Wave motion — OCR A-Level Physics

This row is a sub-heading, not a testable fact. It opens the second part of section 4.4.1, where you move from describing a wave to measuring it. Read it as a signpost: everything under (b) concerns quantities you can read from a displacement–distance or displacement–time graph, and the apparatus used to capture those graphs. Your job is to work through the sub-statements in order, checking that you can define each quantity, label it on a graph with its unit, and then use an oscilloscope to obtain a frequency. Treat the heading as a checklist rather than a definition to memorise, and make sure you can move fluently between a wave's graph and its numerical description before attempting questions.

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.

An oscilloscope displays a signal as a trace on a screen with a calibrated grid. To determine frequency, connect the signal to the input and adjust the time-base control, which sets the time represented by each horizontal division. Read the horizontal distance for one complete cycle, the period T, by counting divisions between successive identical points such as crest to crest, then multiply by the time-base setting to convert divisions into seconds. Frequency is then f = 1/T. For example, if one cycle spans 4.0 divisions and the time-base is 5.0 ms per division, then T = 4.0 × 5.0 ms = 20 ms = 0.020 s, so f = 1/0.020 = 50 Hz. Adjust the vertical gain only to make the trace a convenient size; it does not affect the period measurement.

The equation f = 1/T links frequency f, measured in hertz (Hz), to period T, measured in seconds (s). Frequency is the number of complete oscillations per second, while period is the time for one complete oscillation, so each is the reciprocal of the other. If a wave has a period of 0.25 s, then f = 1/0.25 = 4.0 Hz. Rearranged, T = 1/f. Always convert a period given in milliseconds to seconds before substituting: 20 ms becomes 0.020 s, giving f = 1/0.020 = 50 Hz. The equation applies to any periodic wave, including sound, light and waves on a string, and connects directly to oscilloscope measurements where the period is read from the trace.

The wave equation links the speed of a wave to its frequency and wavelength: v = fλ. Speed v is in metres per second (m s⁻¹), frequency f in hertz (Hz), and wavelength λ in metres (m). Frequency is the number of complete oscillations per second, so f = 1/T where T is the period in seconds. Wavelength is the distance between two successive points in phase, such as crest to crest. For a sound wave of frequency 440 Hz travelling at 330 m s⁻¹, λ = v/f = 330/440 = 0.75 m. Rearranging gives f = v/λ and λ = v/f. When a wave crosses into a new medium its speed and wavelength change, but frequency stays constant because it is set by the source.

A displacement–distance graph shows the displacement of particles from their rest positions along the direction of travel at one instant; a displacement–time graph shows how the displacement of one particle varies with time. For a transverse wave, particle displacement is perpendicular to the direction of energy transfer, so the graph looks like a familiar sine curve. For a longitudinal wave, particle displacement is parallel to the direction of travel, producing compressions where particles bunch together and rarefactions where they spread apart. On a displacement–distance graph, one full cycle spans one wavelength λ; on a displacement–time graph, one full cycle spans one period T. Amplitude is the maximum displacement from the rest position on either graph.

This row is a guided-reading item rather than an assessed answer target. The statement is only the label (f), so the learner should use the surrounding specification section 4.4.1 Wave motion to locate the full learning point that follows this label in the official specification. Read the section as a connected sequence: wave definitions, the wave equation, graphical representations, then the behaviours of waves. As you read, note the command words used in the specification, the quantities and units introduced, and any equations or graphs that are referenced. Build a short summary in your own words and check it against the specification wording. Where the specification refers to a diagram or graph, sketch it and label amplitude, wavelength, period and direction of travel so the reading becomes active rather than passive.

Waves exhibit several key behaviours: reflection, refraction, diffraction, and polarisation. Reflection is the change of direction at a boundary, where the angle of incidence equals the angle of reflection (measured from the normal). Refraction occurs when a wave changes speed upon entering a new medium, altering its wavelength and direction while frequency remains constant. Diffraction is the spreading of a wave as it passes through a gap or around an obstacle, being most pronounced when the gap width is comparable to the wavelength. While reflection, refraction, and diffraction apply to all waves, polarisation—which restricts oscillations to a single plane—is exclusively a property of transverse waves. Longitudinal waves, such as sound, cannot be polarised.

A ripple tank makes water waves visible so you can demonstrate reflection, refraction, diffraction and superposition. Set the tank level, add water about 5 mm deep, and drive a dipper bar with a signal generator so plane waves travel across the tank. Illuminate from above with a lamp; the wave crests focus light and cast bright and dark bands on the screen or bench below, letting you measure wavelength with a ruler. A straight barrier shows reflection, a change of water depth or a glass plate shows refraction, and a gap or obstacle shows diffraction spreading. Two dippers produce two sets of circular waves that overlap to show interference. Adjust the driving frequency to change wavelength and observe how the pattern changes.

Polarisation shows that transverse waves oscillate in one plane. For microwaves, use a transmitter and receiver aligned so the signal is strong, then rotate the receiver about the axis of travel; the detected intensity falls to a minimum when the receiver is at 90° to the transmitter, showing the wave is polarised. A metal grille placed between them also transmits or blocks the wave depending on whether its bars are parallel or perpendicular to the electric field. For light, pass unpolarised light through a polarising filter, then through a second filter. Rotating the second filter changes the transmitted intensity, with a minimum when the transmission axes are perpendicular. These procedures demonstrate that microwaves and light are transverse waves.

Intensity is the power transmitted per unit area perpendicular to the direction of energy transfer, so I = P/A, where P is power in watts and A is area in square metres, giving intensity in W m⁻². For a point source radiating equally in all directions, the power spreads over a sphere of area 4πr², so I = P/(4πr²) and intensity falls with the square of distance. Intensity is proportional to the square of amplitude, so doubling the amplitude quadruples the intensity. This relationship lets you compare waves: if one wave has twice the amplitude of another, it carries four times the intensity. The equation applies to progressive waves and assumes the area is measured perpendicular to the energy flow.

This statement is the second part of the intensity relationship: intensity is proportional to the square of the amplitude. Amplitude is the maximum displacement of a particle from its equilibrium position, measured in metres. Squaring it means that small changes in amplitude produce much larger changes in intensity. For example, if amplitude increases by 20%, intensity increases by a factor of 1.2² = 1.44, a 44% rise. The relationship applies to progressive waves and follows from the energy carried by the oscillation. When comparing two waves, write the ratio of intensities as the square of the ratio of amplitudes, so I₁/I₂ = (A₁/A₂)². This lets you predict how brightness or loudness changes when amplitude changes.