The Wave Machine

The Wave Machine

Ripples on a pond, sound in the air, light from the Sun: all are waves. A wave is a vibration that travels, carrying energy along with it. Learn a handful of terms and one equation and you can describe any of them, from a guitar string to a radio broadcast.

Waves carry energy, not matter

The single most important idea about waves, and the one most often half-remembered: a wave transfers energy (and information) from place to place, but it does not transfer matter. Watch a duck sitting on a pond as ripples pass under it. The duck bobs up and down and stays roughly where it was. It is not carried to the far bank. The water behaves the same way. Each bit of water moves up and down about its resting position while the wave travels onward through it. What crosses the pond is the disturbance, not the water.

Across the room

Someone plays music through a speaker on the far side of a room and you hear it. Does the air travel from the speaker to your ear?

• No. Each bit of air vibrates back and forth about its own position while the disturbance travels across the room, and it is the energy that reaches you
• Yes. The sound pushes a stream of air from the speaker to your ear, which is what you hear
• Partly: some air is carried across and the rest simply vibrates
• No, because sound does not need any air to travel through at all

Transverse and longitudinal 〰️

Waves come in two kinds, and the difference is the direction the vibration happens in relative to the direction the wave travels:

Which are transverse?

Select ALL THREE transverse waves.

• Ripples spreading across a pond
• Light reaching us from the Sun
• A slinky spring shaken from side to side
• Sound travelling through air
• A slinky spring pushed and pulled along its length
• An echo returning from a cliff face

The parts of a wave

Four measurements describe any wave. The first one is where marks are most often dropped, so read it twice:

Label the wave

Drag each label to the right feature of this transverse wave: the peak, the dip, the pink crest-to-crest marker, and the green rest-to-crest marker.

How big is the amplitude?

On a water wave, the crests rise 6 cm above the still-water line and the troughs fall 6 cm below it. A student writes that the amplitude is 12 cm. Is that right?

• No, it is 6 cm: the amplitude is measured from the rest position to a crest, not from a trough all the way up to a crest
• Yes, 12 cm, because that is the total height the wave moves through
• No, it is 3 cm: the amplitude is half of the distance from the rest line to the crest
• It depends on the wavelength, which has not been given

Find the period

A wave has a frequency of 4 Hz. What is its period, in seconds (s)?

The wave equation

Speed, frequency and wavelength are tied together for every wave there is: v = f λ (wave speed in m/s = frequency in Hz × wavelength in m) It rearranges two ways, so any one of the three can be found from the other two: • f = v ÷ λ • λ = v ÷ f A check that costs nothing: hertz means "per second", so multiplying hertz by metres gives metres per second, which is a speed. If your rearrangement would give you seconds per metre, you have divided the wrong way round.

Find the wave speed

A wave has a frequency of 2 Hz and a wavelength of 3 m. What is its speed, in m/s?

Find the wavelength

A wave travels at 12 m/s with a frequency of 3 Hz. What is its wavelength, in metres (m)?

Radio, water and volume

Four questions that all come back to v = f λ, or to what a wave actually is.

• Two radio stations broadcast at 100 MHz and 200 MHz. Both waves travel at the same speed. Which has the longer wavelength?
• Why do both radio waves travel at the same speed in the first place?
• A 500 Hz sound passes from air, where it travels at about 340 m/s, into water, where it travels at about 1500 m/s. What happens to its frequency and its wavelength?
• You turn up the volume on the speaker without changing the note. Which quantity of the sound wave has changed?

The wave rules

Waves transfer _____, not matter: the particles vibrate about a fixed position while the disturbance travels on. In a transverse wave the vibrations are _____ to the direction of travel, while in a longitudinal wave such as sound they are parallel to it. The _____ is measured from the rest position to a crest, not from trough to crest. Wave speed is found from v = frequency × _____.

Demonstrate both

Exam practice. In about 50 words, describe how you could use a single slinky spring to demonstrate both a transverse and a longitudinal wave, and how a watcher would tell them apart. Include:

• what you would do with your hand for each of the two waves
• which direction the coils move relative to the direction the wave travels, in each case
• a real-world example of each kind