Physics-SchoolUK.com

The UK site for KS3 and KS4 Physics

KS4 Waves:
In the first part of the Waves section (4.6.1) we will learn some basic facts about waves; their types, what they do, how to describe them and finally how they can be used.
Please note - the second and third sections, 4.6.2 and 4.6.3 are not yet complete, so are currently not available.

Types of Waves

There are TWO ways to categorise Waves
The first way is the easiest but is very important to understand before encountering the second way.

1. We can put them under the headings Mechanical Waves or Electromagnetic Waves.

When we categorise them under these headings we are focussing on what they are or what they consist of.
For example, a water wave consists of vibrating water particles; mechanical stuff, so a water wave is a mechanical wave.
So is a sound wave in air because it consists of vibrating air particles; mechanical stuff.

But a visible light wave does not consist of anything mechanical; it consists of vibrating electric and magnetic fields, so what type of wave is it? Its an electro - magnetic wave.

Mechanical waves have to travel through some mechanical or physical medium such as air/gas or water/liquid or ground/solid, because they travel by making the mechanical medium vibrate. Electromagnetic waves, on the other hand don't need anything mechanical to travel through; they can travel through a vacuum eg the light from the sun and stars travels easily in space.

Mechanical waves Electromagnetic waves
Sound Visible light
Water Radio wave
Seismic Infra red
Ultra violet
X - ray
Gamma wave
Microwave

2. The second way that we categorise waves is to put them under the headings Transverse Waves or Longitudinal Waves.

When we categorise waves into these 2 categories we are focussing on how they travel rather than on what they consist of.

How Waves Travel

All waves travel by means of some vibration.
The "thing" that vibrates can be a mechanical thing such as a particle (eg water particle) or an electromagnetic thing such as an electric/magnetic field.
If the "thing" vibrates transverse to (which means, at right angles to) the direction of travel of the wave then the wave is of the Transverse type.
If the "thing" vibrates along (or, in line with) the direction of travel of the wave then the wave is of the Longitudinal type.

The following simple diagrams should make the distinction clear.

What do these two types of wave look like?

Notice the repeating pattern of peaks and troughs (maximums and minimums); this is a characteristic of a Transverse wave.

A good example of how you can make a wave like this is - in a swimming pool, push your hand down into the water, then raise it to the surface, then repeat etc; you will see a "ripple" moving away from you. You will have made a water wave.
Another way to make a water wave is to drop a stone into some water and the downward movement of the stone sets up a ripple across the surface of the water.

Another simple way to demonstrate a Transverse wave is to get a skipping rope or any long rope, keep one end still, then vibrate the other end up and down. You will see a transverse wave on the rope and if you vibrate it faster and faster you will see more and more distinct waves along the length of the rope.

Notice - the "thing" that vibrates or which causes the disturbance does not travel along the wave. The dropped stone merely drops into the water, doesn't it; the hand moving up and down in the water doesn't travel along with the resulting ripple, does it?

(NB Sometimes the "thing" that vibrates is called a "disturbance"; dropping a stone into water is an obvious example of a "disturbance"; moving the rope up and down is a "disturbance".)

Interestingly, ALL of the electromagnetic waves, listed in the table above, are of the Transverse type because they are all caused by vibrating electric and magnetic fields which both vibrate transverse to the direction of the wave, as shown below.

The best way to picture such a wave is to use a "slinky". A slinky is a long spring which when stretched out, looks a bit like this:

To demonstrate a Longitudinal type of wave using a slinky, keep one end fixed and vibrate the other end to and fro (forward and backward)

Very quickly you will see a pattern develop in the spring coils where some of the coils are closer together than normal and others are further apart than normal. The areas where the coils are closer together, we call Compressions; the areas where the coils are further apart, we call Rarefactions.

The repeating pattern of Compression - Rarefaction - Compression - Rarefaction... continues along the slinky spring; this repeating pattern is a characteristic of a Longitudinal wave.

