Define wave terms such as amplitude, wavelength, frequency, and period, and apply the wave equation

What this dot point is asking

SEAB wants you to define the basic wave terms (amplitude, wavelength, frequency, period), to distinguish transverse from longitudinal waves, to use the wave equation $v = f\lambda$, and to understand that waves transfer energy without transferring matter. The big idea is that a wave is a travelling disturbance that carries energy, described by a few measurable quantities.

The answer

What a wave is

A wave is a disturbance that travels and carries energy from one place to another. As it passes, the particles of the medium vibrate about fixed positions but do not move along with the wave. This is why a wave transfers energy without transferring matter, a cork on water bobs up and down as waves pass but does not travel across the pond.

Transverse and longitudinal waves

• Transverse wave: the vibrations are perpendicular to the direction the wave travels. Examples: light, water waves, a wave on a rope.
• Longitudinal wave: the vibrations are parallel to the direction of travel, making compressions and rarefactions. Example: sound.

Key wave terms

• Amplitude: the maximum distance a particle moves from its rest position. Larger amplitude means more energy.
• Wavelength ($\lambda$): the distance between two neighbouring points in step (such as crest to crest).
• Frequency ($f$): the number of complete waves passing a point each second, in hertz ($\text{Hz}$).
• Period ($T$): the time for one complete wave to pass, in seconds.

Frequency and period are reciprocals:

The wave equation

The speed of a wave links its frequency and wavelength:

Speed is in $\text{m s}^{-1}$, frequency in hertz, and wavelength in metres. For a wave moving at constant speed, a higher frequency means a shorter wavelength.

Examples in context

Example 1. Radio tuning. A radio station broadcasts at a fixed frequency, and because all radio waves travel at the same speed, that frequency fixes the wavelength through $v = f\lambda$. Tuning the radio selects the frequency you want, picking one station's wave out of the many filling the air.

Example 2. A cork on a pond. Drop a stone in a pond and ripples spread outward, but a floating cork only bobs up and down in place, it does not get carried to the shore. This shows clearly that the wave moves energy outward while the water itself (and the cork) just oscillates about a fixed point.

Try this

Q1. A wave has speed $12\ \text{m s}^{-1}$ and wavelength $3.0\ \text{m}$. Calculate its frequency. [2 marks]

• Cue. From $v = f\lambda$, $f = \dfrac{v}{\lambda} = \dfrac{12}{3.0} = 4.0\ \text{Hz}$.

Q2. State the difference between a transverse and a longitudinal wave. [2 marks]

• Cue. Transverse: vibrations perpendicular to travel; longitudinal: vibrations parallel to travel.

Q3. Explain what is meant by a wave transferring energy without transferring matter. [2 marks]

• Cue. The particles vibrate about fixed positions and do not travel with the wave; only the energy is carried forward.