Professor Sampler’s Notes: Waves

Topics Covered:

  • Definition of a wave
  • Wavelength
  • Frequency

Nothing exists except atoms and empty space; everything else is opinion – Democritus

A wave is a disturbance. Since everything is in motion constantly, waves are everywhere. Anything that moves displaces another thing. This ‘thing’ can be objects, particles or even spacetime. It’s one of those phenomena that we observe as byproducts of our quirky universe.

A wave is a disturbance

Some waves, like sound, need a medium (fancy term for another thing). Other waves, like light (electromagnetic waves) don’t, i.e., they can travel in vacuum. However, don’t let these terms weigh you down – there are some folk who think pure vacuum doesn’t exist, or is just another medium we haven’t understood yet, and so on.

One of the big misconceptions about waves is that they have to be periodic. They don’t have to. They can exist perfectly unnoticed and unrecognizable, like a house e.g., or they can be random, like the flow of particles in vacuum.

So how do we get a handle on waves? One line of action signal processing engineers use is to avoid random waves and just focus on periodic waves. By periodic, I mean those waves that have a repeatable pattern. Ocean waves, light, sound, the earth’s trajectory around the sun, a dripping faucet – all periodic.

What is the great advantage of repetition anyway? Simple, my friend, repetition means predictability. Science is not only about learning the truth, but also about predicting future events from that truth (as well as learning about past events). A thing that repeats itself is extremely calming to the soul, and makes life possible on earth. Think about weather patterns on earth and how we use its predictability for our farming and survival. If things were purely random and chaotic, we wouldn’t exist. Periodic waves are nature’s way of confusing us – the more things change, the more they stay the same!

We can assign periodic waves a few more properties than their unruly brethren (the random waves). How’s that, you ask? Let’s talk about your newspaper delivery boy. If he’s on time everyday, and is polite, and manages to get you your paper in the condition it left the printing house, you will have a great many things to say about him. If he’s late everyday, and is rude, and manages to deliver a rag that does not look anything like a newspaper, you will still have a great many things to say about him. But what if he’s an unpredictable fellow, who keeps to himself? He might be a topic of speculation, but of not much use. But he still delivers the papers! This is exactly how waves are. Out of all the properties of waves that scientists like to tinker with, two of the most famous are wavelength and frequency.

Measuring wavelength

The wavelength of the wave is simply the distance between any two identical and consecutive shape features, like crests, troughs or zero crossings. In the case of earth orbiting the sun, it takes our planet roughly 365 days to come back to its original position (repeatable pattern), and the total distance covered is roughly a billion kilometers. The wavelength of the earth’s orbit around the sun is 1 billion km.

Frequency is a term that can be used for waves or any event that is cyclical in nature. If a wave feature repeats itself over time, then the wave can be assigned a frequency. The number of times an event repeats itself over a fixed length of time or space is its frequency.

The higher the wavelength the lower the frequency, and vice versa

Is wavelength and frequency related? Frequency is inversely proportional to wavelength. In other words, greater the wavelength smaller the frequency, and vice versa. In the above diagram, the last wave has the highest frequency.

The unit of frequency is Hertz (Hz), formerly called cycles per second. In fact, it can be anything per second. 365 days is around 30 million seconds. If our planet takes 365 days to orbit the sun, then the frequency of the earth’s orbit around the sun is 1/30,000,000 Hz. No need to get shell-shocked, it’s just a way to get a handle on things!

One important thing to remember is that a wavelength or frequency does not have to be constant for a wave. If a boxer throws a few fast jabs and then a couple of slow but murderous right hooks, then the frequency of his attack will have changed, though this is not what the guy at the receiving end will be thinking about, if he is thinking at all.

It is also important to be careful about your use of these words. E.g., if my long distance girlfriend’s calls get fewer and further apart does not mean the distance between us is getting smaller. As long as you use these words within its prescribed definitions you’ll be all right, and everyone will be on the same wavelength.


  • A wave is simply a disturbance. Some just happen to be cyclical
  • The wavelength of the wave is the distance between any two identical and consecutive shape features. The standard unit is meters (m).
  • Frequency is the number of occurrences of a cyclical event over a fixed length of space or time. The standard unit is Hertz (Hz).

Links for further study:

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