Apart from slinky springs where else might we encounter Longitudinal waves?

1. Sound travels from place to place by means of Longitudinal waves.
If a small metal bell is rung, causing it to vibrate, it causes the surrounding air particles to vibrate and they will cause neighbouring air particles to vibrate and so on. If we could see the particles we would see them form the exact same Compression - Rarefaction - Compression pattern that we see in the slinky as a result of vibrating one end. So, the vibrating bell has set up a sound wave in the air. Anyone with a functioning ear and an ear drum within a certain distance of the bell will find that their ear drum begins to vibrate in sympathy with the sound wave and the person "hears" the sound!

Notice - the air particles around the bell do not travel to the ear of the listener; the wave travels, carrying the sound energy; the air particles merely vibrate over a very small distance.

2. Seismic effects can travel from place to place by means of Longitudinal waves.
The waves generated by seismic events such as earthquakes travel from the source of the earthquake, through the ground for hundreds of miles.
At the source the ground is pushed and pulled (just like the slinky spring) setting up a massive vibration/disturbance and a resulting Longitudinal wave.
As the ground gets pushed or squashed we have a Compression and the land rises upwards in a bulge; where the ground gets pulled or stretched we have a Rarefaction and the land sinks down, often causing huge cracks.

NB There are a variety of seismic waves, not all of them are Longitudinal types, but the one's that travel fastest are longitudinal.

Longitudinal Transverse
Sound Visible light
Seismic Radio wave
Infra red
Ultra violet
X - ray
Gamma wave
Microwave
Water

What we have learnt about waves (so far)

1. All waves consist of vibrations, but these can be mechanical/physical vibrations or electromagnetic vibrations.
2. Hence waves can be categorised into 2 groups, Mechanical and Electromagnetic.
3. Mechanical waves are those which must travel through a physical medium such as air eg sound wave, water wave.
4. Electromagnetic waves are those which can travel through a vacuum eg radio wave, light wave.
5. Waves can be further categorised into Transverse type or Longitudinal type.
6. All waves are characterised by repeating patterns. Transverse types have repeating Peaks and Troughs. Longitudinal types have repeating Compressions and Rarefactions.
7. All waves transfer energy from place to place without any transfer of matter - we could say that this is the "job" of a wave!

Now its time for you to have a go at a few questions.

Properties of waves or Describing waves

All of the words that are used to describe a wave are best illustrated using a basic Transverse wave like a water wave. We can draw one simply, like this.

Straight away we can see a technical word, "Displacement".
Displacement at any point along the wave is the distance of the point from its rest/undisturbed position (the middle, indicated by the x-axis line).

The Amplitude of the wave is the maximum displacement of the wave from its rest/undisturbed position. So, the amplitude of our wave is indicated by the following :

Notice the letter a, used to represent Amplitude.
The amplitude can equally be indicated on the negative side of the wave, as follows :

The Wavelength of the wave is the distance travelled by one cycle of the wave. This is easier to understand if you look at the following :

One full wave cycle is from the first green dot to the second, so the distance between them is the Wavelength, and the symbol for it is the greek letter λ.
Another way to define Wavelength is - the distance from a point on one wave to the equivalent point on the next wave.
For example from the peak of one wave to the peak of the next, or from the trough of one wave to the trough of the next. See the following :

The next word we are going to use to "describe" our wave is the word Period or Time Period. But to illustrate it we need to change the x-axis of our wave. Up to now we have shown "Distance travelled by the wave" on the x-axis. With a water wave this would be like taking a single photograph of the wave as it passed you in the water. To illustrate Time Period we need to imagine that we are in the water and we watch just one point on the wave and plot its up and down positions or displacements against time. The resulting graph would look almost identical to the ones we have already seen but the x-axis would now be labelled Time.

Using this graph we can now illustrate Time Period :
Time Period, T - the time taken for a wave to complete one full cycle (this is shown by the first T).
Or, the time taken for a point to travel from one displacement position (eg peak or trough) and back to the same displacement position; (this is shown by the second and third T).

