Properties of waves — AQA GCSE Combined Science

Amplitude measures how far a point on a wave moves from its undisturbed position. The undisturbed position is the level the medium would sit at with no wave passing, often shown as the centre line on a graph. Amplitude is the maximum displacement from that line, so it is measured from the centre line to a crest or from the centre line to a trough, not from crest to trough. Amplitude is a distance, so its unit is the metre (m); larger amplitudes carry more energy. For example, on a displacement–distance graph with a centre line at 0 cm, a crest at +3 cm and a trough at −3 cm has amplitude 3 cm. The peak-to-trough distance of 6 cm is twice the amplitude.

Wavelength measures the repeat distance of a wave. Choose any point on one wave, such as a crest, then move to the same point on the next wave; the straight-line distance between them is the wavelength. On a displacement–distance graph, read the horizontal separation between successive crests or successive troughs. For a transverse wave, crest-to-crest or trough-to-trough both work; for a longitudinal wave, use the distance between successive compressions or successive rarefactions. Wavelength is a length, so it is measured in metres, often with prefixes such as cm, mm or nm. It is not the distance from a crest to the next trough, and it is not the amplitude, which measures displacement from the rest position. In the wave equation v = f λ, wavelength is the symbol λ and must be in metres when speed is in m/s and frequency is in Hz.

Frequency counts how many complete waves pass a fixed point every second. One complete wave is one full cycle, such as crest to crest or compression to compression. The unit is the hertz, Hz, where 1 Hz means one wave per second. If 30 waves pass a point in 6 s, the frequency is 30 ÷ 6 = 5 Hz. Frequency is linked to time period by f = 1 ÷ T, where T is the time for one complete wave in seconds. It also links to wavelength and wave speed through v = f λ. Frequency depends on the source of the wave, not on the speed of travel, so a wave keeps the same frequency when it enters a new medium even if its speed and wavelength change. On a displacement–time graph, frequency is the number of complete cycles each second.

The period T of a wave is the time taken for one complete wave cycle to pass a fixed point, measured in seconds (s). Frequency f is the number of complete cycles passing a point each second, measured in hertz (Hz). Because period and frequency describe the same repeating event from opposite viewpoints, they are reciprocals: T = 1 / f, and rearranging gives f = 1 / T. For example, a wave of frequency 4 Hz repeats four times each second, so each cycle lasts 1 ÷ 4 = 0.25 s. A ripple with period 0.02 s has frequency 1 ÷ 0.02 = 50 Hz. Always convert milliseconds to seconds before substituting, and check that the answer is sensible: a high frequency means a short period.

The statement 'T = ¹' is a typographical error in the specification extraction for the period–frequency relationship, T = 1 / f. Period (T) is the time for one complete wave cycle, measured in seconds (s); frequency (f) is the number of cycles per second, measured in hertz (Hz). The two quantities are reciprocals, so f = 1 / T as well. For example, a wave of frequency 2 Hz completes two cycles each second, giving T = 1 ÷ 2 = 0.5 s. A wave with period 0.01 s has f = 1 ÷ 0.01 = 100 Hz. When using this equation, always convert milliseconds to seconds, and check that a high frequency gives a short period.

The period, T, is the time taken for one complete wave cycle to pass a fixed point, or for one point on the wave to complete one full oscillation. It is measured in seconds, s. For example, if a wave crest passes a marker every 0.25 s, then T = 0.25 s. The period links to frequency by T = 1 ÷ f, so a wave with f = 4 Hz has T = 1 ÷ 4 = 0.25 s. On a displacement–time graph, T is the horizontal distance between two identical points on consecutive cycles, such as crest to crest. On a displacement–distance graph, the horizontal distance between identical points gives wavelength, not period, so always check the axis label before reading T.

Frequency, f, is the number of complete wave cycles passing a fixed point each second. It is measured in hertz, Hz, where 1 Hz equals one cycle per second. For example, if 20 crests pass a point in 4 s, then f = 20 ÷ 4 = 5 Hz. Frequency links to period by f = 1 ÷ T, so a wave with T = 0.2 s has f = 1 ÷ 0.2 = 5 Hz. On a displacement–time graph, frequency is the number of full cycles shown divided by the total time. Frequency is not the same as wave speed: a wave can have a high frequency but a long wavelength, and speed depends on both frequency and wavelength through v = f × λ.

Wave speed describes how quickly energy travels through a medium, not how fast individual particles move. In a transverse wave, particles oscillate about fixed positions while the disturbance passes; in a longitudinal wave, particles vibrate along the direction of travel. For example, a sound wave in air has a speed of about 340 m/s, meaning energy reaches a listener 340 m away in roughly one second, even though air molecules only jiggle a few millimetres. Wave speed is calculated using v = f λ, where v is speed in m/s, f is frequency in Hz and λ is wavelength in m. The medium determines the speed: sound travels faster in solids than gases, while all electromagnetic waves travel at 3.0 × 10⁸ m/s in a vacuum.

