What is a wave?

Lets see - our usual ideas of a wave may include water wave, waving our hands, wavy shape of someone's hair, ...

The word "wave" that is used in physics does have some connections with all of these ideas. As is usual in physics, we would learn about a few basic features of this thing called "wave", and then use these to explain the effects of waves that we may see around us.

"Wave" is a topic in physics, maybe the most important. It is the foundation of the modern physics understanding of nature and the universe - that matter and wave are really two sides of the same thing.

Funnily enough, around the start of the 20th century, physicists - scientists that specialises in physics - started to see waves in everything. Atoms are waves, electrons are waves, protons are waves, neutrons are waves, stones are waves, elephants are waves, ...

This is one of the strangest discoveries in physics. And being physicists - meaning scientists that specialise in physics - they have to make very careful measurements to check that their theories are really true.

And they did. So today, we have to study this in physics. You might have heard of it. It is called quantum mechanics.

But I am am getting ahead of the topic. The matter-wave topic - also called quantum physics - will come later in the physics syllabus. For now, this topic on "wave motion" would just be about the common waves that we know, like water waves, sound wave and light wave.

Ok, we cannot really "see" sound wave and light wave. Or wait ... maybe we can. Kind of - as I shall explain in the next topic called "Superposition".

Meanwhile, lets take a look at what are the kind of things this topic on Wave Motion is about.

Take a look at the photo above. There is a guy rowing a boat on a river. That guy was me, and the river was River Mersey in England, which flows past the city of Liverpool into the sea.

In front of my boat, you can see waves. They caused the the water surface to move up and down. The up part is called "crest". The down part is called "trough". The crests and troughs appear to move along the water surface.

This makes it look like the wave is moving. But mostly, the wave just appears to travel. The actual water may be mostly just bobbing up and down in a regular way that makes it look like the waves are travelling over the water surface.

In other words, the appearance of water travelling with the wave is an illusion. The wave travels, the water may not.

According to the syllabus, we need to "show an understanding of and use the terms displacement, amplitude, period, frequency, phase difference, wavelength and speed". That is 7 physics terms to learn and remember!

And as is usual in physics, we start with some simple examples, like a rope. Lets say we tie one end of a long rope to something - maybe one leg of a table. We then pull the other end until the string is slightly taut, and start shaking it up and down a few times.

We would create a wave. We can actually see this wave travel to the table, and then bounce back to us.

This is probably the simplest kind of wave we can easily make and see. It also helps us to learn a few basic features that we would see in other types of waves.

For example, we can see the typical up-down pattern repeated over the string. The length of one of these repeating pattern is called a "wavelength".

We see this pattern travel over the string at a certain speed until the wave pattern hits the table. This speed is called the wave "velocity".

If you are able to look hard at a particular point of the string - maybe mark it with a red marker - you can see the mark going up and down repeatedly as you shake the string. The number of times it goes up and down every second is called the "frequency".

So there you are - you have just seen the meanings of the 3 out of the 7 terms mentioned above, and also the 3 most basic things about a wave: wavelength, frequency and velocity.

The full list is as follows :

1. displacement
2. amplitude
3. period
4. phase
5. wavelength
6. frequency
7. velocity

There is a simple relation between speed, frequency and wavelength.

       velocity  =  frequency  x  wavelength

Students often memorise this for exams without understanding the reason. In fact the reason can be quite simple, though it is not normally explained this way:

Imagine a small ball floating on the water. As the wave passes under it, the ball bobs up and down. Each time 1 wavelength passes under the ball, the ball bobs up and down once. So

       wave speed  =  wavelength  /  period

But 1 period is 1 up down cycle of the wave under the ball. So

       wave speed  =  wavelength  x  1 / period

which is the same as

       wave speed  =  wavelength  x  frequency !

I hope this is an easier way than textbook to understand this important relation between speed, wavelength and frequency of a wave.

With all these motion, there surely must be some energy in there.

First, one thing about this water wave is that all the wave looks like it is travelling over the water, the actual water molecules may just bob up and down on the same spot - without going anywhere.