The final word that we are going to learn to "describe" our wave will also make use of our time x-axis.
It is the word, Frequency and it simply means the number of complete cycles of a wave that pass a point in one second.
To illustrate Frequency we need to add a few numbers to our x-axis as shown below :

So, we can see that there are 2 complete cycles of the wave occuring in 1.0s. Hence, for this wave the Frequency, f is 2.
We could say, the Frequency, f = 2 cycles per second
but the preffered unit is the hertz, Hz, so we say:
The Frequency, f = 2 Hz.

What is the Time Period of this wave?
We can see this easily; the time taken for one full cycle is 0.5 seconds, so Time period, T = 0.5s.

Can you see a connection between the Time period and the Frequency? Look at the two values above, f = 2 and T = 1/2 !!
So, T = 1/f

Time for a few more questions!

Wave Speed and The Wave Equation

Wave speed is the speed at which a wave moves through a medium or through space (in the case of electromagnetic waves).

Or, it is the speed at which energy is transferred as a wave moves from one point to another.

How can we know the speed of a wave?

Its speed must be connected to its Wavelength, mustn't it? ie a wave with a long wavelength might travel 100m in a certain time whilst a wave with half its wavelength will only travel 50m in the same time, so the first wave has a higher speed.

So, the greater the Wavelength the greater the Wave Speed.

Wave speed must also have something to do with Frequency. A wave with a high frequency puts out, say, 10 waves per second, whilst a wave with half its frequency puts out only 5 waves each second. If both waves have the same wavelength, then the one with the higher frequency will have travelled further in one second, so it is faster.

So, the greater the Frequency the greater the Wave Speed.

Super! We have an equation that can be used to find the speed of any wave if we know its Wavelength and its Frequency. We call it "The Wave Equation".
Let's do an example:

Time for a few more questions!

Reflection, Transmission, Absorbtion of Waves

Whenever a wave travelling in one material meets a new material we say that it meets a boundary. For example, a sound wave travelling through the air (material 1) meets a wooden door (material 2); the wooden door is a boundary for this particular sound wave.

At the boundary one or more of three things can happen;

Illustrating the Reflection of Waves

The easiest way to illustrate the reflection of waves is to consider water waves moving in a "Ripple Tank".
When we look down at the tops of the water waves in the tank we see parallel lines moving from the vibrating bar that rests on the surface of the water producing the waves.

.

What happens if we put a solid obstacle such as a plastic or metal bar into the water, as shown below?

The hard solid obstacle is a very particular Boundary which prevents any transmission of the waves or absorbtion of the waves. So, the only option for the waves is that they are reflected when they meet the boundary. And that is what we are seeing in the diagram.

If we simplify the "wave" diagram by turning it into just a "ray" diagram, as shown below, we can see that the reflection of the waves obeys the same Law of Reflection that you should remember from KS3 physics and is usually applied to light rays.


You can see that "the angle of incidence i equals the angle of reflection r." ( i = r)

All types of wave obey this Law of Reflection making it very easy to control the direction of waves. For example:

(Incidentally, it was finding that waves obeyed the same Law of Reflection as light that caused physicists in the 18th century to suspect that light was itself a wave motion.)

The Transmission and Absorbtion of Waves

Transmission

If we go back to our ripple tank, remove the solid obstacle boundary and replace it for some other boundary such as a piece of plastic that simply changes the depth of the water, making it shallower, then we see a different effect when our water waves meet it.

Compared to when we had a solid boundary, the waves are no longer reflected. At first glance they seem to pass "across" the boundary unaffected travelling in their original direction. But at closer inspection we can see that there is a significant change; the wavefronts are closer together, so the wavelength of the waves has decreased2 < λ1).
The waves have been Transmitted across the boundary but not without some change.
In fact, the cause of the decrease in the wavelength is that water wave speed depends only on the depth of the water (as we mentioned above) and in shallower water the waves travel more slowly. The slowing down of the waves means they don't travel so far in the shallower water, which is seen as a decrease in their wavelength.

