# Wave Parameters: Wavelength, Amplitude, Period, Frequency & Speed

## Wave Parameters

So, we’ve learned a little bit about waves, right? We’ve learned that waves originate from vibrations, which are oscillating motions over a fixed position. A vibration can cause a disturbance to travel through a medium, transporting energy without transporting matter. This is what a wave is. But, how do we properly talk about waves? How do we compare them to one another? Can we measure the size and speed of a wave? How do we know how much energy it carries?

To find out, we’ll need to look at the major **wave parameters**: the ways in which we measure waves. We’ll learn how to characterize a wave by its period, frequency, amplitude, speed, and wavelength. Once we get to know the right way to use these parameters, we’ll be able to learn more about how the different waves work.

Let’s start off by remembering what a wave looks like. We’ve seen the picture above before. It’s a wave drawn over a set of X and Y axes. We plotted the wave as a function of time and said that the portion of a wave between two crests or troughs is called a wave cycle. From this image, we can see that waves travel by crests and troughs in a periodic fashion. That is, a full wave cycle always takes the same amount of time. In this case, that amount of time is exactly two seconds. Two seconds is called the *period* of the wave.

## Period and Frequency

The **period** is the time it takes a wave to complete one cycle. We measure the period in seconds, and we symbolize it with the capital letter *T*. You can think of the period as the time it takes for one particle in the medium to move back and forth. If this were a water wave, all the particles in the water would be moving up and down as the wave travels through. The time it takes for one water molecule to move up, move back down, and then return to its original position, is called the period.

Knowing the period of a wave is fine, but we often need to talk about waves in terms of how often the wave cycles are coming. In other words, we want to know the **frequency** of a wave. A wave’s frequency is the number of cycles that are completed in a certain amount of time. The symbol for frequency is the lowercase *f*, and we measure it in cycles per second, which is the same as the unit hertz. A wave with a frequency of 20 Hz completes 20 wave cycles every second.

Be careful that you don’t confuse frequency with period. This is a common mistake. Frequency and period are actually opposites. While period is measured in seconds per cycle, frequency is measured in cycles per second. Consider our wave with a period of 2 seconds. Since the wave completes one cycle every two seconds, then its frequency is one half or 0.5 Hz. So, you see – period and frequency are reciprocals of each other. We can represent their relationship with a simple equation:

The greater the period is for a wave, the less wave cycles can fit within a second, and so the lower the frequency gets. Likewise, a wave with a larger frequency would have to fit more wave cycles into every second, meaning the period of each cycle would have to be smaller. No matter what kind of wave you’re looking at, the period and frequency will always be inversely proportional to each other.

## Amplitude and Energy

So, now we know how to measure a wave based on cycles and time, but what about the height of a wave? Can we measure how high a wave’s crest reaches or how low the trough dips down? We already mentioned the **amplitude** in our previous lesson. It’s the distance between the midline of a wave and its crest or trough. Amplitude measures how much energy is being transported by the wave. The larger the amplitude, the more energy a wave has.

The symbol for amplitude is a capital letter *A*. Be careful not to make the mistake of thinking amplitude is the distance from crest to trough. It’s only the distance from the resting point. Let’s take the example of a giant water wave.

We can see that the crests reach half a meter above the resting point, and the troughs reach half a meter below the resting point. It doesn’t matter whether we look at the crest or the trough. The amplitude for this wave is 0.5 meters.

## Speed and Wavelength

If waves carry energy and the energy of a wave is illustrated by its amplitude, then does that mean high-amplitude waves move faster than waves of low amplitude? You might be tempted to think so. But, the speed of a wave has nothing to do with the amplitude of its crests and troughs. **Speed** is measured by the distance the wave travels in a certain amount of time. Specifically, it’s measured in meters per second. We already have the ‘per second’ part down. Remember, the frequency tells us how many cycles are completed per second. But, how do we know what the distance is for each complete cycle?

The distance per cycle of a wave is called the **wavelength**. It’s easiest to find the wavelength by measuring the spatial distance between two wave crests. Earlier, we were measuring the time it took to complete one cycle. But now, we’re measuring the length of one complete wave cycle. Wavelengths for long waves can be measured in meters, but we use nanometers to measure the length of shorter waves. The character that symbolizes wavelength is the Greek letter lambda.

So, now can we find out the **speed** of a wave? Sure! We’ve got a measure of distance from the wavelength of the wave, and we’ve got a measure of time from the frequency. Wavelength is meters per cycle. Frequency is cycles per second. So, multiplying the two gives us meters per second. In science, we use a lowercase *v* to symbolize speed because it’s also called velocity. So, we can sum up our findings now with the equation: speed equals wavelength times frequency.

Well, that wasn’t so bad, was it? You’ve learned five ways of describing a wave using your **wave parameters**. The period, frequency, amplitude, speed, and wavelength are used to distinguish and categorize waves into groups. Later on, we’ll learn about the many different types of waves that are out there, and how to use these parameters to understand them all.

## Lesson Summary

A wave is a disturbance that travels through a medium in a periodic fashion, carrying energy without transporting matter. Waves are described and measured by five wave parameters: the period, the frequency, the amplitude, the wavelength, and the speed. The period of a wave is the time it takes to complete one cycle. The frequency is just the opposite; it’s the number of wave cycles that are completed in one second. Amplitude and wavelength are both measures of distance. The amplitude measures the height of the crest of the wave from the midline. The wavelength measures the horizontal distance between cycles. Wave speed is found by multiplying the wavelength and the frequency. By learning the five major wave parameters, we can learn about waves more easily and categorize them based on their traits.

## Learning Outcomes

Following this lesson, you’ll be able to:

- Describe each of the five wave parameters: period, frequency, amplitude, wavelength, and speed
- Explain how to find each of the five parameters and identify their symbols
- Provide an equation to find wave speed