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General Studies Science: Help & Review24 chapters | 338 lessons | 1 flashcard set

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Lesson Transcript

Instructor:
*Nissa Garcia*

Nissa has a masters degree in chemistry and has taught high school science and college level chemistry.

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.

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.

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.

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.

**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.

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.

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. *

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:

Okay, we know the velocity, which is 3m/s. We also know the **wavelength**, remember that's the distance between two peaks, so we can call the wavelength 20 meters. We can use these two bits of information to find the frequency. Divide the velocity, 3 m/s, find the wavelength, 20m, and we find that the frequency is 0.15HZ. Or .15 cycles per second. Then we find the reciprocal of that number; 1 over 0.15 will give us the value of 6.67. That tells us that the wave period is 6.67 seconds. Here's another.

Example 2:

The color red has a frequency of 4x10^14 Hz and the color violet has a frequency of 8x10^14 Hz. What are the wave periods for the two colors? Which color has a higher wave period?

Solution:

This one is easy because we already know the frequencies of the waves we're looking at. All we need to do is find the reciprocal of each frequency. The reciprocal of 4x10^14Hz is 2.5x10^-15, which means that the color red's wave period will be 2.5x10^-15 seconds.

Violet's reciprocal and, therefore, its wave period is 1.25x10^-15 seconds. These are complicated numbers but we can still answer the second question: which color has a higher wave period? In this case, the answer is red, whose wave cycle is just a bit slower. We can also figure this out given the frequencies of the two waves. Remember that **frequency is inversely proportional to wave period**. That means the higher the frequency of a wave, the smaller its wave period will be.

Violet waves have a higher frequency than red waves. That means that we know that red waves will have higher wave periods than violet waves without having to plug it in to any equations.

Every day, we encounter waves. Sometimes we see them when we go to the beach and look at the ocean. Other times, they are invisible such as the waves in microwaves and radio waves. Different waves have different frequencies and periods.

The **wave period** is the time it takes to complete one cycle. The standard unit of a **wave period** is in seconds, and it is *inversely proportional* to the **frequency** of a wave, which is the number of cycles of waves that occur in one second. In other words, the higher the frequency of a wave, the lower the wave period.

The wave period is also dependent on the **wavelength** and the velocity. The higher the velocity, the lower the wave period, and the higher the wavelength, the higher the wave period.

**Wave period**: the time it takes to finish one wave cycle**Crests/Peaks**: the highest points of a wave**Troughs**: the lowest points of a wave**Wavelength**: the measurement in meters from one peak to the next peak of a wave**Wave cycles**: one completion of a wave's repeating up-and-down pattern**Frequency**: the number of times the wave cycle repeats in a given time period**Velocity**: speed of the wavelengths is measured in meters per second**Hz (hertz)**: cycles per second**Frequency and wave period are inversely proportional**: if the frequency of a wave increases, the wave period decreases, and vice-versa

When you've finished studying the wave period via this lesson, make certain that you can successfully:

- Write the definition of a wave period
- Verbalize the meaning of the frequency of a wave
- Use frequency to find a wave period

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General Studies Science: Help & Review24 chapters | 338 lessons | 1 flashcard set

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