(i) displacement, amplitude, wavelength, period, phase difference,…

The idea

These seven quantities describe any wave. Displacement is the distance of a point on the wave from its equilibrium position, with a sign showing direction. Amplitude is the maximum magnitude of displacement. Wavelength is the distance between two successive points in phase, such as crest to crest. Period is the time for one complete oscillation at a point. Frequency is the number of oscillations per unit time, measured in hertz (Hz), where 1 Hz = 1 s⁻¹. Phase difference compares two points or two waves and is measured in degrees or radians; a full cycle is 360° or 2π rad. Speed is the distance travelled by the wave per unit time, in m s⁻¹.

For example: A wave of wavelength 0.50 m and frequency 4.0 Hz has speed v = fλ = 4.0 × 0.50 = 2.0 m s⁻¹.

What earns the marks

• Displacement is the distance of a point from its equilibrium position, with direction indicated by sign.
• Amplitude is the maximum magnitude of displacement from the equilibrium position.
• Wavelength is the distance between two successive points in phase, for example crest to crest.
• Period is the time taken for one complete oscillation at a point, measured in seconds.
• Frequency is the number of oscillations per unit time, measured in hertz, where 1 Hz = 1 s⁻¹.
• Phase difference is the fraction of a cycle by which one oscillation leads or lags another, measured in degrees or radians.
• Speed is the distance travelled by the wave per unit time, measured in m s⁻¹, and equals frequency multiplied by wavelength.

Common mistakes and how to put them right

• Confusing amplitude with wavelength.

  Put it right: Amplitude is a maximum displacement from equilibrium; wavelength is a distance along the direction of travel between successive points in phase.

• Treating frequency and period as the same quantity.

  Put it right: Frequency is the number of oscillations per second in Hz; period is the time for one oscillation in seconds, and they are reciprocals.

• Measuring phase difference in seconds.

  Put it right: Phase difference is an angle, measured in degrees or radians, not a time.

• Using the wrong unit for speed.

  Put it right: Speed is in m s⁻¹, obtained from frequency in Hz multiplied by wavelength in m.

Exam tips

• Write the unit next to every quantity before substituting values, so a mismatch is spotted early.
• For phase difference, convert between degrees and radians using 360° = 2π rad.
• Check whether a graph's horizontal axis is distance or time before reading wavelength or period.