The Wave Machine

A wave moves energy, not stuff

Watch a duck bob on a pond as ripples pass. The ripples cross the whole pond, but the duck just goes up and down on the spot: it does not get carried to the far side. That is the heart of it. A wave carries ENERGY from place to place, but it does NOT carry the matter with it. The water only wobbles where it is. ⭐⭐ There are two kinds of wave, told apart by which way the wobble points. In a TRANSVERSE wave the wobble is at right angles to the way the wave travels, like the ripples on the pond or a wave on a rope. In a LONGITUDINAL wave the wobble is back and forth ALONG the direction of travel, like a sound wave squashing and stretching the air. ⭐ Any wave, of either kind, is described by four measurements. The amplitude is how far a point moves from its rest position. The wavelength is the distance from one crest to the next. The frequency is how many waves pass a point each second, in hertz. The period is the time for one whole wave to pass. ⭐⭐ And one equation ties them together: wave speed equals frequency times wavelength. Know any two of speed, frequency and wavelength, and you can find the third. This module is about waves in general. The electromagnetic spectrum, from radio to gamma, belongs to a different module. ⚠️ Carry one question the whole way through: what is wobbling, which way, and what does wave speed equals frequency times wavelength give me?

Two kinds, and four numbers

The first column is a transverse wave, the second a longitudinal one, and the third the measurements that describe either.

Tap the two transverse waves

Tap the TWO waves where the wobble is at right angles to the direction of travel, which makes them TRANSVERSE.

• Ripples spreading across the surface of a pond.
• A wave sent along a rope by shaking one end up and down.
• A sound wave travelling through the air.
• A push sent along a stretched spring, back and forth.

What amplitude measures

What does the amplitude of a wave measure?

• How far a point moves from its rest position
• The distance from one crest to the next
• How many waves pass each second
• The time for one whole wave to pass

The language of waves

Six terms this topic turns on. The first two are the kinds, the rest are the measurements.

Match each to what it means

Two true of every wave

Select the TWO statements that are TRUE of waves in general.

• A wave transfers energy from one place to another
• The medium wobbles on the spot rather than being carried along
• A wave carries the water or air along with it to the far side
• A bigger amplitude always means a faster wave

Answering a wave question

Wave questions reward precise definitions and clean use of the equation. ⭐⭐ START FROM ENERGY, NOT MATTER. If asked what a wave does, say it transfers energy without transferring matter, and that the medium wobbles on the spot. It is a favourite opening mark, and it is easy to lose by saying the water moves across. ⭐ TELL THE TWO TYPES APART BY THE WOBBLE. Transverse means the wobble is at right angles to the travel; longitudinal means it is along the travel. Water ripples and rope waves are transverse; sound is longitudinal. ⭐⭐ USE THE EQUATION CLEANLY. Wave speed equals frequency times wavelength. To find a frequency, divide the speed by the wavelength; to find a wavelength, divide the speed by the frequency. Keep speed in metres per second, frequency in hertz and wavelength in metres. KNOW THE MEASUREMENTS EXACTLY. Amplitude is distance from rest, wavelength is crest to crest, frequency is waves per second, and period is the time for one wave. The period and the frequency are linked: one is one divided by the other. ⚠️ A units habit. Convert first if a frequency is given in kilohertz or a distance in centimetres, then use the equation, so a slip does not creep in. Keep the one question to hand: what is wobbling, which way, and what does wave speed equals frequency times wavelength give me?

Order how to find a wave speed

Put the steps of finding the speed of a wave from measurements into a sensible order.

• Count how many waves pass a point in a measured time
• Work out the frequency, the waves per second
• Measure the wavelength, one crest to the next
• Multiply the frequency by the wavelength
• State the wave speed, in metres per second

Work out the wave speed

A wave has a frequency of 5 hertz and a wavelength of 3 metres. Using wave speed equals frequency times wavelength, what is its speed, in metres per second?

The wave run

Five quick decisions about waves. Three lives.

Wind across a field of wheat

Leave physics aside for a screen. Picture a wide field of wheat on a breezy day, and watch a gust travel across it. ⭐ You see a ripple sweep from one side of the field to the other, as if something is racing across. But no stalk of wheat travels anywhere. Each stalk stays rooted where it grows; it only bends over and springs back as the gust reaches it and passes on. ⭐⭐ So what actually crosses the field is not the wheat, it is the PATTERN of bending, and with it the push of the wind. The energy of the gust travels the whole width of the field while every plant stays exactly where it is planted. Look closely and you can even see a rhythm to it: the bent stripes are spaced a certain distance apart, and a new stripe reaches your edge of the field every so often. The stalks bend further in a strong gust than in a gentle one. ⚠️ Hold that picture. The wheat is the water or the air, the bending that races across is the wave, and the wind pushed along is the energy. Nothing is carried across the field; only the moving pattern, and its energy, travel through the crop that stays rooted in place.

Finish each wave line

The distance from one wave crest to the next crest is the _____. The number of waves passing a point each second, measured in hertz, is the _____. The greatest distance a point moves from its rest position is the _____. A wave whose wobble is at right angles to the direction of travel is _____. A wave whose wobble is along the direction of travel is _____.

Three waves to describe

Three situations arise. For each, choose the response that the wave rules support.

• A student says that when a wave crosses a pond, the water itself is carried from one bank to the other.
• A wave has a frequency of 2 hertz and a wavelength of 6 metres, and you need its speed.
• A student is unsure whether a sound wave in air is transverse or longitudinal.

Describe and compare waves

Explain what a wave transfers and what stays put, describe the difference between a transverse and a longitudinal wave with an example of each, and explain how you would use the wave-speed equation to find a wave speed.

• State that a wave transfers energy, not matter, and what the medium does
• Describe a transverse wave and give an example
• Describe a longitudinal wave and give an example
• Name the four measurements that describe a wave
• Explain how wave speed is found from frequency and wavelength