Transverse and longitudinal waves

Drop a stone in a pond and a leaf floating nearby bobs up and down as the ripples pass, then settles where it started.

The ripples carried energy across the pond; the water itself did not travel with them.

That is true of every wave: it transfers energy (and often information) from one place to another without carrying the medium along.

There are two kinds, told apart by the way the vibrations (oscillations) go:

• Transverse: the vibrations are at right angles to the direction the energy travels. Ripples on water, waves on a string, and every electromagnetic wave (light, radio, X-rays) are transverse.
• Longitudinal: the vibrations are along the same direction the energy travels. Sound is longitudinal, and so is ultrasound, sound too high for us to hear. The medium bunches up into compressions and spreads out into rarefactions.

C marks a compression and R a rarefaction. One wavelength is the distance from one compression to the next.

A graph of displacement against distance is a snapshot of the whole wave at one instant.

• Amplitude: the biggest displacement from the rest position, measured from the middle line to a crest. Here it is 2 cm.
• Wavelength (λ): the distance from a point on one wave to the same point on the next, such as crest to crest. Here it is 8 cm.

Amplitude is middle to crest, not trough to crest. If you measured 4 cm on this graph, halve it.

• Frequency (f): how many waves pass a point each second, in hertz (Hz). 1 Hz is one wave per second.
• Period (T): the time for one complete wave to pass, in seconds.

period = 1 ÷ frequency
T = 1 / f

T in seconds (s), f in hertz (Hz). AQA prints this on its Physics equation sheet; learn it anyway, since it is one line and works both ways (f = 1/T).

1. A loudspeaker vibrates at 250 Hz
2. T = 1 ÷ 250 = 0.004 s
3. 0.004 s × 1000 = 4 ms

Period in milliseconds goes back into seconds (divide by 1000) before you use f = 1/T.