3 wave representations


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3 wave representations

  1. 1. 13 Wave Representations1
  2. 2. IntroductionWe see waves on the surface of water. They travelacross the surface of the water transferring energy:Molecules of the water move up and down.A wave is a periodic disturbance of the water.Wave travels horizontallyMolecules vibrate up and down (approximately)The diagram represents the wave as an idealised sinewave. This idea can be used as a model for otherphenomenaSound waves travel through air (or any other medium)2
  3. 3. Wave travelling horizontally Particles vibrate back andforthcompression rarefactionrarefactionAlthough we may represent sound waves as a sinecurve, the particles move back and forth, not up anddown.Light (and other electromagnetic waves) do notrequire a medium.They are periodic disturbances of the electric andmagnetic fields through which they are travelling.These fields vary at right angles to the direction oftravel.3
  4. 4. Transverse and longitudinal wavesTransverse waves can be made to travel along astretched rope, by moving one end up and down (or fromside to side)Both transverse and longitudinal waves can bedemonstrated using a long spring (slinky).For longitudinal waves, the end of the slinky must bepushed back and forth.But it is simplest to represent both types of waves assine waves.4Longitudinal waveVV Transverse waveVibrations are perpendicular todirection of travel
  5. 5. PolarisationLight and other transverse waves can be polarised.In un-polarised light, the electric and magnetic fieldsvibrate in all directions perpendicular to the directionof travel.After passing through a piece of Polaroid, each vibratesonly in one direction.Only transverse waves can be polarised.Wave fronts and raysThe ripple tank shows another way to represent waves.We draw wave fronts as though we are looking down onthe ripples from above.Rays can be added: these are always perpendicular tothe wave frony5
  6. 6. 6Wave frontsraysCircular waves spreadingout from a point sourceNote that the separation of thewave fronts is constantAll waves can be reflected and refracted.When a wave enters a medium where it travels moreslowly, its wavelength decreases, but its frequencyremains constant.
  7. 7. Questions71. Classify the following as transverse or longitudinal:light, sound, water, infrared waves.2. A guitarist plucks a string. A wave travels along thestring. Is this longitudinal or transverse?3. Draw a ray diagram to show a single ray beingreflected by a mirror at 45o to its path. Add wavefronts to show how these are reflected by themirror.4. Copy and complete the diagram to show what happenswhen waves enter a medium where they travel moreslowly. The boundary is parallel to the wave fronts.slowerfaster
  8. 8. Wave quantitiesSeveral quantities are needed to fully describe a wave:amplitude, wavelength, frequency, phase.Take care not to confuse them.Wavelength and amplitude8yx/tHorizontal axis = distance or timeAmplitude is the height of acrest measured from thehorizontal axisT
  9. 9. Wavelength and amplitudeThe displacement y is the distance moved by anyparticle from its undisturbed position.The wavelength λ of a wave is the distance betweenadjacent crests (or troughs), or between any twoadjacent points which are at the same point in the cycle.(i.e. which are in phase with each other)The amplitude a of a wave is the maximum displacementof any particle.Period and frequencyThe period T is the time for one complete cycle of thewave.This is related to the wave’s frequency f: T = 1 / f(or f = 1 / T)9
  10. 10. 10Frequency is measured in hertz (Hz) 1 Hz = 1 wave/s = 1 s-11 kHz = 103 Hz 1 MHz = 106 Hz 1 GHz = 109 HzThink of it like this: the frequency is the number ofwaves per second; the period is the number of secondsper wave.Phase differenceTwo waves may have the same wavelength but may be outof phase (out of step)Phase difference is expressed as a fraction of a cycle, orin radians (rad) or degrees (o)1 cycle = 1 complete wave = 2π rad = 360o½ cycle = π rad = 180o ¼ cycle = π/2 rad = 90o
  11. 11. Measuring frequencyTo find the frequency of a sound wave, plug a microphoneinto an oscilloscope (c.r.o) and use it to display the sound.Step 1 adjust the time-base setting to give two or threecomplete waves on the screenTime-base setting = 0.02 s div-1 (time-base settingsmay be given in divisions or centimetres)Step 2 measure the width of a number of complete wavesTwo waves occupy 5.0 divisionsStep 3 calculate the time represented by this number ofdivisions.Time = 5.0 div x 0.02 s div-1 = 0.10 sStep 4 calculate the frequency = number of waves / timeFrequency = 2 waves / 0.10 s = 20 Hz11
  12. 12. Questions1. Calculate the period for waves of the followingfrequencies: 2 Hz, 2 kHz, 0.5 MHz.2. On a displacement-time axes, sketch two waves witha phase difference of π radians; one wave has twicethe amplitude of the other.3. An oscilloscope is set with its time-base at 5 ms cm-1.An alternating signal gives foue complete wavesacross the 6 cm screen. What is the frequency ofthis signal.12