# Wave Period: Definition & Formula

Waves are all around us – we can see them in water, and we encounter them everyday in the form of sound waves and microwaves. The cycle of a wave can be fast or slow, and this is determined by the wave period, which is the main focus of this lesson.

What Is A Wave Period?

Have you ever tried surfing? In order to surf, we need waves. However, a surfer doesn’t want to ride just any wave. Surfers want to catch waves that are nice and big or which have a high amplitude. Also, it won’t be any fun if a wave appears and disappears quickly. Surfers like waves that last long, or those with a long wavelength and wave period.

Waves: Surfing

This illustration shows us a simple sign wave. You’ll see patterns like it in sound waves, microwaves and, yes, even ocean waves. Like all waves, it has crests or peaks, which are the highest points. It also has troughs, the lowest points. The wavelength of this wave is the distance between one of its peaks and the next peak. Wavelength is represented by the Greek letter lambda.

You may notice that the distance between peaks is the same as the distance between troughs. We can also measure wavelength from one trough to the next. Either way, the wavelength will measure the distance of one wave cycle, or one completion of the wave’s repeating up and down pattern.

The wave period is the measure of time it takes for the wave cycle to complete. We usually measure the wave period in seconds and represent it with the letter T.

Crest, Trough, Wavelength

Frequency of a Wave

Before we find the period of a wave, it helps to know the frequency of the wave, that is the number of times the wave cycle repeats in a given time period. This graph shows us five different waves with different frequencies. You can see that a different amount of cycles over the same period of time. We could find the exact number by counting the peaks or troughs. The red wave has the lowest frequency among the five because it has the least number of repeating cycles, and the pink wave has the highest frequency because it has the highest number of repeating cycles.

Wave Frequency

Frequency (f), can be obtained by dividing the wave’s velocity, usually symbolized by the letter v, by its wavelength. Remember, we represent it with the Greek symbol: lambda. We usually measure the wavelength in meters and the velocity in meters per second. The frequency found using these units will be measured in Hz (hertz), another way of saying cycles per second.

Let’s say we determine a wave moves at 60 Hertz; that wave will have 60 cycles per second. When writing formulas, Hertz is usually abbreviated to Hz.

Formula For Frequency

Finding a Wave Period

So how can knowing the frequency help us find a wave period? The higher the frequency of a wave, the lower the wave period. After all, if you’re going to fit more cycles into a certain period of time, the cycles need to be shorter.

Wave Period Formula

We can say that the frequency and wave period are inversely proportional to each other, so if the frequency increases, the period decreases, and vice-versa. In other words if the frequency is large, then the period is short and if the frequency is small, then the period is long.

Remember that wavelength and velocity both affect the frequency, so we can also say, the higher the wavelength, the higher the wave period and the lower the velocity, the higher the wave period.’

The wave period is actually the reciprocal of the frequency, which means that any wave will have a wave period of 1 over the wave’s frequency. The standard unit for period is in seconds, abbreviated as the letter S.

Practice Questions

Let do a little bit of practice. Here’s a word problem:

Example 1:

You’re on vacation at the beach, and its a windy day. While looking at the ocean waves, you observed that the approximate velocity of a wave is 3 m/s, and the distance between the peaks of two waves is approximately 20 m. What are the frequency and wave period for these waves?

Solution:

Wave Period Example 1 Solution

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