest frequency you can get from the configuration (1st Harmonic)
   • Boundary Conditions
     • Closed Boundary
       • First Harmonic is (1/4)lambda=L. f1=v/4L
       • Each harmonic is + 2/4 lambda and +2v
     • Open Boundary
       • First Harmonic is (1/2)lambda=L. f1=v/2L
       • Each harmonic is + 1/2 lambda and +v