What this means is the wave whole impression of the wave travelling along the water surface may be just an illusion!

But although water molecules can produce the wave motion without actually travelling with the wave, there is something that does travel with the wave. It is the energy.

The up down motion of the water means that there is kinetic and potential energies in every wavelength. As the wave motion travels, so these energies are carried over the water along with the travelling wave.

In other words, energy is transfered by the wave over the distance that the wave travels.

Waves in 3D

The above ideas are the basic part of the physics of waves. We have talked about two simple examples - wave along a string, and wave over water surface.

Notice something about these two types of waves :

- Wave along a string travels in 1 dimension, along the string.

- Wave on water spreads out in 2 dimensions, over the water surface.

Can we have wave in 3 dimensions?

Of course. These are the two waves all around us that we are most familiar with, but which most people have no idea they are waves - sound, and light.

Most people might have heard about phrases like "light wave" and "sound wave". But unless they have studied physics diligently, they may not know how or why light and sound are actually waves.

I shall talk about this in my next blog - in a topic called "superposition".

People often associate sound and light with energies, even if they may not know much about the nature of these energies. For sound, the energy is carried as kinetic energy of air molecules. For light, it is carried by a combination of electric and magnetic energy.

So the understanding of sound and light energies requires some imagination, like water wave that we can see with our eyes.

I have talked about wave along a string, and wave over water surface. These are familiar waves we can easily see in everyday life.

You might have heard people say "sound wave" or "light wave". What to they actually nean?

We cannot actually "see" sound or light. But lets see how much I can say about these without going into the heavy physics and maths.

Just as water wave happens when something disturbs a water surface, so sound wave happens when something disturbs the air.

Like when I wave my hand?

No. When I wave my hand, it can make some waves in the air. But we cannot "hear" this wave. Our ears can only hear waves in the air when the frequency is at least 20 Hertz, or 20 cycles per second.

Can you wave your hand 20 times per second? A hummingbird can actually flap it wings 40 times per second. That is why we can hear its humming sound.

If the sound comes from a source that is further away, then it can sound softer. The reason is that the sound power has spread out more, so less of it comes into our ears. We describe this wave power falling on a fixed area (like our ears) by calling it "sound intensity"

Lets go back to the string wave and water wave above. In both examples, the actual motion in actually at right angles to the wave travel.

Like - when we shake one end of the string up and down, the wave travels away from us along the horizontal string. The bit of the string I am holding is still between my fingers and has not travelled away.

In this example, notice that the actual string material just moves up and down and does not go anywhere. The end of the string that I holds on to is still in my hand, no matter how many waves I make when I shake the string.

So is all this just an illusion?

Well, yes and no. It is an illusion that the string is or water is moving away as fast as the wave. But it is real that energy is being carried away by the waves.

For the string or water wave described above, notice each point on the string or water surface just moves up and down - in a direction perpendicular to wave travelling.

This type of wave is called "transverse wave".

There is another type of wave where the oscillation is along the direction of the way. An example is sound wave.

When say a loudspeaker makes a sound, a piece of paper in the speaker vibrates rapidly. This pushes and pulls at the air in front of it. So the air molecules actually move back and forth in the same direction as the sound.

This type of wave is called "longitudinal wave".

Have you heard of polarised sunglasses?

It all started when people tried to overcome to glare of sunlight reflected from sea water.

As it turns out, light wave is a transverse wave. Oscillations in light wave from the sun can be in any random directions that are at right angles to the sun's ray.

When sunlight falls seawater, only the horizontally oscillations of the light gets reflected.

Polarised sunglasses can block of the horizontal oscillations of sunlight, but still allows the vertical part to go through.

In this way, it is better than the simple dark glasses which blocks out most of the light.

Finally, students also need to learn how to "measure" waves - using an oscilloscope. Students will not actually be tested on operating a real oscilloscope. Instead, they would get questions on oscilloscope displays that show some wave forms.

One common question, for example, is about sound reflected from a wall. A microphone connected to an oscilloscope would be moved to and from the wall. The question would ask students to explain how or why the wave changes.

You can learn these concepts and more at Dr Hock's maths and physics tuition.