The Wave Equation

Wave speed is defined as:

The distance travelled by a wave each second

Wave speed is given the symbol ν and is measured in metres per second (m/s)
Wave speed is the speed at which energy is transferred through a medium
Transverse and longitudinal waves both obey the wave equation:

$v = f \times λ$

Where:
- v = wave speed in metres per second (m/s)
- f = frequency in hertz (Hz)
- λ = wavelength in metres (m)

The wave speed equation may need to be rearranged, which can be done using this formula triangle:

Equation Triangle for the Wave Equation

Wave speed triangle (2), IGCSE & GCSE Physics revision notes

Worked example

A wave in a pond has a speed of 0.15 m/s and a time period of 2 seconds. Calculate:

a) The frequency of the wave

b) The wavelength of the wave

Answer:

(a)

Step 1: List the known quantities

Time period, T = 2 s

Step 2: Write out the equation relating time period and frequency

$f = \frac{1}{T}$

Step 3: Rearrange for frequency, f, and calculate the answer

$f = \frac{1}{2}$

Frequency, f = 0.5 Hz

(b)

Step 1: List the known quantities

Wave speed, v = 0.15 m/s
Frequency, f = 0.5 Hz

Step 2: Write out the wave speed equation

$v = f \times λ$

Step 3: Rearrange the equation to calculate the wavelength

$λ = \frac{v}{f}$

Step 4: Use the frequency you calculated in part (a) and put the values into the equation

$λ = \frac{0.15}{0.5}$

Wavelength, λ = 0.30 m

Examiner Tip

When stating equations make sure you use the right letters:

For example, use λ for wavelength, not L or W

If you can’t remember the correct letters, then just state the word equations

Be careful with units: wavelength is usually measured in metres and speed in m/s, but if the wavelength is given in cm you might have to give the speed in cm/s

Likewise, watch out for frequency given in kHz: 1 kHz = 1000 Hz

The Wave Equation (Cambridge O Level Physics)

Revision Note