# 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

## Exercises about the speed of a wave

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

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