Waves

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12.1 Waves and Vibrations

  • Waves that pass through a substance (vibrate) are called mechanical waves. eg sound or seismic waves.
  • Electromagnetic waves are vibrating electric and magnetic waves that progress through space without the need for a medium. They include all the waves in the EM spectrum
  • Longditudinal waves contain particles that travel  parallel to the direction which the wave travels.
  • Transvere waves contain particles that travel perpendicular to the direction which the wave travels.
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12.1 Waves and Vibrations (cont)

  • If the vibrations of a transverse wave stay in one plane, the wave is plane polarised.
  • Longditudinal waves cannot be polarised.
  • When unpolarised light passes through a polaroid filter, the transmitted light becomes polarised, as only light in a certain plane is able to pass through.
  • Polarised light in one plane cannot then pass through a polaroid at a different rotation to the first one. 
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12.1 Waves and Vibrations (cont)

  • Polaroid sunglasses reduce glare of light reflected from water or glass. The reflected light is partly polarised, so it's intensity is reduced (light cannot pass through filter).

                      (http://www.olympusmicro.com/primer/images/polarization/polarizedglasses.jpg)

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12.2 Measuring Waves

  • The displacement of a vibrating particle is its distance and direction from its equilibrium position. 
  • The amplitude of a wave is the maxiumum displacement of a vibrating particle from equilibrium.
  • The wavelength of a wave is the smallest distance between 2 adjacent vibrating particles with the same displacement and velocity at the same time.
  • One complete wave cycle is from maximum displacement to the next maximum displacement
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12.2 Measuring Waves (cont)

  • The period of a wave is the time for one complete wave to pass a fixed point
  • The frequency of a wave is the number of cycles of vibration of a particle per second (number of complete cycles per second).
  • Frequency= 1/time period
  • The higher the frequency of a wave, the shorter its wavelength.
  • Wave speed, c= frequency x wavelength.
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12.2 Measuring Waves (cont)

  • The phase difference between 2 vibrating particles is the fraction of a cycle between the vibration of the two particles.
  • It is measured either in degrees or radians, with 360 or 2pi being a full cycle respectively. 
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12.3 Wave Properties 1

  • Straight waves directed at a certain angle to a reflecting surface reflect off at the same angle. The angle of reflection is equal to the incident angle
  • When waves pass across a boundary that changes the wave's speed, the wavelength also changes. This also changes the direction of the waves. This is called refraction
  • When a wave goes from air into another medium, it is directed closer to the normal line to the medium. 
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12.3 Wave Properties 1 (cont)

  • Diffraction occurs when waves spread out after passing through a gap or round an obstacle.
  • The closer the gap length is to the wavelength, the more diffraction occurs

        (http://www.gcsescience.com/Diffraction-Water-Waves.gif)

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12.3 Wave Properties 1 (cont)

  • The bigger the dish, the stronger the signal it can recieve, because more radio waves are reflected from the dish onto the aerial.
  • But a bigger dish reflects the radio waves to a smaller focus, because it diffracts the waves less
  • Therefore, a bigger dish needs to be aligned more carefully to its aerial.
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12.4 Wave Properties 2

  • When waves meet, they pass through eachother.
  • At the point where they meet, they combine for an instant before they move apart. 
  • This combination effect is called superpositioning.
  • The principle of superpositioning states: when two waves meet, the total displacement at a point is equal to the sum of the individual displacements at that point. 
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12.4 Wave Properties 2 (cont)

  • When a crest meets a crest, a supercrest is formed- the two waves reinforce eachother.
  • When a trough meets a trough, a supertrough is formed- the two waves reinforce eachother.
  • When a crest meets a trough, the resultant displacement is zero, the two waves cancel eachother out. 
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12.4 Wave Properties 2 (cont)

  • Stationary waves are formed on a rope if two waves are sent continuously along the rope at either end.
  • The two inividual waves that form the stationary waves are called progressive waves.
  • The progressive waves combine at fixed points along the rope.
  • The points of no displacement formed are called nodes. At each node, the two waves are 180 degrees out of phase, so they cancel eachother out. 
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12.4 Wave Properties 2 (cont)

  • As the waves continuously pass through eachother at a constant frequency and a constant phase difference, cancelation and reinforcement happens at fixed positions.
  • Thi effect is called interference, causing an interference pattern (stationary wave) when they overlap.
                               (http://bugman123.com/Physics/Interference.gif) 
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12.4 Wave Properties 2 (cont)

  • As well as sending 2 waves down either end of a string to form a stationary wave, you can also acheive this by sending a wave in both directions through the middle of a string in tension, attached to fixed points on either side.
  • The progressive waves travel down each end, reflect, and then pass through eachother on the way back. 
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12.5 Stationary and Progressive Waves

  • The simplest stationary wave pattern is called the fundimental mode of vibration. It contains 2 nodes at either end with an antinode (max displacement) in the middle. 
  • Therefore, the wavelength of the stationary node is twice the distance between the nodes in the fundimental node. 
  • If the frequency were steadily increased, a new pattern would emerge with 3 nodes and 2 antinodes. 
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12.5 Stationary and Progressive Waves (cont)

  • Stationary waves that vibrate do not transfer energy.
  • Stationay waves occur because the progressive waves switch between reinforcing eachother and cancelling eachother out every quarter of a cycle (90 degrees).
  • All particles except for those at the nodes oscillate up and down in a stationary wave.
  • So the amplitude of a particle varies from 0 at a node to maximum at an antinode
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12.5 Stationary and Progressive Waves (cont)

  • The frequency of all particles in a stationary wave is the same, except for those at the nodes (don't vibrate). 
  • In a progressive wave, the frequency is always the same
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12.6 More about Stationary Waves on a String

  • A controlled arrangement for producing a stationary wave requires a mechanical ******** attacher to a frequency generator.
  • A string is attached to the ********, and is hung over a pulley at the other end, witha weight attached to the string as it turns vertical.
  • The weight keeps the tension in the string constant.
  • No matter what the frequency, there are always at least 2 nodes, one at the ******** and the other at the start of the pulley.
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12.6 More about Stationary Waves on a String (cont

  (http://www.animatedscience.co.uk/ks5_physics/general/Oscillations%20&%20Waves,%20Reflection%20&%20Refraction/Waves%20(Part%202)_files/Image625.gif)

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12.6 More about Stationary Waves on a String (cont

  • The fundimental pattern of vibration contains 2 nodes and 1 antinode in the centre. 
  • The wavelength is 2L, where L is the distance between 2 nodes.
  • The next stationary wave pattern is the first overtone.
  • This is where there is a node in the centre as well as at the ends (3), so 2 antinodes form in between them.
  • The wavelength is L.
  • The following overtone in a pattern will always have 1 node and 1 antinode more than the previous one. 
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12.6 More about Stationary Waves on a String (cont

  • The pitch of a note corresponds to frequency, so the pitch of a note formed from a stretched string can be altered by changing the tension of the string or by altering its length.
  • Raising the tension or shortening the length increases the pitch.
  • Lowering the tension or increasing the length decreases the pitch.
  • This is how instruments are tuned to a tuning fork.
  • The two will end up having the same fundimental frequency. 
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