Lesson A · 3.1–3.9, 3.23
By the end you should classify a wave, label a diagram, and choose $v=f\lambda$ or $T=1/f$ without being told.
How I start this topic
A wave is a repeating disturbance that carries energy. The water does not travel across the pond — the ripple does. That one picture is specification 3.4. If your answer says “the particles travel with the wave,” you have already lost the mark.
3.1 · Units
| Quantity | Symbol | Unit | What I say in class |
|---|---|---|---|
| Angle | $i$, $r$, $c$ | degree (°) | Always from the normal |
| Frequency | $f$ | hertz (Hz) | Waves per second. kHz $\times 10^3$, MHz $\times 10^6$ |
| Wavelength | $\lambda$ | metre (m) | cm $\div 100$. A radio wave can be metres long |
| Wave speed | $v$ | m/s | Sound in air $\approx 340\,\text{m/s}$. Light in vacuum $3.0\times 10^8\,\text{m/s}$ |
| Period | $T$ | second (s) | Time for one wave. $T=1/f$ |
Convert before you calculate
$8.0\,\text{cm} = 0.080\,\text{m}$. $150\,\text{MHz} = 1.50 \times 10^8\,\text{Hz}$. Leaving cm or MHz in $v=f\lambda$ gives a speed that is nonsense, and you often will not notice.
3.2, 3.23
The examiner wants the direction of the vibration compared with the direction the energy travels.
Transverse
Oscillations are perpendicular to the direction of energy transfer. Examples: all electromagnetic waves, water ripples, a rope, S-waves.
Longitudinal
Oscillations are parallel to the direction of energy transfer. Sound in air is longitudinal (3.23). You see compressions (particles closer) and rarefactions (particles further apart).
A slinky can do both: flick the end sideways for transverse; push and pull along the spring for longitudinal. I use that demo so the words “perpendicular” and “parallel” have a picture.
2-mark “describe the difference”
In a transverse wave the oscillations are at right angles to the energy transfer [1]. In a longitudinal wave the oscillations are in the same direction as the energy transfer [1]. Naming one example of each is extra insurance.
3.3–3.4
Waves transfer energy and information without transferring matter (3.4). A cork on a pond bobs up and down; it does not ride to the far bank.
3.5–3.7
Same method every time: list and convert, write the equation, substitute, unit, sense-check. Specification 3.7 wants this used for sound and for electromagnetic waves, not just water ripples.
Board example — sound
A note has frequency $680\,\text{Hz}$. Speed of sound in air is $340\,\text{m/s}$. Find $\lambda$ and $T$.
$v=340\,\text{m/s}$, $f=680\,\text{Hz}$.
$$\lambda = v/f = 340/680 = 0.50\,\text{m}$$ $$T = 1/f = 1/680 = 1.47 \times 10^{-3}\,\text{s}$$Sense-check: half a metre is a reasonable wavelength for a fairly high note. $T$ is a small fraction of a second because 680 waves pass each second.
Board example — radio
A radio station broadcasts at $100\,\text{MHz}$. EM waves travel at $3.0 \times 10^8\,\text{m/s}$ in air.
$f = 100 \times 10^6 = 1.00 \times 10^8\,\text{Hz}$.
$$\lambda = v/f = 3.0\times 10^8 / 1.00\times 10^8 = 3.0\,\text{m}$$Watch
3.8–3.9
The Doppler effect is a change in the observed frequency and wavelength when the source moves relative to the observer. The source’s own frequency does not change.
The classic picture is an ambulance. The same idea appears as water ripples in front of a moving boat. Do not drag in redshift of galaxies — that is Topic 8.
3-mark Doppler explain
The source is moving towards the observer [1]. Wavefronts are closer together / wavelength decreases [1]. So the observed frequency is higher [1].
Specification 3.9 is short and easy to forget: all waves can be reflected and refracted — sound (echoes), water, and light. Lesson C does the light diagrams in detail.
1.
Water ripples have $f=5.0\,\text{Hz}$ and $\lambda=4.0\,\text{cm}$. Calculate the wave speed.
2.
A police car moves away from you with its siren on. What happens to the wavelength and frequency you hear? Name the effect.