The wave equation links wave speed, frequency and wavelength: v = f λ. Wave speed v is measured in metres per second (m/s), frequency f in hertz (Hz) and wavelength λ in metres (m). Frequency is the number of complete waves passing a point each second, while wavelength is the distance between two identical points on adjacent waves, such as crest to crest. For example, a wave with frequency 50 Hz and wavelength 2 m has speed v = 50 × 2 = 100 m/s. The equation applies to all waves, including sound, water and electromagnetic waves. Rearranged forms are f = v ÷ λ and λ = v ÷ f, which are useful when speed is known and either frequency or wavelength must be found.

This equation links the speed of a wave to its frequency and wavelength. Speed v is measured in metres per second (m/s), frequency f in hertz (Hz) and wavelength λ in metres (m). Frequency is the number of complete waves passing a point each second, while wavelength is the distance from one point on a wave to the same point on the next wave, such as crest to crest. Rearranging gives f = v ÷ λ and λ = v ÷ f. For example, a sound wave of frequency 250 Hz travelling at 340 m/s has wavelength 340 ÷ 250 = 1.36 m. The equation applies to all waves, including sound, light, water and seismic waves, provided consistent units are used.

This statement expresses the wave equation in words: wave speed equals frequency multiplied by wavelength. Wave speed is the distance a wave travels each second, measured in metres per second (m/s). Frequency is how many complete waves pass a point each second, measured in hertz (Hz). Wavelength is the distance between two identical points on neighbouring waves, such as trough to trough, measured in metres (m). For instance, a wave with frequency 50 Hz and wavelength 2 m travels at 50 × 2 = 100 m/s. The word equation is useful because it shows the relationship directly: increasing frequency or wavelength increases wave speed, provided the other quantity stays constant.

Wave speed, v, is the distance a wave crest travels each second, measured in metres per second (m/s). It links frequency f in hertz (Hz) and wavelength λ in metres (m) through the equation v = f λ. For example, a wave with f = 50 Hz and λ = 2 m has v = 50 × 2 = 100 m/s. You can also measure v directly: time a crest over a known distance, or use a ripple tank and stopwatch. In exams, you may calculate v, convert units such as cm/s to m/s, or compare speeds of different waves. Always write the unit m/s, not m or Hz, and show substitution clearly.

Wavelength, λ, is the distance between two identical points on consecutive waves, such as crest to crest or trough to trough, measured in metres (m). It is the spatial period of a wave: a longer wavelength means fewer waves pass a point each second if speed is constant. You can measure λ on a displacement–distance graph by reading the horizontal distance for one complete cycle, or in a ripple tank by measuring across several wavelengths and dividing. Wavelength links to frequency and wave speed through v = f λ. In exams, you may read λ from a graph, convert cm to m, or calculate λ using λ = v / f. Always include the unit m.

This statement requires students to read wave diagrams and extract two specific measurements. Amplitude is the maximum displacement of a point on the wave from its rest position, measured in metres; on a displacement–distance graph it is the vertical distance from the centre line to a crest or trough. Wavelength is the distance between two successive crests, two successive troughs, or any two equivalent points on consecutive waves, also measured in metres. For example, if a diagram shows a crest 0.20 m above the centre line and crests 1.50 m apart, the amplitude is 0.20 m and the wavelength is 1.50 m. Students should also recognise that peak-to-trough height is twice the amplitude.

To measure the speed of sound in air, use a direct distance-and-time method. Two students stand a measured distance apart, for example 100 m, in an open space. One student holds two wooden blocks and claps them together sharply; the other student starts a stopwatch when they see the blocks meet and stops it when they hear the clap. Because light travels much faster than sound, seeing the blocks gives a near-instant start signal. Repeat the timing several times and calculate a mean time. Then use speed = distance ÷ time. For 100 m and a mean time of about 0.29 s, the speed is roughly 340 m/s. The method measures the time for sound to travel the measured distance through air, so the calculated value is the speed of sound in air.

To measure the speed of ripples on a water surface, use a ripple tank. A vibrating bar or dipper touches the water and produces regular ripples. Place a lamp above the tank so the ripples cast shadows on a screen or paper below. Measure the wavelength by recording the distance across several ripple crests and dividing by the number of wavelengths. Measure the frequency from the number of ripples passing a point each second, or read it from the signal generator driving the vibrator. Then calculate speed using speed = frequency × wavelength. For example, if the wavelength is 0.02 m and the frequency is 10 Hz, the speed is 0.2 m/s. This method measures the speed of the water surface waves.

This practical develops your ability to judge whether apparatus is fit for purpose and to obtain reliable measurements of wave properties. In a ripple tank, a vibrating bar or dipper creates water waves; you observe the pattern and decide whether a stroboscope, a slow-motion camera or a metre rule and timer are suitable for measuring wavelength and frequency. For waves in a solid, a vibration generator attached to a string produces a stationary wave; you assess whether a signal generator, pulley and ruler allow you to measure wavelength and frequency accurately. You then calculate speed using v = f λ. Suitability depends on resolution, range, stability and whether the wave pattern is clear enough to measure. You must record raw measurements with units and consider repeats to reduce random error.