Wave Calculations

How do frequency, period, and speed apply to waves?

Frequency and period calculations can be applied to waves.  You can also use the frequency and period to find the speed of a wave.

You have probably already encountered the speed equation in a math class. The speed equation is a specific rate equation, s = d/t (where s stands for speed, d stands for distance, and t stands for time), but the wave form of this equations, where ‘lambda’ stands for wavelength, is

You can think of the speed of the wave as the number of meters a crest moves in a second.  This speed is not how fast the particles in the medium are vibrating, rather it is how fast a particular ‘spot’ on the wave (like a crest), is moving from one place to the next. Reminder: the wavelength of a wave is the distance from one crest to the next crest or similarly one trough to the next trough.

Figure 1, The waves in this figure are moving to the right and passing a post from a fallen pier.

Example 2.3.1

The wave above moves to the right as you watch from a pier.  You count 38 wavelengths pass by in 26.5 seconds.  What is the wavelength of this wave?  What is the frequency of this wave?  What is the period of this wave?  What is the speed of the wave?

(3) Shown below is the calculation for the period of the wave.

(1) The wavelength can be measured from the scale on the picture.

(2) The frequency of the wave can be calculated as follows.

(4)  The calculation of the speed of the wave is shown below.

crest moves in this direction

vibration

direction

Example 2.3.2

An earthquake wave has a period of  0.01 s/cyc.  The speed of the wave is 10 km/s.  What is the frequency of the wave?  What is the wavelength of the earthquake?

(2) Now we can find the wavelength using the speed and the frequency.

(1) The calculation of the frequency of the wave is shown below.

Example 2.3.3

A red light wave leaves a prism.  The wavelength of the light is 650nm and one cycle passes every 2.22 x 10-15 seconds.  Calculate the frequency of the light and the speed of light.

(2) Now we find the speed of the light.

(1) The frequency of the light wave is calculated as follows.

Example 2.3.4

A blue light wave has a speed of 3 x 108 m/s and a wavelength of 452nm.  What is the light’s frequency?  What is the light’s period?

(2) Now we find the period of the light.

(1) The frequency of the light wave is calculated as follows.

Often, calculations with waves involve very large or very small numbers.  You may want to review the notes you took in class on metric units before proceeding.

Copyright  © 2009-2012, by Marcus Milling

edited by Julia Pian