Waves (2) - traveling waves, standing waves, beats and the Doppler effect Each section will open directly in a new window. Close each window as you finish. You might find it helpful to print this list of Essential questions.
1 The wave equation ... v = fl ... and ... f = 1/T
Read the waves and pulses section in the Waves index.
Essential questions
1 What is the difference between a longitudinal pulse and a transverse pulse?
2 What is the difference between a closed boundary and an open boundary?
3 How does a pulse reflect from a closed boundary and from an open boundary?
4 How does a wave reflect from a closed boundary and from an open boundary?
Learn the wave equation ... v = fl
Learn the connection between frequency (of the wave generator) and the period.
f = 1/T ... and ... T = 1/f 5 What is added when waves are superimposed?
2 Transverse waves on strings ... y = A sin 2p/l (x) ... and ... v = (T/m )0.5
Read the waves article in the waves index and this waves article in the IB labs section.
Essential questions
1 What is the equation of a sine wave with amplitude 1 and wavelength 2p?
2 That is the wavelength of the function sin 2p/l (x)?
3 What is the amplitude and wavelength of the function 5 sin 2x ?
4 What is the symbol for the mass per unit length of a rope chain etc.?
5 What are the two variables that determine the speed of a transverse wave on a string?
3 Traveling waves ... y = A sin 2p/l (x ± vt)
Read the traveling waves section in the Waves index.
Essential questions
1 In what way is a mathematical equation 'better' than language for describing a traveling wave?
2 What is a phase constant and where does it go in the wave equation?
3 What is the effect of replacing x in a function with (x-t) where t is the time?
4 The functions y = A sin 2p/l (x + vt) ... and ... y = A sin 2p/l (x - vt) are traveling waves. Which one moves to the right?
4 Standing waves ... y = A sin 2p/l (x + vt) + A sin 2p/l (x - vt)
Read the standing waves section in the Waves index.
Essential questions
1 Why is a standing wave called 'standing'?
2 What is meant by a node and an antinode?
3 Define open and closed boundaries in terms of the presence of a node and an antinode.
4 Describe the motion of a point at an antinode of a standing wave.
5 Beats ... f beat = f2 - f1 ... and ... f = 1/T
Read the beats section in the Waves index.
Essential questions
1 What two waves when added lead to a beat?
2 What does a beat (for sound waves) sound like when the beat frequency is 4 Hz and 40 Hz?
3 What is the beat frequency in terms of the frequencies of the two component waves?
4 What is the effect of reducing the amplitude of one of the component waves?
6 The Doppler effect
Read the Doppler effect section in the Waves index.
Essential questions
1 Describe one simple example of the Doppler effect.
2 Draw diagrams to explain the effect in front of and behind a moving source.
3 Write down the frequency in front of a moving source.
4 Write down the frequency for an observer moving towards a source (the equations are different)
7* Polarization
Read the polarization section in the waves index
Essential questions
1 Which type of waves cannot be polarized?
2 What field vectors are associated with electromagnetic waves?
3 What is the relationship between amplitude and wave intensity?
4 How exactly does Polaroid sheet polarize light?
5 At what angle is polarization by reflection complete?
8* Dispersion
Read the dispersion section in the Waves index.
Essential questions
1 What has dispersion got to do with wave speed?
2 What does does dispersion in glass have to do with refractive index?
3 What is the effect of dispersion that requires repeater stations on internet cables?
4 How may dispersion be observed for water waves?
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