Speed of a wave
Recommended for You
Not sure where to start? These are the lessons and games we recommend most to students, parents and teachers on Basic-mathematics.com. Each lesson explains the topic in plain language, walks you through worked examples step by step, and ends with practice so you can check your understanding. Pick one below, or use the menu to find lessons on fractions, algebra, geometry, statistics and more.
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 × ΛWe 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 = 0.5 Hertz × 5 meters
We write v = 2.5 meters per second