Nature and Properties of Waves

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1Summary 重點摘要

A wave carries energy from place to place while the medium only vibrates in place: transverse waves have crests and troughs, longitudinal waves compressions and rarefactions. Describing waves by amplitude, wavelength, period and frequency, and using T = 1/f and v = fλ, you can read waveform graphs and calculate speeds and wavelengths.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: Waves carry energy, not matterThe most basic property of wave motion: energy travels with the wave while the particles of the medium merely oscillate about their own positions. When water waves pass a buoy, it bobs up and down but is not carried to the shore; a wave running along a rope leaves every point of the rope back where it started. The key sentence for concept questions is 'a wave transfers energy without transferring matter'. For example, float a sheet of cling film on water and dip a finger beside it: as the ripples pass, the film only rises and falls in place — a direct demonstration.
2. Step 2: Transverse and longitudinal wavesIn a transverse wave the vibration is perpendicular to the direction of travel, and crests and troughs are plainly visible: flick a rope or shake a long spring sideways to make one. In a longitudinal wave the vibration is parallel to the travel: push and pull a spring a few times and pulses of compressions and rarefactions run along it; sound in air travels exactly like this. For example, when you speak, your vocal folds vibrate and squeeze the air into alternating compressions and rarefactions that reach the listener's eardrum. The two wave shapes differ, but the quantities and calculations are identical.
3. Step 3: Amplitude and wavelengthThe amplitude A is the maximum displacement of a particle from equilibrium, measured on a waveform from the zero line to a crest (or trough); the larger the amplitude, the more energy the wave carries. The wavelength λ is the distance between two neighbouring in-phase points — most easily two adjacent crests or two adjacent compressions — in metres. For example, if two adjacent crests on a waveform are 0.5 m apart on the horizontal axis, the wavelength is 0.5 m; if a crest rises 2 cm above the zero line, the amplitude is 2 cm. Do not measure amplitude from trough to crest — that doubles the answer.
4. Step 4: Period and frequency, T = 1/fThe period T is the time for one complete oscillation, in seconds; the frequency f is the number of complete oscillations per second, in hertz. They are reciprocals: T = 1/f and f = 1/T. The frequency is fixed by the source and does not change when the wave enters another medium. For example, a buoy bobbing 20 times in 8 s takes 8 ÷ 20 = 0.4 s per oscillation, so T = 0.4 s and f = 1 ÷ 0.4 = 2.5 Hz — that is, 2.5 oscillations per second. On a displacement-time graph, the gap between adjacent crests is the period.
5. Step 5: The wave equation v = fλIn one period a wave advances one wavelength, so each second it advances f wavelengths: v = fλ. Given any two of the three quantities, the third follows. For example, a 400 Hz tuning fork in air, where the speed of sound is 340 m s⁻¹, produces waves of wavelength λ = v ÷ f = 340 ÷ 400 = 0.85 m; again, water waves of frequency 4 Hz and wavelength 0.05 m travel at v = 4 × 0.05 = 0.2 m s⁻¹. Speed depends only on the medium: light is fastest in vacuum, sound fastest in solids; when a wave crosses into a new medium, its speed and wavelength change while its frequency stays put.
6. Step 6: Two graphs, two readingsDisplacement-time and displacement-distance graphs look alike; the difference is the horizontal axis. A displacement-time graph follows one particle, with time on the axis: the gap between adjacent crests is the period T. A displacement-distance graph is a snapshot of the whole wave at one instant, with distance on the axis: the gap between adjacent crests is the wavelength λ. Crest height gives the amplitude on both. For example, crests 0.25 s apart mean T = 0.25 s and f = 4 Hz; crests 0.6 m apart mean λ = 0.6 m. This is where exams most often trip candidates, so check whether the axis reads seconds or metres before you start.
7. Step 7: Wavefronts and the road aheadA wavefront is the line joining the points a wave has just reached: water wavefronts are concentric circles, and plane waves have straight fronts perpendicular to the direction of travel — the basic tool for drawing reflection and refraction diagrams in the next two lessons. The ripple tank lets us watch both effects directly: entering shallow water, waves slow down, their wavelength shortens and the fronts change direction. For example, lay a glass plate to make half the tank shallow and refraction appears before your eyes. The next lesson puts rays of light on stage and makes reflection and refraction quantitative.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• A wave transfers energy from place to place while the medium's particles only vibrate in place
• Transverse waves have crests and troughs (rope, water); longitudinal waves have compressions and rarefactions (sound)
• Amplitude is the maximum displacement from equilibrium; wavelength is the distance between neighbouring in-phase points
• T = 1/f and v = fλ; the source fixes the frequency — across media it is the speed and wavelength that change
• Read the period from a displacement-time graph and the wavelength from a displacement-distance graph — check the axis first