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Wave characteristicsThe wave pulse transfers energy
If the source continues to oscillate, then a continuous progressive wave is produced.
Students should be able to distinguish between oscillations and wave motion, and appreciate that in many examples, the oscillations of the particles are simple harmonic.
Travelling WavesDefinition: A travelling wave (or “progressive
wave”) is one which travels out from the source that made it and transfers energy from one point
to another.Energy dissipation
Clearly, a wave will get weaker the further it travels. Assuming the wave comes from a point source and travels out equally in all directions we can say:
Energy flux =
(in Wm-2)
Power (in W)
Area (in m2)φ =
P
4πr2
An “inverse square law”
Example questions1) Darryl likes doing his homework. His work is 2m from
a 100W light bulb. Calculate the energy flux arriving at his book.
2) If his book has a surface area of 0.1m2 calculate the total amount of energy on it per second (what assumption did you make?).
3) Matti doesn’t like the dark. He switches on a light and stands 3m away from it. If he is receiving a flux of 2.2Wm-2 what was the power of the bulb?
4) Matti walks 3m further away. What affect does this have on the amount of flux on him?
State that progressive (travelling)waves transfer energy.
Students should understand that there is no net motion of the medium through which the wave travels.
Transverse vs. longitudinal wavesTransverse waves are when the displacement is at right angles to the direction of the wave…
Longitudinal waves are when the displacement is parallel to the direction of the wave…
Dis
pla
cem
en
tDirection
Direction
Displacement
Transverse waves
Students should describe the waves in terms of the direction of oscillation of particles in the wave relative to the direction of transfer of energy by the wave. Students should know that light waves and water waves are transverse and that water waves cannot be propagated in gases or liquids.
http://www.acoustics.salford.ac.uk/feschools/waves/bungyvideo.htm
http://www.acoustics.salford.ac.uk/feschools/waves/wavetypes.htm
http://www.acoustics.salford.ac.uk/feschools/waves/guitarvideo.htm
Longitudinal waves
Sound waves and earthquake P-waves are longitudinal
Longitudinal slinky
http://www.acoustics.salford.ac.uk/feschools/waves/slinkyvideo.htm
Loudspeaker
Describe waves in two dimensions,including the concepts of wavefrontsand of rays.
Energy is transferred in 2 dimensions
Watch the wavefront(s) propagate
http://www.acoustics.salford.ac.uk/feschools/waves/dripvideo.htm
http://www.acoustics.salford.ac.uk/feschools/waves/dropvideo.htm
Wavefronts and rays.
Wavefronts and rays
Rays show the direction of travel of the energy. The wavefronts are where the crests of the waves are. The rays are always at 90 deg to the wavefronts.
rays
Wavefronts
Ray point of view Wave point of view
Light travels out instraight lines from asmall source
Light spreads out inspherical wavefrontsfrom a small source
Wavefronts in a parallelbeam or from a very distantsource are straight (notcurved) and parallel
Light in a parallel beam orfrom a very distant sourcehas rays (approximately)parallel to one another
Ray and wave points of view show the same thing butin different ways
Longitudinal waves
Compressions and rarefactions
Transverse waves
Crests
Troughs
Displacement graphs
Define the terms displacement, amplitude, frequency, period,wavelength, wave speed and intensity
WAVELENGTH
- the distance from one crest to another or one trough to another. (In fact generally from any point on the wave to the next exactly similar point i.e. 2 consecutive points in phase)
FREQUENCY
- the number of vibrations of any part of the wave per second. The bigger the frequency the higher the pitch of the note or the bluer the light
AMPLITUDE
- the maximum distance that any point on the wave moves from its mean position. The bigger the amplitude the louder the sound, the rougher the sea, or the brighter the light
Period (T)The time it takes for one complete cycle of the wave.
Displacement (x)How far the “particle” has travelled from its mean position.
Wave speed (v)The speed at which the wavefronts pass a stationary observer
Intensity (I)The power per unit area that is received by an observer. Students should know that intensity α amplitude2
Derive and apply the relationship between wave speed, wavelength and frequency.
Speed = Dist/time
For 1 cycle of the wave, dist = λ and time =T
Speed = λ/T f = 1/T
Therefore V=fxλ
The Wave EquationThe wave equation relates the speed of the wave to its frequency and wavelength:
Wave speed (v) = frequency (f) x wavelength ()
in m/s in Hz in m
V
f
1) A water wave has a frequency of 2Hz and a wavelength of 0.3m. How fast is it moving?
2) A water wave travels through a pond with a speed of 1m/s and a frequency of 5Hz. What is the wavelength of the waves?
3) The speed of sound is 330m/s (in air). When Dave hears this sound his ear vibrates 660 times a second. What was the wavelength of the sound?
4) Purple light has a wavelength of around 6x10-7m and a frequency of 5x1014Hz. What is the speed of purple light?
Some example wave equation questions
0.2m
0.5m
0.6m/s
3x108m/s
Electromagnetic wavesClick to play
4.5 Wave properties
Wave diagrams1) Reflection
4) Diffraction3) Refraction
2) Refraction
The pulse keeps its shape
It is inverted It has undergone a
180o phase change ( change in phase)
Reflection in one dimensionReflection of a Pulse at a Fixed End
Video: Transverse Wave Along A Bungee Cord Video
http://www.acoustics.salford.ac.uk/feschools/waves/bungyvideo2.htm
This is because the instant the pulse hits the fixed end, the rope attempts to move the fixed end upwards
It exerts an upwards force on the fixed end By Newton’s third law, the wall will exert an
equal but opposite force on the rope This means that a disturbance will be created
in the rope which, however is downwards and will start moving to the left
Reflection in one dimensionReflection of a Pulse at a Free End
The pulse reflects off the free end and returns with the same direction of displacement which it had before reflection:
a pulse with an upward displacement will reflect off the end and return with an upward displacement.