An even more interesting thing happens if we alter the angle of this kind of boundary:

Now we can see that, as before, the wave is transmitted ("passes over") at the boundary but that it is made to change its direction. This is due to the decrease in the wavelength as the wave enters the shallower water, as we found in the previous example, but in this diagram you should be able to see that some of the waves enter the shallower water before others so they slow down whilst the others keep moving in the deep water at their original speed; this causes the wavefronts to shift as shown. Eventually all the wavefronts reach the shallower water but are travelling in the new direction.

If we simplify the "wave" diagram (as we did in the reflection example) by turning it into just a "ray" diagram, as shown below, we can see that the ray or the wave direction has been refracted.

So, once again, waves are found to behave just like light rays.

Absorbtion

The ripple tank with its water waves doesn't really provide a suitable demonstration for the Absorbtion of waves. However, a really simple example is one that we rely on every day:
When our brother/sister or friend/neighbour is playing their music in another room next to ours, not too loudly, we expect that the wall in between will "block out the sound". What we really mean is - we expect that sound waves from the other room will travel to the wall but the wall will absorb them such that they do not pass through to our room. Another way to think of this is: The wall is absorbing the energy of the sound wave as it passes deeper and deeper into the wall until, hopefully, there is no energy left and the waves stop.
Of course there are occasions when the sound in the other room is so loud that some sound waves manage to pass through the wall into the ajoining room, although at reduced amplitude (volume).

All waves can be absorbed like this.
Another simple example involves light waves; when we wear sunglasses we expect that a fair amount of the energy of the Sun's light waves gets absorbed by the material of the glasses, and this is indeed what happens. Sunglasses are simple "light wave absorbers".

Sound Waves and Human Hearing

First a bit of revision:

1. You should remember that sound travels as a Mechanical wave, so it needs a material (or medium) through which to travel; sound can travel through solids (eg wood), liquids (eg water) and gases (eg air). But sound can't travel through a vacuum such as in space.

2. Also remember that sound travels as a longitudinal wave, so it pushes and pulls the particles of the material through which it travels, forming areas of high pressure called compressions and areas of low pressure called rarefactions.

Converting a Longitudinal Sound wave to a Transverse String wave!

(This heading might seem a bit odd, but you will see its relevance in a little while.)

If we use a piano to play a single sound note, a longitudinal wave, near to a tight string fixed at both ends, the string will begin to vibrate as a transverse wave (if its length is suitably chosen).

You can do a similar thing with a guitar: if you hold down the thickest string at its 5th fret and pluck the string, producing a longitudinal sound wave, you will see the next string vibrate as a transverse wave even though you didn't pluck it!

The longitudinal sound wave from the piano or from one string of a guitar is converted into a transverse wave on a suitably tensioned/length nearby string.

In Physics we call this phenomenon, resonance.
The untouched tight string is said to "resonate" with the forcing sound.

This same phenomenon takes place in our ears!

Converting a Longitudinal Sound wave to a Transverse wave on our ear drum.

When sound (a longitudinal wave) enters our ears it causes our ear drum (which is like the tight string, except its a bit more disc shaped) to vibrate (as a transverse wave).

And since the ear drum has a fixed size and tension there is a limited frequency range over which incoming sound waves can make it vibrate by resonance.
This is why we have a limited, although quite good, frequency range of hearing. It is from a very low value of 20 Hz to a more than sufficient high value of 20,000 Hz (20 KHz).
Not surprisingly our ear drum works best roughly in the middle of this range, so our hearing is most sensitive in the 2000Hz to 5000Hz range.

The transverse vibration of the ear drum is passed through the middle ear via 3 tiny bones (the smallest in the body) to the inner ear where in conjunction with the auditory nerve the vibrations are converted to electrical signals and transferred to the brain.

