Lesson 44: Frequency, Wavelength, & Amplitude

Now that you know something about the properties of the two main types of waves (Lesson 43), we need to make sure that you can look at individual characteristics that waves can have.


When we first started looking at SHM we defined period as the amount of time it takes for one cycle to complete... seconds per cycle

Since frequency and period are exact inverses of each other, there is a very basic pair of formulas you can use to calculate one if you know the other…

It is very easy to do these calculations on calculators using the x-1 button.

Example 1: The period of a pendulum is 4.5s. Determine the frequency of this pendulum.

The period means that it will take 4.5 seconds for the pendulum to swing back and forth once. So, I expect that my frequency will be a decimal, since it will complete a fraction of a swing per second.


Wavelength is a property of a wave that most people (once they know what to look for) can spot quickly and easily, and use it as a way of telling waves apart. Look at the following diagram...

Figure 1
Figure 2

On a longitudinal wave, the wavelength is measured as the distance between the middles of two compressions, or the middles of two expansions.

Figure 3

This leads us to one of the most important formulas you will use when studying waves.

v = velocity of the wave (m/s)
f = frequency (Hz)
λ = wavelength (m)

Example 2: A wave is measured to have a frequency of 60Hz. If its wavelength is 24cm, determine how fast it is moving.

Example 3: The speed of light is always 3.00e8 m/s. Determine the frequency of red light which has a wavelength of 700nm.

Be careful when changing the 700nm into metres. Some people get really caught up with changing it into regular scientific notation with only one digit before the decimal. Why bother? It's only being used in a calculation. You’ll probably just make a mistake changing the power of 10, so just substitute in the power for the prefix and leave everything else alone…700 nm = 700 x 10-9 m since “nano” is 10-9.


Amplitude is a measure of how big the wave is.

The amplitude of a wave is measured as:

  1. the height from the equilibrium point to the highest point of a crest or
  2. the depth from the equilibrium point to the lowest point of a trough
Figure 4

When you measure the amplitude of a wave, you are really looking at the energy of the wave.