What a wave is

1. A wave is a disturbance that moves through a material or through space, carrying energy from one place to another.
2. As a wave passes, each point it reaches makes an oscillation, moving back and forth about its rest position.
3. The points themselves stay in about the same place, so the wave transfers energy without carrying the material along with it.
4. Flicking one end of a long rope tied to a post sends a hump along the rope, yet each piece of rope only moves up and down as the hump goes by.
5. A wave that repeats regularly can be described fully using four quantities: amplitude, wavelength, frequency and period.
6. Amplitude and wavelength are distances, while frequency and period describe the timing of the oscillations.

Amplitude

1. As a wave passes, the displacement of each point keeps changing, from zero at the rest position to a maximum on one side and then a maximum on the other side.
2. On a drawing of a transverse wave, the peaks are called crests and the dips are called troughs.
3. The amplitude is the height of a crest above the rest position, which is the same as the depth of a trough below it.
4. Amplitude is always measured from the centre line, which marks the rest position, to the top of a crest or the bottom of a trough.
5. The vertical distance from the top of a crest to the bottom of a trough is twice the amplitude.
6. Amplitude is a distance, so it is measured in metres, $m$, or in centimetres, $cm$, for small waves.
7. A wave with a larger amplitude carries more energy, so a sound wave with a larger amplitude is louder and a water wave with a larger amplitude rocks a boat harder.
8. Changing the amplitude does not change how far apart the waves are or how often they arrive, so amplitude is independent of wavelength and frequency.

Wavelength

1. The wavelength is the length of one complete wave, measured along the direction in which the wave travels.
2. Wavelength has the symbol $\lambda$, the Greek letter lambda, and is measured in metres, $m$.
3. On a transverse wave, you can measure the wavelength from one crest to the next crest, or from one trough to the next trough.
4. Any pair of matching points works, as long as both points are at the same stage of the cycle, for example both on the centre line and both about to move upwards.
5. The distance from a crest to the next trough is only half a wavelength, because a crest and a trough are at opposite stages of the cycle.
6. Wavelengths vary enormously, from a few centimetres for ripples in a puddle to more than $100m$ for the long swells that roll onto the beaches of Cornwall.

Frequency and period

1. The frequency of a wave is how many complete waves pass a fixed point every second.
2. Frequency has the symbol $f$ and is measured in hertz, $Hz$.
3. A frequency of $50Hz$ means that 50 complete waves pass the point each second.
4. The frequency is set by the source of the wave, so a hand shaking a rope three times every second makes waves with a frequency of $3Hz$.
5. The period is the time taken for one complete wave to pass a point, which is also the time for one complete oscillation.
6. Period has the symbol $T$ and is measured in seconds, $s$.
7. Frequency and period describe the same repeating motion in two ways, so a high frequency always goes with a short period.
8. The two are linked by $T=\frac{1}{f}$, which can also be written as $f=\frac{1}{T}$.
9. A wave with a frequency of $4Hz$ has a period of $\frac{1}{4}=0.25s$, because four waves share each second equally.
10. The UK mains supply oscillates at $50Hz$, so each cycle of the mains lasts $\frac{1}{50}=0.02s$.

Reading wave graphs

1. Waves are usually drawn on one of two kinds of graph, so the first thing to check is the label on the horizontal axis.
2. A displacement-distance graph is like a photograph of the whole wave at one instant, with distance along the wave on the horizontal axis.
3. On a displacement-distance graph, the horizontal gap between neighbouring crests is the wavelength.
4. A displacement-time graph follows one single point as time passes, with time on the horizontal axis.
5. On a displacement-time graph, the horizontal gap between neighbouring crests is the period, which you can turn into a frequency using $f=\frac{1}{T}$.
6. On both kinds of graph, the amplitude is read from the vertical axis as the height of a crest above the zero line.
7. A wavelength can never be read from a displacement-time graph, and a period can never be read from a displacement-distance graph.