# Waves

?

## 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.
1 of 21

## 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.
2 of 21

## 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).

3 of 21

## 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
4 of 21

## 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.
5 of 21

## 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.
6 of 21

## 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.
7 of 21

## 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

8 of 21

## 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.
9 of 21

## 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.
10 of 21

## 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.
11 of 21

## 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.
12 of 21

## 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.

13 of 21

## 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.
14 of 21

## 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.
15 of 21

## 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
16 of 21

## 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
17 of 21

## 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.
18 of 21

19 of 21

## 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.
20 of 21

## 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.
21 of 21