Define wavelength, frequency, amplitude and speed, and use the wave equation v = f times wavelength

What this dot point is asking

SEAB wants you to define wavelength, frequency, amplitude and wave speed, to tell transverse waves from longitudinal waves, and to use the wave equation $v = f\lambda$. The big idea is that a wave carries energy from one place to another without carrying the material itself, and that its speed, frequency and wavelength are linked by one simple equation.

The answer

What a wave is

A wave is a disturbance that carries energy from one place to another without carrying matter with it. When a wave passes through water, the water bobs up and down but does not travel along with the wave; only the energy moves forward.

Transverse and longitudinal waves

There are two kinds of wave, depending on the direction of the vibrations:

• In a transverse wave, the vibrations are at right angles to the direction the wave travels. Examples are water waves and light.
• In a longitudinal wave, the vibrations are along (parallel to) the direction the wave travels, making regions of squashed-together and spread-out particles. The main example is sound.

The key wave quantities

• Wavelength ($\lambda$): the distance from one point on a wave to the next matching point (for example, crest to crest). Measured in metres.
• Frequency ($f$): the number of complete waves passing a point each second. Measured in hertz ($\text{Hz}$), where one hertz is one wave per second.
• Amplitude: the maximum distance a point moves from its rest position. A bigger amplitude means more energy.
• Speed ($v$): how fast the wave travels, in $\text{m s}^{-1}$.

The wave equation

These quantities are linked by the wave equation:

So the speed equals the frequency multiplied by the wavelength. You can rearrange it: $f = \dfrac{v}{\lambda}$ to find frequency, or $\lambda = \dfrac{v}{f}$ to find wavelength.

If the speed stays the same, a higher frequency means a shorter wavelength, and a lower frequency means a longer wavelength.

Examples in context

Example 1. Tuning a radio. Radio stations broadcast at different frequencies. Because all radio waves travel at the same speed (the speed of light), a higher-frequency station has a shorter wavelength. Tuning the radio selects the right frequency to pick up one station and reject the others.

Example 2. Ripples in a pond. Dropping a stone in a pond sends out circular ripples. A floating leaf bobs up and down as each ripple passes but stays in the same place, showing that the wave carries energy outward while the water itself does not travel. The distance between ripples is the wavelength.

Try this

• Cue. A wave has frequency $5.0\ \text{Hz}$ and wavelength $0.40\ \text{m}$. Find its speed. [2 marks] $v = f\lambda = 5.0 \times 0.40 = 2.0\ \text{m s}^{-1}$.

• Cue. State whether sound is transverse or longitudinal and describe its vibrations. [2 marks] Sound is longitudinal; the particles vibrate back and forth along the same direction the wave travels.

• Cue. A wave travels at $6.0\ \text{m s}^{-1}$ with a wavelength of $1.5\ \text{m}$. Find its frequency. [2 marks] $f = \dfrac{v}{\lambda} = \dfrac{6.0}{1.5} = 4.0\ \text{Hz}$.