3.3.1.1
Worked example: reading amplitude, wavelength and phase from a diagram
Progressive Waves — AQA A-Level Physics
Worked Example
Plane waves on the surface of water have a frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). of 2.5 Hz. From the diagram, the total vertical distance peak-to-trough is 7.50 mm and 25 cm covers 3 and 3/4 wavelengths. Points A and B are separated by half a wavelengthThe minimum distance between two points on a wave that are in phase (e.g. crest to crest). Measured in metres (m).. Determine the amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m)., wavelengthThe minimum distance between two points on a wave that are in phase (e.g. crest to crest). Measured in metres (m). and phase differenceThe fraction of a cycle by which one wave leads or lags behind another, measured in degrees or radians. between A and B.
Show Solution
1
Find the amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m).
AmplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m). = maximum displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). from equilibriumAn object is in equilibrium when the resultant force on it is zero. The object is either stationary or moving at constant velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.. = total peak-to-trough / 2:
$$A = \frac{7.50}{2} = 3.75 \text{ mm}$$2
Find the wavelengthThe minimum distance between two points on a wave that are in phase (e.g. crest to crest). Measured in metres (m).
25 cm covers 3.75 wavelengths:
$$\lambda = \frac{25}{3.75} = 6.67 \text{ cm}$$3
Find the phase differenceThe fraction of a cycle by which one wave leads or lags behind another, measured in degrees or radians. between A and B
A and B are separated by $\frac{1}{2}\lambda$:
$$\text{Phase differenceThe fraction of a cycle by which one wave leads or lags behind another, measured in degrees or radians.} = \frac{1}{2} \times 360^{\circ} = 180^{\circ}$$They are in antiphase.
Answer
Amplitude = 3.75 mm, wavelength = 6.67 cm, phase $difference = 180 degrees (antiphase)$