# Waves

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- Created by: teague sheldon
- Created on: 20-12-12 21:36

## 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).

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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.

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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.

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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

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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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