Waves

Waves

1. Definitions

   • Wavelength λ is the distance between successive points in a wave which have the same phase
   • Velocity is the distance traveled by the wave in one second
   • Amplitude is the maximum displacement from the rest position
   • The frequency is the number of complete oscillations per second

2. Transverse

   • Electromagnetic waves
     • Travel at the speed of light
     • Can be polarised
     • X Rays have highest f and shortest λ
     • Radio have largest λ and lowest f
     • X ray, UV, Visible, IR, Micro, Radio
   • Water waves
   • The disturbance is perpendicular to the direction of propagation
   • Peaks and troughs
   • Polarisation
     • When a transverse wave has only one plane of vibration
     • Only way to distinguish between the two types of waves
     • Light which is reflected off a surface is polarised
     • Used in photography, 3D movies, stress and strain testing...

3. Longidudinal

   • Sound
   • Particles move parallel to direction of propagation
   • Compressions and rarefactions

4. Phase

   • Waves are in phase if their peaks and troughs or compressions and rarefactions occur at the same time
   • Difference of 2nπ = in phase
   • Difference of (2n+1)π = anti phase

5. c=fλ

6. Superposition

   • The resultant disturbance from two waves at any point is the sum of the separate disturbances of the two waves
   • Stationary/standing waves
     • If a wave is reflected, then under certain conditions, a stationary wave is produced
     • Produced when:
       • Two waves are travelling in opposite directions
       • The two waves have the same frequency and wavelength
       • Similar amplitudes
     • Properties
       • Nodes are points where displacement is always 0
       • All points between adjacent nodes are in phase with eachother
       • Each point on the wave has a different amplitude to its neighbour
       • Where amplitude is a maximum there is an antinode
       • Distance between adjacent nodes =λ /2
     • On strings
       • eg. string instruments
       • One antinode = first harmonic
         • Length of string = λ /2
   • Diffraction
     • When a plane wave hits a barrier with a small gap, gap width ≈ λ , the wave becomes circular around the gap
     • When light shone through single slit diffraction occurs
       • With white light the central band is white, with a dark band on either side, fringed with colour
         • Blue on the inside, red on outside.
   • Interference
     • Two coherent waves
       • Coherent means same wavelength and constant phase difference
     • Bright fringe when path difference between the two waves is equal to nλ.
       • Waves are in phase so constructive interference occurs
     • Dark fringe when path difference is an odd number of half wavelengths
       • Waves in antiphase so destructive interference occurs
     • Double slit experiment
       • Interference graph looks like this
       • Equally spaced bright and dark parallel fringes
       • Two sources are coherent
       • w= λD/s
         • w = fringe separation
         • s = separation of double slits
         • D = separation of slits and screen
         • λ =wavelength
       • If the source is moved closer, separation is unaffected but intensity increases
       • If distance between double slits is decreased, separation increases
       • If source slit is widened, fringes disappear as the waves are no longer coherent
       • Fringes merge together is one slit is covered up
       • If white light is used, the central fringe is white and the others are coloured
     • Diffraction grating
       • Piece of glass with a large number of equally spaced parallel lines on it
       • Each slit diffracts light, producing parallel lines all angled at θ degrees to the normal
       • This occurs at several θ values
       • dsinθ = nλ
         • d = distance between adjacent slits
         • n = order of the maxima
       • = nλ and as Δl= n sinθ from trig... dsinθ = nλ

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