Describe waves using frequency, wavelength and amplitude, apply the wave equation, and explain how sound travels as a wave that needs a medium

What this dot point is asking

SEAB wants you to describe a wave using frequency, wavelength and amplitude, to use the wave equation, and to explain how sound travels as a wave that needs a material to pass through. The central idea is that a wave carries energy from place to place without carrying the material along with it.

The answer

What a wave is

A wave is a disturbance that carries energy from one place to another without moving the material itself permanently. When a wave passes through water, the water bobs up and down but does not travel along with the wave. We describe a wave with three quantities:

• Wavelength: the distance from one point on a wave to the same point on the next wave (for example, crest to crest), measured in metres.
• Frequency: the number of complete waves passing a point each second, measured in hertz ($\text{Hz}$).
• Amplitude: the greatest distance a point moves from its rest position. A bigger amplitude means more energy (a louder sound or brighter light).

The wave equation

The speed, frequency and wavelength of a wave are linked by:

where $v$ is the wave speed in $\text{m/s}$, $f$ is the frequency in hertz, and $\lambda$ is the wavelength in metres.

How sound travels

Sound is produced when something vibrates, such as a loudspeaker cone or your vocal cords. The vibration pushes and pulls the air particles next to it, which pass the vibration on to the next particles, and so on. This is why:

• Sound needs a medium (a material) to travel through. It cannot travel through a vacuum, because there are no particles to pass it on.
• Sound travels fastest in solids, slower in liquids, and slowest in gases, because the particles are closer together in solids and pass the vibration on more quickly.

Pitch and loudness

A higher frequency gives a higher-pitched sound. A larger amplitude gives a louder sound. The human ear can hear frequencies roughly from $20\ \text{Hz}$ to $20\,000\ \text{Hz}$.

Examples in context

Example 1. Why you see lightning before you hear thunder. Light reaches you almost instantly, but sound travels at only about $340\ \text{m/s}$, so the thunder arrives seconds later. Counting the seconds and multiplying by $340$ gives roughly how far away the storm is.

Example 2. An ultrasound scan. Very high-frequency sound waves (ultrasound, above human hearing) are sent into the body and reflect off internal structures. The reflections are used to build an image, for example of a baby before birth, because sound passes through the soft tissue as a wave.

Try this

• Cue. A wave has frequency $25\ \text{Hz}$ and wavelength $2\ \text{m}$. Find its speed: $v = 25 \times 2 = 50\ \text{m/s}$.
• Cue. Explain why an astronaut on the airless Moon cannot hear a colleague shout. There are no air particles to carry the sound, so it cannot travel.
• Cue. State what happens to the pitch of a sound if the frequency increases. The pitch gets higher.