3.1 PROGRESSIVE WAVES


v   Relevant equations from GCSE:  c  =  f λ,   f = 1/T



v   Particles in the medium oscillate as the wave passes by.

v   Amplitude = maximum displacement of a particle from its mean position

v   Phase Difference between particles is measured in radians or fractions of a cycle.

     eg. phase difference between A and E = 2π or 1 cycle .  

v   Wavelength = distance between 2 consecutive particles which are in phase

v   Longitudinal wave = vibrations of the medium are parallel to the wave direction

v   Transverse wave = vibrations of the medium are perpendicular to wave direction




v   Plane polarized wave = one whose associated vibrations occur in 1 plane only

v  In this case the first slit produces vertically polarised waves (it absorbs vibrations in all other directions)

The second slit absorbs all vibrations except horizontal ones, therefore nothing passes through.


v  TV aerials are aligned accordingly, to either pick up vertically or horizontally polarised waves as required.  

v  Longitudinal waves cannot be polarised




3.3 STATIONARY WAVES (formed by superposition of 2 waves)

v   Superposition – when 2 or more waves combine a resultant wave is formed whose

    displacement at any point = vector sum of displacements at that point

v   Stationary wave – formed by superposition of 2 waves of same frequency,

     speed and amplitude moving in opposite directions.

v  The fundamental, or first harmonic, is the lowest frequency possible to set up a stationary wave.

 The particles vibrate vertically. So exactly half a time period later the string will be where the tips of the arrows are.

 If the frequency is doubled, the second harmonic is seen, etc:


v   Antinode = position of max. displacement, Node = position of min. displacement

NB. Required practical 1: Investigation into the variation of frequency of stationary waves

on a string with length, tension, and mass per unit length.



 3.4 INTERFERENCE (for observable interference 2 coherent sources are needed)

v   Coherent sources  - waves from these have the same frequency and have a constant

    phase difference (to get an observable outcome they should also have similar amplitudes)

A LASER is often the preferred method to obtain 2 coherent sources for interference:



In the set up above, S1 and S2 are the coherent sources.

v   Phase difference between 2 waves is measured in radians

v   Path difference = difference in path length in λ or m 

v  Constructive interference occurs where the path difference is a WHOLE number of wavelengths.

v   Destructive interference occurs where the path difference is an ODD number of half wavelengths

v  Use of the fringe spacing formula:  w = λ D / s , where w = fringe spacing,

     λ = wavelength, D = distance between slits and fringes, and s = slit separation.

v  If white light is used instead of laser light, then a central white fringe is seen and each other

   bright fringe is a separate spectrum of white light with blue on the inside and red on the outside: 

NB. Required practical 2: Investigation of interference effects using Young's Double Slit and Diffraction Grating.


v  Diffraction is the spreading of a wave around an obstacle or spreading after

passing through a gap. It is caused by superposition.         

v   Single slit diffraction patterns:

                      NB1. when the slit is narrowed, the central maxima widens and fewer subsidiary maxima are visible.

                      NB2. if the wavelength is increased then again, a wider diffraction pattern occurs (see above)  

v   Diffraction gratings - Proof and use of  d sinθ  = nλ,  where n = order number,

      d = grating spacing =  1 / number of lines per m



                3.6 REFRACTION




v   Snell’s Law -   n1sin θ1  =n2 sin θ2 ,  sin θ1 / sin θ2  = c1 / c2 , where:  n1  , n2 

     are absolute refractive indicies of media 1 and 2,  θ1 = angle of incidence,

      θ2 = angle of refraction, c1 , c2 are speeds in media 1 and 2.   

    Also, since  c  =  f λ  then Snell could be written in terms of wavelengths:


    sin θ1 / sin θ2  = c1 / c2  = λ1 / λ2   (frequency cancels).


v   AQA define refractive index of a substance or material from  n = c / cs

v   Critical angle is the maximum angle of incidence for which light inside the

      denser medium can still enter the less dense medium.(this happens when

      the angle of refraction = 90˚)

                                                          sin θc  = n2 /  n1


v   Total internal reflection occurs when the angle of incidence is greater than the

     critical angle for the material., then all the light is reflected inside the denser material.

v   Cladding acts as a separator between fibres AND provides a material of suitably lower

     refractive index than the fibre itself. 

v   Step index fibre is when a fibre of constant refractive index is clad with a different

     material of lower constant refractive index giving a ‘stepped variation in n with x’

v   Monomode fibre optic has a small diameter to reduce the number of reflections,

    therefore reducing the attenuation and spreading effects.

   NB. If the input light is not monochromatic (eg white light) then material dispersion will also

    occur since red light travels faster than blue. 

Notice that the output pulse has been both decreased in amplitude and spread out.