Progressive waves, phase and stationary waves
A progressive wave carries energy from place to place. When two identical waves travel in opposite directions they combine into a stationary wave, which stores energy instead, and this explains how strings and pipes make musical notes.
Part 1 of 3: Learn it
In short
- v = fλ for every wave; phase difference = 2πd ÷ λ for two points a distance d apart.
- Polarisation works for transverse waves but never for longitudinal ones.
- On a string fixed at both ends, the first harmonic has λ = 2L.
Where this is in your specification
Spec points: AQA 7408 3.3.1.1 to 3.3.1.3, OCR A H556 4.4.1, 4.4.2 and 4.4.4, Edexcel 9PH0 Topic 5
| Board | Topic: Waves, interference and diffraction |
|---|---|
| AQA 7408 | 3.3 |
| Edexcel 9PH0 | Topic 5 |
| OCR H556 | 4.4 |
| Higher C857 76 | Particles and waves: interference, refraction of light |
Progressive waves
Amplitude, wavelength, frequency, period and speed are linked by v = fλ and T = 1/f. Phase difference measures how far one point on a wave is behind another, as a fraction of a cycle, usually in radians: points one whole wavelength apart are in phase; points half a wavelength apart are in antiphase (π radians).
Polarisation
A transverse wave vibrates in one plane after it passes through a polarising filter. Two filters at 90° to each other block it completely. Longitudinal waves cannot be polarised, so polarisation is evidence that light is transverse. Uses include polarising sunglasses, which cut glare reflected from water, and aligning TV aerials with the plane of the transmitted signal.
Stationary waves
- Formed by the superposition of two waves with the same frequency and amplitude travelling in opposite directions, often a wave and its reflection.
- Nodes are points that never move; antinodes are points of maximum amplitude.
- Neighbouring nodes sit half a wavelength from each other.
- All points between two adjacent nodes vibrate in phase; points in neighbouring sections are in antiphase.
Harmonics on a string
The first harmonic has a node at each end and one antinode in the middle, so L = λ/2. The nth harmonic has n loops and frequency nf₁. Here T is the tension and μ the mass per unit length: a tighter or lighter string gives a higher note.
What is the distance between two adjacent nodes?
Show the answer
Half a wavelength.
Part 2 of 3: See it worked
Worked examples
Example 1
A string 0.80 m long vibrates in its first harmonic at 120 Hz. Find the wave speed on the string and the frequency of the third harmonic.
- First harmonic: λ = 2L = 1.6 m
- v = fλ = 120 × 1.6 = 192 m/s
- Third harmonic: 3 × 120
Answer: 192 m/s and 360 Hz.
Example 2
Two points on a progressive wave of wavelength 0.60 m are 0.15 m apart. Find their phase difference.
- Fraction of a wavelength: 0.15 ÷ 0.60 = 0.25
- Phase difference = 0.25 × 2π
Answer: π/2 radians (90°).
Common mistakes
- Saying a stationary wave transfers energy along the string.
- Taking the distance between adjacent nodes as a whole wavelength.
- Saying sound can be polarised.
- Using the total mass of the string for μ instead of mass per metre.
Why can light be polarised but sound cannot?
Show the answer
Light is a transverse wave; sound in air is longitudinal.
Part 3 of 3: Test yourself
Check yourself
Answer each one in your head or on paper first, then open it to check.
What is the distance between two adjacent nodes?
Half a wavelength.
Why can light be polarised but sound cannot?
Light is a transverse wave; sound in air is longitudinal.
What is the phase difference between two points one and a half wavelengths apart?
3π radians, which means they are in antiphase.
Jobs that use this
Each link opens the job profile on the National Careers Service (England). In the rest of the UK: My World of Work (Scotland), Careers Wales, nidirect careers (Northern Ireland).
Full lessons and marked practice for this course are coming soon to Brainlag Learn. See courses