Describe transverse and longitudinal waves and the wave equation, and apply the laws of reflection and refraction of light

What this dot point is asking

SEAB wants you to describe waves, distinguishing transverse from longitudinal, to use the terms frequency, wavelength, amplitude and speed with the wave equation $v = f\lambda$, and to apply the laws of reflection and refraction of light. The maths is one simple equation; the rest is careful use of definitions and measuring angles from the normal.

The answer

Describing a wave

A wave carries energy from one place to another without transferring matter. Key terms:

• amplitude: the maximum displacement from the rest position,
• wavelength ($\lambda$): the distance for one complete wave,
• frequency ($f$): the number of complete waves passing a point each second, in hertz ($\text{Hz}$),
• period: the time for one complete wave.

Transverse and longitudinal waves

In a transverse wave the vibrations are at right angles to the direction the wave travels, like a wave on a rope or light. In a longitudinal wave the vibrations are along the direction of travel, with compressions and rarefactions, like sound in air.

The wave equation

The speed, frequency and wavelength are linked by:

So a higher frequency at the same speed means a shorter wavelength.

Reflection of light

When light hits a plane mirror it reflects so that the angle of incidence equals the angle of reflection, both measured from the normal (the line at $90^\circ$ to the surface). The image in a plane mirror is the same size, upright, and as far behind the mirror as the object is in front (a virtual image).

Refraction of light

When light passes from one material into another, such as from air into glass, it changes speed and so bends. Going into a denser medium (air to glass) it slows down and bends toward the normal; going into a less dense medium (glass to air) it speeds up and bends away from the normal. If the ray meets the surface along the normal it passes straight through without bending.

Examples in context

Example 1. A swimming pool looks shallower than it is. Light from the bottom speeds up as it leaves the water into the air and bends away from the normal. Your eye traces the rays back in straight lines, so the bottom appears raised and the pool looks shallower than its true depth.

Example 2. Echoes from a cliff. Sound is a longitudinal wave that reflects off a hard surface. If you shout at a cliff, the reflected wave returns as an echo, and timing the delay lets you estimate the distance using the speed of sound.

Try this

Q1. State the difference between a transverse and a longitudinal wave. [2 marks]

• Cue. In a transverse wave the vibrations are at right angles to the direction of travel; in a longitudinal wave they are along the direction of travel.

Q2. A wave travels at $340\ \text{m/s}$ with a wavelength of $0.20\ \text{m}$. Find its frequency. [2 marks]

• Cue. $f = \dfrac{v}{\lambda} = \dfrac{340}{0.20} = 1700\ \text{Hz}$.

Q3. Explain why a ray of light bends as it passes from air into glass. [2 marks]

• Cue. Light slows down in the denser glass, and this change of speed at the boundary makes it bend toward the normal.