Waves for detection and exploration

The fact that we discovered above, that waves can be reflected/ transmitted/ absorbed when they meet a boundary, can be made use of in a number of ways to learn more about the world by detecting what lies around us and what lies inside us! We will focus on two particular types of wave that are used in this way; first, ultrasound waves that can be used to detect both within and outside of us; second, seismic waves which can be used to explore the structure of the earth around us.

Ultrasound Waves

Ultrasound waves are sound waves that have a frequency above the upper limit of the human hearing range.
So, ultrasound waves are sound waves with frequencies greater than 20 KHz.

If ultrasound waves are just sound waves with a particularly high frequency, what makes them special or useful?

Good question!
The high frequency of ultrasound waves (compared to ordinary sound waves which we can detect with our hearing) gives them a VERY small wavelength.
This means that they can be used to detect small objects or to distinguish between two or more close spaced objects.
The technical term for this is "resolving power" and it is the very small wavelength of the ultrasound waves which enables them to be used to "resolve" closely spaced small objects.

NB. Resolving power or resolution ability is inversely proportional to wavelength, so the smaller the wavelength, the greater the resolution ability of a wave.

We experience/make use of this physics fact every moment of our waking lives if we have sight; the unbelievably small wavelength of light waves enables them to reflect off very small objects or closely spaced objects such that we can detect or "see" tiny objects and can distinguish between small closely spaced objects. If the wavelength of light was much larger we wouldn't be able to do this. We take it all for granted, don't we!

The diagram above illustrates how a short wavelength wave enables two closely spaced objects to be seen or resolved as two objects instead of just one.

Using ultrasound to detect the world around us

1. To measure the depth of water and to find fish!

Look at the following diagram:

The ultrasound wave is sent out by a transmitter on the ship, it travels down through the water (sound travels very readily through liquids), it reflects off the sea bed and returns to the ship's receiver.
On board the ship the captain will see something like the following on his "echo-sounding screen".

The captain can see the time that it took for the ultrasound wave to be sent out (the first pulse) and return to the ship (the second pulse) after it reflected off the sea bed, and from this he can work out the distance that the sound travelled and hence, the depth of the water!

Let's look at an example.

The technique of using ultrasound to find the depth of water is known as "Echo-sounding" because it relies on the ultrasound wave being reflected off the sea bed which is an example of an "Echo".

The same technique is used by sea fishermen in their trawlers to find shoals of fish. They first use their echo-sounding equipment to get the depth of the water, then they watch for further reflections that occur with smaller time delays indicating that the ultrasound has reflected off something in between the ship and the sea bed, ie a shoal of fish!


Its not difficult to imagine how useful this "Echo-sounding" is for ships to avoid rocks, sudden changes in depth, underwater debris etc. Also, the small wavelength of the ultrasound enables it to be directed very precisely, allowing the captain to "resolve" very small changes in depth or "resolve" the size of individual fish!

2. To "see" inside our bodies

X-Rays ( very high frequency electromagnetic waves) have been used for about 100 years to enable doctors to see broken bones and fractures that otherwise might have been untreated or treated incorrectly, but X-rays are harmful to us fragile humans!

In recent decades ultrasound waves (very high frequency sound waves) are being used to "see" within our bodies. Perhaps their most common use is in pre-natal baby scanning where a mother can have a view of the baby inside her! The reason that ultrasound is used for this delicate procedure is that, unlike X-rays, ultrasound waves are harmless to humans.

The use of ultrasound to "see" a baby inside its liquid filled "bag" is similar to the depth finding technique described above, but since a foetus is mostly made of soft materials (at least until nearly ready to be born), the ultrasound pulses are only ever partially reflected off the different layers of material that make up the foetus. But the advantage of this is that it enables not only the foetus to be seen but to see inside the foetus as the ultrasound pulses pick out the slightly harder spine or skull as well as the outer softer muscle layers and skin.


