3.3.1.1
Worked example: wave equation with period
Progressive Waves — AQA A-Level Physics
Worked Example
A wave has a speed of 340 m \(s^{-1}\). The periodThe time taken for one complete oscillation or wave cycle. Measured in seconds (s). from the graph is 0.28 ms. Calculate the wavelengthThe minimum distance between two points on a wave that are in phase (e.g. crest to crest). Measured in metres (m)..
Show Solution
1
Write the wave equation
$$v = f\lambda$$
2
Rearrange for wavelengthThe minimum distance between two points on a wave that are in phase (e.g. crest to crest). Measured in metres (m).
$$\lambda = \frac{v}{f}$$
3
Calculate frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). from periodThe time taken for one complete oscillation or wave cycle. Measured in seconds (s).
$$f = \frac{1}{T} = \frac{1}{0.28 \times 10^{-3}} = 3571 \text{ Hz}$$
4
Substitute and evaluate
$$\lambda = \frac{340}{3571} = 0.095 \text{ m (2 s.f.)}$$
Answer
$\lambda = 0.095$ m