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(b) Properties of waves

Syllabus
2024
Topic
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Level
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Learning objectives

3.2Longitudinal and transverse wavesExplain the difference between longitudinal and transverse waves3.3Wave definitionsKnow the definitions of amplitude, wavefront, frequency, wavelength and period of a wave3.4Wave energy transferKnow that waves transfer energy and information without transferring matter3.5Wave speed equationKnow and use wave speed = frequency × wavelength, v = fλ.3.6Frequency and periodUse frequency = 1 ÷ time period, f = 1/T.3.7Wave equations in contextUse the above relationships in different contexts, including sound waves and electromagnetic waves3.8Doppler effectExplain why there is a change in the observed frequency and wavelength of a wave when its source is moving relative to an observer and that this is known as the Doppler effect3.9Reflection and refractionExplain that all waves can be reflected and refracted

Distinguish transverse and longitudinal waves

Wave type is determined by comparing the direction of the oscillations with the direction in which the wave travels and transfers energy. It is not determined by the shape of a drawn line alone.

Feature Transverse wave Longitudinal wave
Direction of oscillations Perpendicular (at right angles) to wave travel Parallel to wave travel
Repeating pattern Crests and troughs Compressions and rarefactions
Example Light and surface water waves Sound waves in air

In a transverse water wave, the surface moves mainly up and down while the disturbance travels across the water. In a longitudinal sound wave, air particles move backwards and forwards along the same line as the travelling disturbance, producing alternating compressions and rarefactions.

The particles or fields oscillate; the wave pattern travels. Saying only that one wave is ‘up and down’ and another is ‘side to side’ is incomplete unless the direction is compared with the direction of wave travel.

Read the five quantities that describe a wave

A wave can be described by how far it oscillates, how its repeating pattern is spaced, and how quickly each cycle occurs.

Quantity Definition How to identify or measure it Unit
amplitude maximum displacement from the equilibrium position equilibrium to a crest or trough m
wavefront line or surface joining points at the same stage of an oscillation for example, one crest line -
frequency, ff number of complete cycles passing a point each second cycles divided by time Hz
wavelength, λ\lambda shortest distance between two neighbouring points in the same phase crest to next crest, or compression to next compression m
period, TT time taken for one complete cycle total time divided by number of cycles s

Amplitude is measured from equilibrium, not from crest to trough; crest-to-trough height is twice the amplitude. A wavelength must join equivalent points on consecutive cycles, not just any two nearby points.

Waves carry energy and information, not matter

A wave transfers energy from one place to another without carrying matter along with the travelling wave pattern. Changes in a wave can also carry information.

In a material medium, each particle oscillates about its equilibrium position and passes the disturbance to neighbouring particles. Energy therefore moves through the medium even though the particles have no overall journey with the wave.

A floating cork rises and falls as a water wave passes rather than travelling all the way with a crest. In sound, air particles vibrate locally while energy reaches a listener. In a communication signal, controlled changes in the wave represent information sent to a receiver.

Matter may oscillate while a mechanical wave passes, but oscillation is not the same as net transfer of that matter from source to receiver.

Use wave speed, frequency and wavelength

During one period, a wave travels one wavelength. Therefore its speed equals the number of wavelengths produced each second multiplied by the length of each wavelength.

v=f\lambda

vv is wave speed in m/s, ff is frequency in Hz, and λ\lambda is wavelength in m. Rearrangements are f=v/λf=v/\lambda and λ=v/f\lambda=v/f.

For sound travelling at 340 m/s with frequency 1.7 kHz, first convert 1.7 kHz=1700 Hz1.7\text{ kHz}=1700\text{ Hz}. Then λ=v/f=340/1700=0.20 m\lambda=v/f=340/1700=0.20\text{ m}.

Convert all values to compatible units before substituting. A frequency in kHz or a wavelength in cm cannot be used directly with a speed in m/s.

Convert between frequency and period

Frequency counts cycles per second, while period is the time for one cycle. They are reciprocals: more cycles each second means less time for each cycle.

f=\frac{1}{T}\qquad T=\frac{1}{f}

ff must be in hertz and TT must be in seconds when these equations are used with SI units.

If T=2.5 msT=2.5\text{ ms}, convert first: 2.5 ms=2.5×10−3 s2.5\text{ ms}=2.5\times10^{-3}\text{ s}. Then f=1/T=1/(2.5×10−3)=400 Hzf=1/T=1/(2.5\times10^{-3})=400\text{ Hz}.

A period of 2.5 ms is not 2.5 s. Missing the milli conversion changes the answer by a factor of 1000.

Apply wave equations in sound and electromagnetic contexts

The same wave relationships apply to sound and electromagnetic waves. Identify the wave and medium, select the speed stated or appropriate to that context, convert prefixes, and then rearrange before substituting.

Context Speed to use Common conversion Example result
sound in air use the value given for that air condition kHz to Hz: multiply by 10310^3 v=330 m/sv=330\text{ m/s} and f=660 Hzf=660\text{ Hz} give λ=0.50 m\lambda=0.50\text{ m}
electromagnetic wave in free space 3.0×108 m/s3.0\times10^8\text{ m/s} MHz to Hz: multiply by 10610^6 f=100 MHzf=100\text{ MHz} gives λ=3.0 m\lambda=3.0\text{ m}

If a wave enters a region where its speed changes, the source still fixes the frequency. From v=fλv=f\lambda, the wavelength changes in the same ratio as the speed.

Do not use 3.0×108 m/s3.0\times10^8\text{ m/s} for sound, and do not assume every sound-speed value is identical; use the speed for the named wave and medium.

Explain the Doppler effect from moving wavefronts

The Doppler effect is the change in observed frequency and wavelength caused by relative motion between a wave source and an observer.

A moving source emits each new wavefront from a different position. Ahead of an approaching source, successive wavefronts are closer together; behind a receding source, they are farther apart. The wave speed in the same medium remains constant, so v=fλv=f\lambda links the changed wavelength to the changed observed frequency.

Relative motion Observed wavelength Observed frequency or pitch
source approaching observer shorter higher
source receding from observer longer lower

The source does not need to emit at a different frequency. Motion changes the spacing and arrival rate of wavefronts at the observer; with no relative motion towards or away from the observer, there is no Doppler shift.

Recognise reflection and refraction in every kind of wave

All types of wave can be reflected and refracted. These behaviours occur at boundaries, but they describe different changes to the wave.

Behaviour What happens Cause Examples
reflection the wave returns into the original region interaction with a boundary a sound echo; light from a mirror
refraction wave speed and wavelength change as the wave enters a different medium or region; its direction can also change wave speed differs across the boundary light entering glass; water waves entering shallower water

During refraction the frequency remains fixed by the source. Since v=fλv=f\lambda, a change in speed produces a change in wavelength.

Refraction does not always mean bending: a wave crossing the boundary along the normal changes speed and wavelength without changing direction. Detailed ray laws are taught later.