IB DP Physics · Theme C Wave behaviour · C.2 · ~6 min read
C.2 Wave model
Transverse and longitudinal travelling waves, wavelength, frequency, period and wave speed, displacement–distance and displacement–time graphs, sound waves, the electromagnetic spectrum, and mechanical versus electromagnetic waves.
Transverse & longitudinalWavelength, frequency & speedWave graphsSoundElectromagnetic spectrumMechanical vs EM waves
RSby Riyaz Sir
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No tag = SL and HLHL ONLY HL students onlyDATA BOOKLET given in the examM1A1 how marks are awardedhighlight = comes up again and againTest yourself at the end
In 30 seconds
- A travelling wave transfers energy without transferring matter. Each particle of the medium just oscillates about its equilibrium position.
- Transverse: oscillation perpendicular to the energy transfer (light, waves on a string). Longitudinal: oscillation parallel to it, in compressions and rarefactions (sound).
- v = fλ = λ/T links speed, frequency and wavelength for every wave.
- Mechanical waves need a medium; electromagnetic waves do not and all travel at c = 3.00 × 108 m s−1 in a vacuum.
- C.2 is the same at SL and HL.
By the end you can
- Describe transverse and longitudinal waves and give examples of each.
- Define and use wavelength, frequency, period, amplitude and wave speed.
- Read λ, T and A from displacement–distance and displacement–time graphs.
- Describe sound waves and the electromagnetic spectrum.
- Compare mechanical and electromagnetic waves.
1Two kinds of wave
| Transverse | Longitudinal | |
|---|---|---|
| oscillation | perpendicular to energy transfer | parallel to energy transfer |
| features | crests and troughs | compressions and rarefactions |
| examples | EM waves, waves on strings, water ripples (roughly) | sound, P-waves in earthquakes, pressure waves in a spring |
- Polarisation only happens with transverse waves, so it is evidence that light is transverse.
2Describing a wave
Wavelength λ — the distance between two adjacent points in phase (crest to crest, compression to compression).
Frequency f — number of oscillations per second, in Hz. Period T = 1/f is the time for one oscillation.
Amplitude A — the maximum displacement from equilibrium. Wave energy (intensity) is proportional to A2.
v = fλ = λT DATA BOOKLET
wave speedWorked example
Middle C on a piano has f = 256 Hz. Find its wavelength in air (v = 340 m s−1).
- λ = v/f = 340/256 M1
- = 1.33 m A1
Worked example
A displacement–distance graph shows λ = 0.80 m and a displacement–time graph of one point shows T = 0.020 s. Find the wave speed.
- f = 1/T = 50 Hz M1
- v = fλ = 50 × 0.80 = 40 m s−1 A1
Common mistakeReading the wavelength from a displacement–time graph. A time graph gives the period; only a distance graph gives the wavelength.
Exam tipChanging the frequency of a source does not change the wave speed in the same medium; the wavelength changes instead. Changing the medium changes the speed (and λ), but the frequency stays the same.
3Sound waves
- Sound is longitudinal and mechanical: it needs a medium. It is fastest in solids, slower in liquids and slowest in gases (about 340 m s−1 in air at room temperature).
- Human hearing: about 20 Hz to 20 kHz. Ultrasound (above 20 kHz) is used in medical imaging and sonar.
- Pitch depends on frequency; loudness depends on amplitude (intensity).
Worked example
A ship's sonar pulse returns from the sea bed after 0.80 s. Sound travels at 1500 m s−1 in sea water. How deep is the water?
- total distance = 1500 × 0.80 = 1200 m M1
- there and back, so depth = 600 m A1
4Electromagnetic waves
- EM waves are oscillating electric and magnetic fields, perpendicular to each other and to the direction of travel. They travel at c in a vacuum and need no medium.
- Uses and hazards: radio (communication), microwaves (cooking, phones), infrared (heating, remote controls), visible (sight), UV (sterilising; skin damage), X-rays (imaging; ionising), gamma (cancer treatment; ionising).
Worked example
Find the frequency of green light of wavelength 500 nm, and the wavelength of a 98 MHz radio station.
- f = c/λ = 3.00 × 108/500 × 10−9 = 6.0 × 1014 Hz A1
- λ = c/f = 3.00 × 108/98 × 106 = 3.1 m A1
5Mechanical versus electromagnetic
| Mechanical | Electromagnetic | |
|---|---|---|
| medium | needed (particles oscillate) | not needed (fields oscillate) |
| speed | depends on the medium, much less than c | c in a vacuum, less in materials |
| type | transverse or longitudinal | always transverse |
| examples | sound, water waves, seismic waves | light, radio, X-rays |
Linking questionEvery wave equation in C.3–C.5 starts from v = fλ. The particles of the medium move in SHM (C.1), and the energy carried connects to intensity and the inverse-square law in B.1.
Idea for your IA / explorationMeasure the speed of sound in air with two microphones and a data logger (time of flight), or with a resonance tube, and compare with how it changes with temperature.
Test yourself — cover the answers first
Quick check
- What does a wave transfer?
- Give one example of a longitudinal wave.
- Which graph gives the period: displacement–distance or displacement–time?
- The frequency of a sound doubles in the same air. What happens to its speed and wavelength?
- Why can sound not travel through space?
- Which EM waves have the highest frequency?
Exam-style
- A water wave travels 12 m in 4.0 s. Its crests are 1.5 m apart. Find its speed and frequency.
- Light (λ = 600 nm in air) enters glass where its speed is 2.0 × 108 m s−1. Find its frequency and its wavelength in the glass.
Show answers
- energy (not matter)
- sound
- displacement–time
- speed unchanged; wavelength halves
- it needs a medium; space is (almost) a vacuum
- gamma rays
- v = 12/4.0 = 3.0 m s−1
f = v/λ = 3.0/1.5 = 2.0 Hz - f = c/λ = 3.0 × 108/600 × 10−9 = 5.0 × 1014 Hz (unchanged)
λglass = v/f = 2.0 × 108/5.0 × 1014
= 400 nm
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