Physics

3.2 - Wave Equations

3 min

note 1 of 6

The wave speed equation

Wave speed is the speed at which the wave - and the energy it carries - travels.
The wave equation applies to all waves, linking wave speed to frequency and wavelength.

Formula for wave speed

$v = f λ$

Where:

$v$ = Wave speed, in metres per second (m/s)
$f$ = Frequency, in hertz (Hz)
$λ$ = Wavelength, in metres (m)

A formula triangle with v in the top section and f multiplied by lambda below, labelled wave speed (m/s), frequency (Hz) and wavelength (m). — Cover the quantity you want to find to rearrange the equation.

note 2 of 6

Worked example - Wavelength from frequency

A radio wave has a frequency of 7.5 × 10⁶ Hz. The speed of radio waves in air is 3.0 × 10⁸ m/s. Find its wavelength.

Step 1 - Rearrange the formula

Starting from v = fλ, divide both sides by f to make λ the subject:

$λ = \frac{v}{f}$

Step 2 - Substitution and calculation

$λ = \frac{3.0 \times 10^{8}}{7.5 \times 10^{6}} = 40 m$

The wavelength of the radio wave is 40 m.

note 3 of 6

Formula for wave speed from distance and time

$v = \frac{x}{t}$

Where:

$v$ = Wave speed, in metres per second (m/s)
$x$ = Distance travelled by the wave, in metres (m)
$t$ = Time taken, in seconds (s)

Wave speed can also be calculated from the distance travelled and the time taken. The same equation is also written $v = \frac{d}{t}$ , with $d$ for distance.

note 4 of 6

Worked example - Wave speed from distance and time

A wave travels a distance of 120 m in 4.0 s. Find its speed.

Step 1 - Formula

$v = \frac{x}{t}$

Step 2 - Substitution and calculation

$v = \frac{120}{4.0} = 30 m/s$

The wave speed is 30 m/s.

note 5 of 6

The period-frequency equation

The period is the time for one complete wave.
The frequency is the number of waves per second.

Formula for period

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

Where:

$T$ = Period, in seconds (s)
$f$ = Frequency, in hertz (Hz)

note 6 of 6

Worked example - Period from frequency

A wave has a frequency of 50 Hz. Find its period.

Step 1 - Formula

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

Step 2 - Substitution and calculation

$T = \frac{1}{50} = 0.02 s$

The period of the wave is 0.02 s.

key terms

TermDefinition

Wave speedThe speed at which a wave moves, which is also the speed at which it transfers energy.

PeriodThe time taken for one complete cycle of something that repeats, such as one complete wave passing a point, one swing of a pendulum or one orbit.

FrequencyThe number of times something happens each second. For a wave, it is the number of complete waves passing a point each second, measured in hertz (Hz).

end of notes

Key points to remember

The wave speed equation

Wave speed is the speed at which the wave - and the energy it carries - travels.

The wave equation applies to all waves, linking wave speed to frequency and wavelength.

Formula for wave speed

$v = f λ$

Where:

v

= Wave speed, in metres per second (m/s)

f

= Frequency, in hertz (Hz)

λ

= Wavelength, in metres (m)

Worked example - Wavelength from frequency

A radio wave has a frequency of 7.5 × 10⁶ Hz. The speed of radio waves in air is 3.0 × 10⁸ m/s. Find its wavelength.

Step 1 - Rearrange the formula

Starting from v = fλ, divide both sides by f to make λ the subject:

$λ = \frac{v}{f}$

Step 2 - Substitution and calculation

$λ = \frac{3.0 \times 10^{8}}{7.5 \times 10^{6}} = 40 m$

The wavelength of the radio wave is 40 m.