O-Level Physics · Secondary 3 and 4
General Wave Properties
Waves carry energy from one place to another without carrying matter with them. This topic introduces transverse and longitudinal waves, the terms used to describe any wave, the wave equation v = fλ, and how to read displacement-distance and displacement-time graphs. It is the foundation for the later wave topics on light, the electromagnetic spectrum and sound, which all use the same vocabulary and the same equation.
What the syllabus expects
- Explain that waves transfer energy without transferring matter
- Describe transverse and longitudinal waves and give examples of each
- Define amplitude, wavelength, frequency, period, wave speed and wavefront
- Recall and use v = fλ and f = 1/T
- Interpret displacement-distance and displacement-time graphs of a wave
- Describe compressions and rarefactions in a longitudinal wave
What a wave is
A wave is a disturbance that transfers energy from one place to another without transferring the medium it travels through. The particles of the medium oscillate about their rest positions, passing the disturbance along, but they do not travel with the wave. A cork floating on a pond simply bobs up and down as ripples pass under it. Waves can be shown with a rope or a slinky spring, or with water ripples in a ripple tank. In a ripple tank it is useful to draw wavefronts. A wavefront is a line joining points on a wave that are in phase, such as all the points along one crest. The distance between two neighbouring wavefronts is one wavelength.
Transverse and longitudinal waves
In a transverse wave, the particles oscillate at right angles (perpendicular) to the direction in which the wave travels, producing crests and troughs. Water ripples, waves on a rope and all electromagnetic waves, including light, are transverse. In a longitudinal wave, the particles oscillate parallel to the direction of travel. This produces compressions, where particles are pushed close together and the pressure is higher, and rarefactions, where particles are spread out and the pressure is lower. Sound waves and a slinky pushed and pulled along its length are longitudinal. For a longitudinal wave, one wavelength is the distance between the centres of two neighbouring compressions, or two neighbouring rarefactions.
Describing a wave
The amplitude is the maximum displacement of a particle from its rest position. It is measured from the middle line to a crest, not from crest to trough. The wavelength λ is the shortest distance between two points in phase, such as crest to crest. The period T is the time for one complete oscillation, and the frequency f is the number of complete waves produced per second, measured in hertz (Hz). They are linked by f = 1/T. The wave speed v is the distance travelled by the wave per unit time. In one period the wave moves forward one wavelength, which gives the wave equation v = fλ. The frequency is set by the source. In a given medium the speed is fixed, so if the frequency is increased the wavelength becomes shorter.
Reading wave graphs
Two kinds of graph look alike but tell you different things. A displacement-distance graph is like a snapshot of the whole wave at one instant, with distance along the horizontal axis, so the length of one complete cycle on it is the wavelength. A displacement-time graph follows one particle as time passes, with time along the horizontal axis, so one complete cycle on it is the period. Both show the amplitude as the height from the middle line to a peak. To find the wave speed you often need one of each. If a displacement-distance graph shows λ = 0.40 m and a displacement-time graph shows T = 0.020 s, then f = 1 ÷ 0.020 = 50 Hz and v = fλ = 50 × 0.40 = 20 m/s.
Worked example
In a ripple tank, a student measures the distance from the first crest to the sixth crest as 10 cm. She also counts 20 waves passing a fixed point in 4.0 s. Calculate (a) the wavelength, (b) the frequency, (c) the period and (d) the speed of the waves.
- From the first crest to the sixth crest there are 6 − 1 = 5 complete wavelengths.
- Wavelength λ = 10 ÷ 5 = 2.0 cm = 0.020 m.
- Frequency f = number of waves ÷ time = 20 ÷ 4.0 = 5.0 Hz.
- Period T = 1/f = 1 ÷ 5.0 = 0.20 s.
- Wave speed v = fλ = 5.0 × 0.020 = 0.10 m/s.
Answer: (a) 2.0 cm (0.020 m) (b) 5.0 Hz (c) 0.20 s (d) 0.10 m/s (10 cm/s)
Common mistakes
- Measuring amplitude from crest to trough. That distance is twice the amplitude. Measure from the rest position to a crest.
- Counting crests instead of gaps. Across n crests there are only n − 1 wavelengths.
- Reading a wavelength off a displacement-time graph. The horizontal axis there is time, so one cycle gives the period, not the wavelength.
- Thinking the particles of the medium travel along with the wave. They only oscillate about fixed positions while the energy moves on.
- Assuming a higher frequency makes a wave travel faster in the same medium. The speed depends on the medium, so a higher frequency gives a shorter wavelength instead.
Exam tips
- Convert to base units before using v = fλ: kHz to Hz, MHz to Hz, cm to m and ms to s. A wrong power of ten is the most common lost mark here.
- Check the horizontal axis label on any wave graph first. Distance gives the wavelength, time gives the period.
- When describing a wave type, use the phrases oscillate about a fixed position and direction of energy transfer, and state whether they are perpendicular or parallel.
Practice questions
1. Easy: A sound wave has a frequency of 680 Hz and travels through air at 340 m/s. Calculate its wavelength.
Show answer
λ = v ÷ f = 340 ÷ 680 = 0.50 m.
2. Medium: A wave has a period of 0.025 s and a wavelength of 1.6 m. Find its frequency and its speed.
Show answer
f = 1/T = 1 ÷ 0.025 = 40 Hz. v = fλ = 40 × 1.6 = 64 m/s.
3. Harder: A boat bobs up and down 12 times in one minute as waves pass it. The distance between neighbouring crests is 15 m. Find the frequency, the period and the wave speed, and the time a crest takes to travel 300 m.
Show answer
f = 12 ÷ 60 = 0.20 Hz. T = 1 ÷ 0.20 = 5.0 s. v = fλ = 0.20 × 15 = 3.0 m/s. Time = distance ÷ speed = 300 ÷ 3.0 = 100 s.
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