3. Industrial uses.

Ultrasound waves have found many uses in industry, for example detecting cracks in metal strctures or pipes when the crack is below the visible surface of the structure or when the structure (eg a pipe) is buried below the ground.

Consider the following; a pipe is buried but engineers suspect that there is a crack at some point along a certain section.

Ultrasound waves can be directed down through the earth and the reflection from the pipe can be detected. Along the section where there is no crack, the reflected pulses will returned at constant time intervals, as the ultrasound source is moved along the course of the pipe. But at the point where the crack occurs, the returned pulses will suddenly change; they may be of different amplitude and take longer to return because the waves will travel further into the crack before being reflected. The engineers will detect the change and know that they have discovered the place of the crack. Now they can dig down, find the crack and hopefully repair it.

Similar techniques are used to look for cracks in aircraft undercarriage (ie the metals structures that hold the wheels). Engineers will scan over the surface of the structures and the presence of even tiny cracks will show up as changes in the reflection of the ultrasound pulses.

Seismic Waves

Seismic waves are waves that are produced by "seismic events", notably earthquakes. They are, obviously, mechanical in nature, but they can be transverse and longitudinal.

The first type of seismic wave that occurs following the start of an earthquake is called a Primary wave (because its the first) or P - wave. P waves are longitudinal.

Soon after the P wave, comes another seismic wave, called the Secondary wave (pretty obvious, eh!) or S - wave. S waves are transverse.

Now our knowledge of how these waves move or travel has enabled us to build up a picture of what lies beneath the surface of the earth!
For example we know that the push-pull vibration of the longitudinal wave means that it can travel through liquid but the side to side vibration of the transverse wave means that it can NOT travel through liquid!
Think of standing in a swimming pool and pushing water infront of you with your two hands; you will produce a wave which will travel. Your longitudinal vibration travels through the water. Now imagine - you see if you can have the same success moving your hands side to side; you will find that you will NOT produce a wave which will travel ahead of you.
So longitudinal vibrations travel in liquids, transverse vibrations don't.
Also that waves will travel faster in mediums/materials of greater density eg faster in solid than in liquid.
This is the knowledge that you have to remember about the seismic waves in order to use seismic waves to find out about the structure of the earth.

Using Seismic Waves To See Inside the Earth

When seismic waves were first used to explore the structure of the earth, it was thought that the earth was essentially a solid structure, possibly consisting of rocks of different densities.
Scientists or specifically seismologists, set up seismometers (seismic listening devices) all over the earth.
When an earthquake occured, the seismometers closest to the epicentre of the seismic event recorded the P waves first, obviously, then the S waves. But when the data from all the seismometers was analysed it was found that some detectors didn't detect any S waves at all! The results did NOT fit the conclusion that the earth was essentially solid. Instead it suggested that a significant section of the earth's core had to be liquid.


So the core of the earth, shown in an orange colour above, had to be liquid.
With this updated picture of the earth clearly established seismologists continued to monitor earthquakes and analyse the seismic activity in order to generate a more detailed picture of the "liquid" core and also of the density of the mantle (the vast section of the earth between the core and the earth's crust).

By analysing P waves passing through the suspected liquid core they found that some reached the far side of the earth much faster than others. Notably, those that were passing right through the centre of the earth; this suggested that these P waves were encountering a solid region within the liquid core, giving rise to the current theory that at the centre of the earth there is a solid inner core with a liquid outer core surrounding it.


Also, whilst observing the progress of both P and S waves through the mantle region, seismologists realised that the wave paths were not straight but were curved, as is shown in the above two diagrams.

The only way to explain this was that the waves were being refracted as they travelled at different speeds through the mantle and the reason for this was that the density of the rocks was changing. The suggestion was that rocks closer to the centre were more dense; this explains the direction of curvature of the paths of the waves.

So, you can see how study of seismic waves provided new evidence that has led to discoveries about parts of the Earth which are not directly observble.

Time for a few more questions!