superposition of waves

superposition of waves

1. principle of superposition: when 2 or more waves meet at a point, the resultant displacement is the algebraic sum of the displacements of the individual waves

2. diffraction: the spreading of a wave as it passes through a gap or around an edge.(applies to all waves)

   • diffraction effects are greatest when waves pass through a gap with a width equal to their wavelength(pic on the left has greatest diffraction)
   • RLS: cars need external radio aerials because radio waves have wavelengths longer than the size of the windows and so cannot diffract into the car.
   • RLS: microwave ovens have a metal grid that enables only light to diffract out but not microwaves

3. interference: the formation of points of cancellation and reinforcement where 2 coherent waves pass through each other

   • constructive intereference: when 2 waves arrive at a point in phase with one another so that they add up.
   • destructive interference: when 2 waves meet each other with a phase difference of 180 degrees and cancel to give 0 amplitude.
   • whether a wave combines constructively or destructively depends on the path difference of the waves(the extra distance travelled by one of the waves compared with the other)
     • for destructive interference, the path diff is an odd number of half wavelengths, eg, 0.5 wavelengths, 1.5 wavelengths, 2.5 wavelengths.....
   • for constructive interference, the path difference is a whole number of wavelengths, eg 1 wavelength, 2 wavelengths......

4. interference of light

   • experiment: shine a laser through a pair of slits, you will see that there is a series of equally spaced dots of light form on the screen placed a certain distance away from the slits. these dots are known as "fringes".
     • fringes are regions where light waves from the 2 slits are arriving in phase with each other. the dark areas are the result of destructive interference.
     • determining wavelength from experiment
       • measure slit separation(a): distance between centres of the slits. measure fringe separation(x): measure across several fringes and then calculate average separation. use travelling microscope or metre rule. measure slit to screen distance: use metre rule.
         • • slits are a fraction of a mm, to allow light to diffract effectively. narrower slits would cause low light intensity. wide slits cause brighter fringes, but fewer fringes will be observed since there will be less diffraction and therefore less interference. there is no change in the fringe separation however
           • slits are about a mm away from each other. increased separation will lead to less interference between waves and therefore fringes would get closer together. no change in brightness however
           • slits are about a metre away from the screen to give clearly separated fringes which are not too dim
     • alternative arrangement for double slit experiment.
     • using laser instead of white light has advantages. for example, the lasers greater intensity means that the screen can be further apart so that the fringes can be further apart, reducing % error in the measurements of x and D. furhtermore, laser is monochromatic unlike white light . with white light, different wavelengths form fringes at different points across the screen, smearing them out so they are not as clear

5. coherence: this is when 2 sources emit waves that have a constant phase difference. to have a constant phase diff, these waves have to have the same frequency.

   • coherent sources are needed to produce measurable interference. RLS: if 2 loudspeakers emitted sound waves of slightly different frequencies, the waves would start of in phase, but would soon go out of phase causing the interference pattern to shift around the room.
     • interference patterns would change far too fast for our eyes to detect if coherent sources are not used, so in order to observe intereference we need coherence

6. diffraction gratings

   • fringes here are also referred to as maxima. e.g, central fringe is the zeroth order max, next fringe is the 1st order max and so on. the pattern is symmetrical so there are 2 of each maxima(except 0).
   • the 1st order maxima is formed when rays from adjacent slits have a path diff of 1 wavelength, and 2nd order when the rays have a path diff of 2 wavelengths, and so on
   • determining wavelength from a grating
     • • d= distance between adjacent lines of the grating
       • theta= angular separation between maxima
       • n= order of the maximum(only integer values)
     • advantages of many slits over only just 2 slits
       • maxima are sharp
       • maxima are bright due to contributions from many slits
       • slit separation can be measured more precisely
       • maxima are more widely spread, so angle of separation between maxima can be measured to a higher degree of accuracy

7. diffracting white light

   • dispersion: the splitting of white light into its different wavelengths.
   • from the equation...., we see that the grater the wavelength, the greater the angle theta

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