7.1 Progressive waves
- Syllabus
- 9702–2028–2029
- Topic
- 7.1
- Level
- AS
Learning objectives
7.1.1What is meant by wave motion as illustrated by vibration in ropes, springs• describe what is meant by wave motion as illustrated by vibration in ropes, springs and ripple tanks7.1.2The terms displacement, amplitude, phase difference, period, frequency• understand and use the terms displacement, amplitude, phase difference, period, frequency, wavelength and speed7.1.3The use of the time-base and y-gain of a cathode-ray oscilloscope (CRO) to• understand the use of the time-base and y-gain of a cathode-ray oscilloscope (CRO) to determine frequency and amplitude7.1.4The definitions of speed, frequency and wavelength, the wave equation v = f• derive, using the definitions of speed, frequency and wavelength, the wave equation v = f λ7.1.5V = f λ• recall and use v = f λ7.1.6Energy is transferred by a progressive wave• understand that energy is transferred by a progressive wave7.1.7Intensity = power/area and intensity ∝ (amplitude)2• recall and use intensity = power/area and intensity ∝ (amplitude)2 for a progressive wave
Wave motion carries a disturbance while local parts oscillate
Wave motion is the progression of a disturbance from one position to another. It transfers energy, while particles of a mechanical medium oscillate about equilibrium rather than travelling with the wave overall.
| Illustration | What progresses | What oscillates locally |
|---|---|---|
| Rope | a pulse or repeated shape along the rope | each section moves across the rope's length direction |
| Spring | a compression/rarefaction pattern along the spring | coils move backwards and forwards along the spring |
| Ripple tank | a ripple pattern across the surface | small surface regions move mainly up and down |
Particle motion and propagation direction are different ideas. The medium does not flow from source to receiver at wave speed, and electromagnetic waves can propagate without a material medium.
Seven quantities describe oscillation and wave progression
| Quantity | Meaning | Unit / relation |
|---|---|---|
| Displacement | signed distance of an oscillating point from equilibrium at an instant | m |
| Amplitude | maximum magnitude of displacement | m |
| Phase difference | difference in position within a cycle | rad or degrees; one cycle = 2π rad = 360° |
| Period T | time for one complete cycle | s |
| Frequency f | cycles per second | Hz; f = 1/T |
| Wavelength λ | shortest distance between points in phase; distance advanced in one period | m |
| Wave speed v | speed at which a fixed phase/disturbance progresses | m s⁻¹ |
A 5.0 Hz source has period 0.20 s. Two points separated by λ/2 are 180° (π rad) out of phase; points separated by one wavelength are in phase.
Amplitude is not wavelength, frequency is not wave speed, and wave speed is not the instantaneous speed of a particle oscillating about equilibrium.
CRO scales convert divisions into period, frequency and amplitude
| CRO direction | Setting | Count | Result |
|---|---|---|---|
| Horizontal | time-base in s/div | divisions for one cycle | T = divisions × time/div; f = 1/T |
| Vertical | y-gain in V/div | divisions from centre line to peak | amplitude = divisions × V/div |
One cycle spans 4.0 divisions at 2.0 ms div⁻¹: T = 8.0 ms and f = 125 Hz. A peak 3.0 divisions above the centre at 0.50 V div⁻¹ has amplitude 1.5 V.
Peak-to-peak height is twice the amplitude, so halve it before applying y-gain. Do not use vertical divisions to find period or horizontal divisions to find amplitude.
Derive wave speed from one wavelength per period
In one period T, a fixed phase of a progressive wave advances one wavelength λ. Speed = distance/time, so v = λ/T. Frequency is f = 1/T. Therefore v = λ(1/T) = fλ.
v=fλ
v is propagation speed in m s⁻¹, f is source frequency in Hz and λ is wavelength in m. The derivation tracks the travelling pattern, not the local speed of an oscillating particle.
The equation is not dimensional guesswork: its physical step is that one wavelength passes in one period.
Wave speed, frequency and wavelength satisfy v=fλ
For a progressive wave, v=fλ: the wave speed equals frequency multiplied by wavelength.
If the medium fixes v, a change in source frequency changes wavelength inversely. Use metres and hertz so the result is m s⁻¹.
If a wave travels at 12 m s⁻¹ with frequency 4.0 Hz, its wavelength is 3.0 m.
The wave speed is not the same as the speed of individual particles oscillating in the medium.
A progressive wave transfers energy from source to receiver
A progressive wave transfers energy away from its source as the disturbance reaches new positions. The transferred energy can produce an effect at a receiver.
In a mechanical wave, neighbouring parts of the medium interact: local oscillations pass energy onward while particles have no overall journey with the wave. A water ripple can make a floating cork oscillate and deliver energy to the edge.
A material medium is not required for every progressive wave. Electromagnetic waves transfer energy through vacuum as well as through materials.
Energy transfer does not imply net transport of matter, and wave propagation speed is not the same as a medium particle's instantaneous speed.
Intensity depends on power per area and amplitude squared
I=P/SandI∝a2
I is intensity in W m⁻², P is wave power crossing an area S in m², and a is wave amplitude. Distinct symbols prevent transmission area from being confused with amplitude.
A 6.0 W wave spread uniformly over 3.0 m² has intensity 2.0 W m⁻². Under otherwise unchanged conditions, doubling amplitude makes intensity four times larger; halving amplitude makes it one quarter.
The amplitude-squared rule compares the same wave type under comparable medium conditions. Intensity is not amplitude itself, and area in P/S is not the oscillation amplitude.