# Speed of a wave

The speed of a wave, the frequency of a wave, and the wavelength of a wave are all related. Suppose you are closely observing the waves of the sea with a stopwatch and you made the following observation. 1 cycle every second.

Wavelength  = 1 meter

Recall that 1 cycle every second means that after you see the first crest, it will take 1 second to see another.

The wavelength is the horizontal distance a crest moves each second.

Since the wavelength or distance between two crests is 1 meter and it takes 1 second for this wavelength to form, the speed of the wave is 1 meter per second.

(1 times 1)

In many cases, you may see more than 1 crest in one second.

Example #2

Pretend the frequency is 3 cycles in 1 second and the wavelength is 1 meter.

If one cycle creates a wavelength of 1 meter, then 3 cycles will give a distance of 3 meters.

If the wave moves 3 meters every second, then the speed is 3 meters per second. (3 times 1)

Example #3

Pretend the frequency is 3 cycles in 1 second and the wavelength is 2 meters.

If one cycle creates a wavelength of 2 meters, 3 cycles will give a distance of 6 meters.

If the wave moves 6 meters every second, then, the speed is 6 meters per second. (3 times 2)

## Important observations about the speed of a wave

Notice that we can get the speed of the wave if we just multiply the frequency and the wavelength together.

In example #3 for instance, the frequency is 3 cycles in 1 second and the wavelength is 2 meters.

Speed  = frequency times wavelength = 3 times 2 = 6 m / s

Generally speaking we use the Greek letter Lambda Λ to represent the wavelength.

We write v = f × Λ

Exercise #1: A wave has a frequency of 20 Hertz and a wavelength of 8 meters. Use the formula above to find the speed of the wave.

We write v = f × Λ

We write v = 50 Hertz × 8 meters

We write v = 400 meters per second

Exercise #2: A wave has a frequency of 0.5 Hertz and a wavelength of 5 meters. Use the formula above to find the speed of the wave.

We write v = f × Λ

We write v = 0.5 Hertz × 5 meters

We write v = 2.5 meters per second

## Recent Articles 1. ### Introduction to Physics

Nov 18, 20 01:20 PM

Top-notch introduction to physics. One stop resource to a deep understanding of important concepts in physics

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius! Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.