# 6 wave behaviour basic wave properties

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6 WAVE BEHAVIOUR Basic wave properties. Review key wave properties Explain the meaning of the terms phase , phasor and superposition. Starter: Q1. Define the following wave terms: wavelength, frequency, amplitude, period, wave speed. - PowerPoint PPT PresentationTRANSCRIPT

Newtons second law of motion

6 WAVE BEHAVIOURBasic wave propertiesReview key wave properties

Explain the meaning of the terms phase, phasor and superposition

Starter: Q1. Define the following wave terms: wavelength, frequency, amplitude, period, wave speed.

Q2. What is the wavelength of radio waves whose period is 9 ns?

Add on the labels: peak, trough, wavelength, amplitude.Think about what frequency, wave speed, period areFrequency is the number of wave cycles per secondPeriod is the time it takes for one complete oscillationWaves have phaseWaves with 90 phase difference

Waves in phaseWaves out of phaseUsing phasors to describe the phase of a wave

1. A phasor is a rotating arrow that represents the phase of wave without having to draw it out.2. The higher the frequency of the wave the more rapidly the phasor rotates.3. The larger the amplitude of the wave the longer the phasor.4. Different representations of the waves describe exactly the same thing.

Adding waves with different phasesThe principle of superposition says that the resultant amplitude of two waves in the same point is the sum of their individual amplitudes at this point.

Phasors can also be used to describe what the resultant wave looks like when two waves superimpose. See page 126

Superposition phenomenaObserve and explain some phenomena involving wave superpositionExplain how superposition is used in some practical situations

Starter: Q1. If two waves are to constructively interfere, what must be true about their frequency, wavelength and phase? Q2. Sound waves from two speakers driven from the same signal generator arrive at a point, 180o out of phase. What must be true about the path lengths taken by the two wave trains?Path difference: the difference in distance (path) two waves have travelled to reach the receiverMaxima occur where the path difference is a whole number of wavelengths e.g. 1, 2, 3.. (the waves arrive in phase)

Minima occur when the path difference is an odd number of half wavelength e.g. 0.5, 1.5, 2.5. (the waves arrive out of phase)Now try questions 30SIn order for stable superposition effects it is necessary to have waves that are coherentCoherence means waves that have constant phase difference

If incoherent waves are used then the superposition effects will vary such as the beats observed with two slightly different frequencies.

All waves from the same source are inherently coherentRadar guns

If the path to the car and back is a whole number of wavelengths then there is a maxima.If it is a whole number of half wavelengths then it is a minima.When the car moves towards the detector maxima and minima are recorded sequentially.The frequency the signal varies at can be used to calculate the speed the car is approaching Now try questions 70SWhen you have finished; read textbook page 127 on oils and soap colours and take down enough notes that you can explain the phenomenon to your partnerLook at the pretty bubbles!

Can you explain, in terms of wave superposition, why yousee a spectrum of colours in the surface of the bubble?

Can you work out the superimposed wave from these phasors?++==Standing wavesDescribe how standing (stationary) waves are created by superposition of travelling waves

Describe and explain the pattern of nodes and antinodes formed by standing waves on strings and in pipes

Standing waves in airInvestigate and explain standing waves patterns in air columns

Starter:Write down two similarities and two differences between transverse waves and longitudinal waves

Apply your understanding of standing wavesQ1. What is the frequency of thesecond harmonic note produced byan organ pipe 1.3 m long, which is closedat one end? (Speed of sound in air = 340 ms-1.)

Q2. Can you explain, in termsof standing waves, why a flute produces higher pitch notes thana clarinet?

Generate questions from these answersHalf a wavelength

A node at each end

A node at one end and an antinode at the other

The harmonics follow the pattern f, 2f, 3f, 4f,.....

The speed of sound will increase and the frequency will increase but the wavelength will remain the sameFiendish problemSuppose while an orchestra was playing you pumped out all of the air from the concert hall and replaced it with helium, through which sound travels much faster than through air. What would happen to the pitch of the different instruments? Would all types be affected equally? Hints: The pitch is an indication of the frequency. All of the sounds are produced by standing waves, either on strings under tension or in columns of air.

