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Introduction to Waves

Written by tutor James F.

Waves are extremely important, without them we wouldn't have cell phones, microwave ovens, cable TV and the Internet. As waves appear everywhere in our everyday lives, it makes sense that we should know exactly what they are and how they behave. So what is a wave?

Think of hand moving back and forth, or waves on water. Both these things have something in common: repeating movement over time. That is what waves are about, something moving back and forth repeatedly. The "something" could be almost anything, like particles (so small and fast we cannot see), large objects like a pendulum, and even energy. Let us think of certain facts that we know, so that we can construct a general wave model. Firstly, we will call the size of the movement the displacement, like the height of a wave, with the maximum height called the amplitude (always measured from the midpoint – see the diagram below). Next is the wavelength, which is the distance between two successive identical points on a wave (think of the repetition again, it is the distance between repeats). If we draw a diagram to show the displacement changing (going back and forth) along a distance scale, we have a wave, and it looks like this:

A diagram of a wave

Notice the wavelength measured in three places, always between two successive (identical) points. The amplitude is always measured from the midpoint to the wave in a vertical line. Another thing to realize is that if you take a walk along the wave, you would be repeatedly going up and down, just like you do floating in the sea as waves go past!

However, this diagram is like a snapshot, but we know there is movement back and forth in waves, and this gives rise to a frequency. Think of buses: some are frequent, some are not. If we consider the distance between buses to be a wavelength, then we could sit and measure how many buses come past every minute, or every hour. Frequency is measured in Hertz (Hz), which means "per second." So if there were 10 buses every second (unlikely, I know) then the buses have a frequency of 10Hz.

We can also quickly thing of something else - what about the time between repeats? This is called the period, and is linked to the frequency. If the period is short, we will have many repeats (high frequency), if the period is long, we will have less repeats (low frequency). The formula here is just

frequency = 1 / period

We now have to start thinking about an extra thing - what is the wave itself is moving? Some waves are "still" (like the hand waving back and forth, a clock pendulum), but most waves actually move from one place to another with a speed. What if the buses from the example before stayed the same distance apart (the wavelength stays the same) but they all drive twice as fast - will that change how frequent the buses are? Yes - we will see twice as many buses per second! So the speed of the wave is also important, and there is a formula called the "wave equation" which links the wavelength, frequency and speed for waves that travel from one place to another:

speed = wavelength x frequency

Types of Waves

One type of wave is known as longitudinal, and the other is transverse. Which type it is depends on something quite simple. We start with the direction the wave is going. Let us take a wave moving horizontally left to right. Now we think about the repeating part.

  • If it moves back and forth along the same line (horizontal), then the wave is longitudinal
  • If it moves back and forth at right angles (vertical) to the wave direction, it is transverse

It is easy to give examples. A sound wave is longitudinal; the air particles that carry the sound move back and forth along the direction the wave travels. A water wave is transverse; imagine again floating in the sea. As a wave travelling toward the beach (horizontal direction) goes past you, you will float up high and then back down (move in the vertical direction). Your motion (the thing repeating back and forth) is at right angles to the direction the waves are going in.

Most waves (e.g. light, microwaves, x-rays) are actually transverse, with sound being one example of a longitudinal wave.

Important Wave Facts

A couple of last things to note on wave basics: first is that with the exception of light waves, all waves need a medium to travel in, e.g. sound waves need air. (Sound can therefore not travel in a vacuum!) The second point is that waves transfer energy from one place to another.

Practice Questions

Question 1

Look at the wave below. Work out:
A) The wavelength
B) The amplitude

A sample question about waves
The solution to a practice problem about waves

Question 2

If the wave in the question above is travelling at 390m/s, what is the frequency of the wave? Also, what is the period of the wave?

speed = frequently x wavelength

frequency = speed / wavelength

frequency = 390 / 30

frequency = 13 Hz

Question 3

Imagine two astronauts on a spacewalk; they usually communicate using radios. These electromagnetic waves can travel through space, so they can talk. If their radios were to break, how could it still be possible to still communicate with each other in space? Click next for a hint!

Hint: their spacesuits contain oxygen for them to breathe.

They could place their helmets in contact with each other and just talk normally. The particles in the helmet and the oxygen molecules inside would allow sound waves to travel.

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