Wave Equations

Wave speed is defined as:

The distance travelled by a wave each second

The wave speed can be calculated in a similar way to calculating the speed of moving objects:

$wave speed = \frac{distance}{time}$

Where:
- Wave speed is measured in metres per second (m/s)
- Distance travelled by the wave is measured in metres (m)
- Time taken is measured in seconds (s)
All waves obey the wave equation, which is another way to calculate the wave speed:

$\begin{array}{rcl} wave speed & = & wavelength \times frequency \end{array}$

$\begin{array}{rcl} ν & = & f λ \end{array}$

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

Higher tier students may need to rearrange the wave equation, which can be done using a formula triangle

Formula Triangle Relating Wave Speed, Frequency and Wavelength

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

A formula triangle can be used to help rearrange the wave equation

Worked example

Sound waves in air travel with a frequency of 170 Hz and a wavelength of 2 m. Calculate the speed of sound waves in air.

Answer:

Step 1: List the known quantities

Frequency, $f$ = 170 Hz
Wavelength, $λ$ , = 2 m

Step 2: Write out the wave equation

$ν = f λ$

Step 3: Substitute the known quantities into the wave equation to calculate wave speed

$\begin{array}{rcl} ν & = & 170 \times 2 \\ ν & = & 340 m / s \end{array}$

Worked example

Higher Tier

A wave in a pond has a speed of 0.15 m/s and a frequency of 0.5 Hz. Calculate the wavelength of the wave.

Answer:

Step 1: List the known quantities

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

Step 2: Write out the wave equation

$ν = f λ$

Step 3: Substitute the known quantities into the wave equation

$0.15 = 0.5 \times λ$

Step 4: Rearrange to calculate the wavelength

$\begin{array}{rcl} λ & = & \frac{0.15}{0.5} \\ λ & = & 0.30 m \end{array}$

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 sometimes wavelength may be given in other units, such as cm or km. When calculating wave speed, check what units for speed the question requires and be prepared to convert the wavelength accordingly.
Likewise, watch out for frequency given in kHz: 1 kHz = 1000 Hz

Wave Equations (WJEC GCSE Physics: Combined Science)

Revision Note

Wave Equations

Formula Triangle Relating Wave Speed, Frequency and Wavelength

Worked example

Worked example

Examiner Tip

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Author: Caroline