Ignore the fact that all of the members of the orchestra would be asphyxiated!The nature of lightExplain Romers method for estimating the speed of light

Discuss differences between wave and particle models of light

Review evidence for light behaving as either wave or particle

What evidence from every day life is there to suggest that the speed of light is much higher than the speed of sound?

Sketch diagrams to illustrate reflection, refraction, diffraction and interference.

Which of the 4 wave phenomena above can be explained ONLY by a wave model of light? Why?

Looking at the night sky is looking back in time. Explain this statement.

Light interferenceObserve light interference and explain it in terms of superpositionMeasure the wavelength of light of a laser using Youngs slits

Starter: Use the transparencies to create 2-source interference patterns. What happens to the spacing between the regions of constructive and destructive interference when the sources are moved apart?Can you describe the interference pattern of sound and water waves?RIPPLETankIf we were to try the same experiment with light. What problems might we face?

Youngs slits experimentScreendPRQLx33

sin q = nl/dnl = dsinqBright fringes occur when this length is a whole number of wavelengthsScreendPRQLxqsin q can also be calculated by looking at the big triangle that the fringes createtanq = x/Lsinq = x/LPredicting where bright fringes will be:sinq = nl/dsinq = x/Lx/L = nl/d

x = nLl/dl = xd/LWrite down an estimation of the uncertainty in the measurements of x, d and LLook at the equations we have derived and make a prediction about what effect changing the slit spacing have on this experiment.The diffraction gratingObserve and explain transmission and reflection diffraction grating effectsMeasure a laser wavelength using a transmission grating

Starter: Use the equation n= d sin to predict the effect on a 2-slit interference fringe pattern of changing to slits that are further apart. Verify using the transparencies.

dGratingsd is the spacing between adjacent slits on the gratingThe first maximum occurs when the length indicated is equal to lGratingsdThe angle is increased until the length indicated becomes equal to 2lThe order of the maxima corresponds to the number of l difference in the path lengthNote that by the same argument it can be shown that: n l=d sinqNow calculate the wavelength of the maxima.

Can you explain why the maxima are more spread out than when we used a double slit?Diffraction gratings can be used in:Separating different frequencies of light for analysisObserving the spectrum of starsSelecting particular wavelength for useNow try Qs 3-6 p144Reflection grating

Starter: Draw a diagram to show how plane waves diffract when they pass through an aperture:

when the aperture is much larger than the wavelength of the waveswhen the aperture is comparable in size to the wavelength of the waveSingle aperture diffractionObserve and explain single slit diffraction

Explain some practical consequences in astronomy and every day life

DiffractionPatterns

1. How does the diffraction spreading depend on the wavelength of light?2. Carefully adjust the width of the slit. How does the diffraction spreading depend upon slit width?.

Beam width

sin q =W/L = l/dso for small angles:beam angle in radian q = l/dLinkNote that W is really referring to half the beam widthAngular resolutionHow close can two objects be and still be resolved?What is the beam half width?

separation of objects wavelength of radiationbeam width

W = l ( = sin ) L d distance to object size of aperture

Synthetic Aperture Radar

Problem:Can you see evidence of Apollo landingon the Moon? Eagle module base = 4.3 m acrossEarth-Moon distance = 384 000 kmWavelength of light = 550 nmLargest telescope mirror diameter (La Palma) = 10.4 m.

From these data, angular resolution needed = 10-8 radians; angular resolution available = 5 x 10-8, so would not be able to resolve module from surroundings.

Starter: The diagram shows light rays from a star arriving at a concave telescope mirror.Q1. How can you tell that the star is very far away?Q2. What can you say about the phasors for each of the light rays as they pass the line XX ?Q3. Why must the mirror be shaped as shown in order to focus the light? Explain your answer in terms of path lengths and phasor rotations.

X

XUsing phasors to explain superpositionUse the phasor model to explain interference and diffraction

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