This behavior of non-inversion will always be observed when the end of the medium is free to move.
http://www.youtube.com/watch?v=11_fRmvzqIY&feature=player_embedde
Video: Free End Reflection
Transmission of a pulse_ Boundary Behaviour
the wave speed is always greatest in the least dense medium,
the wavelength is always greatest in the least dense medium,
the frequency of a wave is not altered by crossing a boundary,
the reflected pulse becomes inverted when a wave in a less dense medium is heading towards a boundary with a more dense medium,
the amplitude of the incident pulse is always greater than the amplitude of the reflected pulse.
TOP: An incident pulse is introduced into the right end of the wave machine. It travels through the less dense medium until it reaches the boundary with a more dense medium.
MIDDLE: At the boundary, both reflection and transmission occur.
BOTTOM: The reflected pulse is inverted and of about the same length (though a smaller amplitude) as the incident pulse. The transmitted pulse is shorter and slower than the incident and transmitted pulse.
TOP: An incident pulse is introduced into the left end of the wave machine. It travels through the more dense medium until it reaches the boundary with a less dense medium.MIDDLE: At the boundary, both reflection and transmission occur. BOTTOM: The reflected pulse is NOT inverted and of about the same length (though a smaller amplitude) as the incident pulse. The transmitted pulse is longer and faster than the incident and transmitted pulse.
Wave Behaviour
Reflection in two dimensions_ water ripple tan
http://www.youtube.com/watch?v=leKDzn6RLDw&feature=related
Normal
Angle of
incidence
Angle of
reflection=
The Law for Reflection
• The angle of incidence is equal to the angle of reflection
• Also - The incident ray, the reflected ray and the normal lie on the same plane
• Use this rule for any ray or wave diagram involving reflection from any surface
• For circular waves hitting a flat reflector, the reflected waves appear to come from a source, which is the same distance behind the reflector as the real source is in front of it
• Also a line joining these 2 sources is perpendicular to the reflecting surface
O I
• If a plane wave is incident on a circular reflector then the waves are reflected so that they–Converge on a focus if the surface
is concave–Appear to come from a focus if the
surface is convex
Echos
• In the case of sound, a source of sound can be directed at a plane, solid surface and the reflected sound can be picked up by a microphone connected to an oscilloscope.
• The microphone is moved until a position of maximum reading on the oscilloscope is achieved.
• When the position is recorded it is found that again the angle of incidence equals the angle of reflection.
The amount of transmission and reflection depends upon the difference in the “density” of the 2 media. i.e the bigger the difference, the greater the amount of reflection.
Refraction through a glass block:
Wave slows down and bends towards the normal due to
entering a more dense medium
Wave speeds up and bends away from the normal due to entering a less dense
medium
Wave slows down but is not bent, due to
entering along the normal
Refraction of Light applet
Hyperlink
Refraction of light as a wave representation: http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=16
Finding the Critical Angle…1) Ray gets refracted
4) Ray gets internally reflected3) Ray still gets refracted (just!)
2) Ray still gets refracted
THE CRITICAL ANGLE
Optical fibres
Uses of Total Internal Reflection
Optical fibres:
An optical fibre is a long, thin, _______ rod made of glass or plastic. Light is _______ reflected from one end to the other, making it possible to send ____ chunks of information
Optical fibres can be used for _________ by sending electrical signals through the cable. The main advantage of this is a reduced ______ loss.
Words – communications, internally, large, transparent, signal
Other uses of total internal reflection
1) Endoscopes (a medical device used to see inside the body):
2) Binoculars and periscopes (using “reflecting prisms”)
Huygen’s principle1. Velocity decreases
2. Wavelength decreases
3. Frequency same
DiffractionMore diffraction if the size of the gap is similar to the
wavelength
More diffraction if wavelength is increased (or frequency decreased)
http://www.acoustics.salford.ac.uk/feschools/waves/diffract.htm#diffraction
http://www.acoustics.salford.ac.uk/feschools/waves/diffract3.htm
Diffraction in light
Diffraction at a single aperture
intensityacrossscreen
Single slit
distant screen
Diffraction in light is to be studied later as part of Option A SL and Topic 11 AHL
Sound can also be diffracted…
The explosion can’t be seen over the hill, but it can be heard. We know sound travels as waves
because sound can be refracted, reflected (echo) and diffracted.
Diffraction depends on frequency…
A high frequency (short wavelength) wave doesn’t get diffracted much – the house won’t be able to receive
it…
Diffraction depends on frequency…
A low frequency (long wavelength) wave will get diffracted more, so the
house can receive it…
i) Diffraction by a "large" object
ii) Diffraction at a "large" aperture
iii) Diffraction by a "small" object
iv) Diffraction by a "narrow" aperture
SuperpositionSuperposition is seen when two waves of the same type cross. It is defined as “the vector sum of the two displacements of each wave”:
Superposition
Superposition of pulses: http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=18.0
Superposition of waves:
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=19.0
Constructive interference i.e. Loud or bright. Waves are in phase
Destructive interference i.e. dark or quiet. Waves are π rads out of phase.
http://www.acoustics.salford.ac.uk/feschools/waves/super2.htm
