Classification by the need for a medium
Every wave of the last lesson travelled through some material. Is a material always needed? The answer sorts waves into two families. On the basis of the need for a medium, a wave is either mechanical or non-mechanical.
A mechanical wave needs a material medium to travel. A non-mechanical wave needs no medium and can travel through a vacuum.
Mechanical waves
A mechanical wave is passed along by the parts of a material pushing and pulling on their neighbours. With no material, there is nothing to pass it along. Here are four mechanical waves.
- Sound waves in air, or in any other medium. Without a medium, sound waves cannot travel.
- Water waves on the surface of a pond. Without a medium, water waves cannot travel.
- Seismic waves, which travel through the Earth during an earthquake. Without a medium, seismic waves cannot travel.
- Waves on a stretched string, the main subject of this chapter. Without a medium, waves on a string cannot travel.
In every case the medium is what carries the disturbance: the air, the water, the rock of the Earth, the string. Take the medium away and the wave has nothing to travel in.
Non-mechanical waves
A non-mechanical wave does not need a medium. It can travel through a vacuum. There are two kinds.
- Electromagnetic waves: light, radio waves, X-rays and microwaves. Without a medium, electromagnetic waves can travel. Light from the Sun crosses the vacuum of space to reach the Earth.
- Gravitational waves, disturbances of spacetime itself, first detected in 2015. Without a medium, gravitational waves can travel.
In a vacuum, both kinds travel at one constant speed, the speed of light, written \(c\), about \(3 \times 10^8\,\text{m/s}\). Sunlight takes about \(500\,\text{s}\), a little over \(8\) minutes, to cross the \(1.5 \times 10^{11}\,\text{m}\) from the Sun to the Earth. None of that path contains air.
Can astronauts standing on the surface of the Moon hear the sound of an explosion on the Moon?
Which of these waves could travel from a satellite to another satellite through empty space?
On 14 September 2015, two detectors of the LIGO observatory in the United States recorded a tiny signal within a few milliseconds of each other. It was a gravitational wave from two black holes that had merged more than a billion years earlier. The wave had crossed empty space to reach the Earth. It stretched and squeezed the detectors by far less than the width of a proton. Scientists from Indian institutes, among them IUCAA in Pune, were part of the team that analysed it. India is now building a detector of its own, LIGO-India, in Maharashtra.
Classification by the direction of particle motion
A mechanical wave can also be sorted by the way the particles of its medium move. Compare the direction in which each particle oscillates with the direction in which the wave travels. On this basis, a wave is either transverse or longitudinal.
In a transverse wave, the particles of the medium oscillate perpendicular to the direction in which the wave travels. In a longitudinal wave, the particles of the medium oscillate parallel to the direction in which the wave travels.
Transverse waves
In a transverse wave the particles move across the direction of travel. Here are three transverse waves.
- A wave on a rope or a string. Each piece of the rope oscillates perpendicular to the direction in which the wave travels.
- Ripples on the surface of water. Each water molecule at the surface oscillates perpendicular to the direction in which the ripple travels.
- The stadium wave. Each fan simply stands up and sits down, and stays in the same seat. The motion of each fan is perpendicular to the direction in which the wave goes round.
In each case, the wave goes one way along the medium, and each particle moves at right angles to that way.
The ripples on water are not purely transverse. As a water wave passes, each bit of water near the surface moves in a small loop, very nearly a circle in deep water. It goes up and forward on a crest, and down and back in a trough. The up-and-down part of that motion is transverse, and the forward-and-back part is longitudinal. So a water wave is really a mixture of the two kinds. The list above names the up-and-down part, the one the eye sees. The loop ends where it began, so the water is still not carried along.
Longitudinal waves
In a longitudinal wave the particles move along the direction of travel. The wave moves forward as a series of compressions, where the particles are crowded together, and rarefactions, where they are spread apart. Each compression is followed by a rarefaction, and the pattern moves on through the medium. Here are three longitudinal waves.
- Sound waves in air. Each molecule of air oscillates back and forth along the direction in which the sound travels.
- A slinky pushed and pulled along its length. The coils move parallel to the direction of the pulse.
- Seismic P-waves. The particles of the Earth vibrate parallel to the direction in which the wave travels.
In each case, the particles and the wave move along the same line.
Watch the painted particle in each panel of Fig 2.1. At the top it moves only up and down on its dashed line, while the crests move to the right. At the bottom it moves only left and right on its short dashed line, while the compressions move to the right. In both panels the painted particle ends each cycle where it began. The wave travels, and the particle stays at home.
A longitudinal wave you can control
The full description of a longitudinal wave comes in the chapters on sound. For now, the model below shows how the particles of a longitudinal wave move. Every particle oscillates strictly parallel to the direction of travel. Regions of compression and rarefaction travel along the medium.
Try the amplitude slider first. At zero amplitude the particles stay evenly spaced, and there is no wave. At \(0.30\,\text{m}\) the compressions are much more crowded, and the rarefactions much emptier. Now try the frequency slider. The speed stays at \(2\,\text{m/s}\), because the medium sets it. At \(0.5\,\text{Hz}\) the compressions are \(4.0\,\text{m}\) apart. At \(1\,\text{Hz}\) they are only \(2.0\,\text{m}\) apart. Lesson 5 explains this spacing.
You tie a long rope to a doorknob and flick it up and down, so that a pulse travels along the rope. You watch one small section of the rope. Compared with the direction in which the pulse travels, in which direction does that section move?
A slinky lies stretched on a smooth floor. You push its end forward and pull it back once, along its length. What kind of pulse travels along the slinky?
An earthquake sends out both kinds of wave through the rock. The P-wave is longitudinal and travels at about \(6\,\text{km/s}\) in the crust. The S-wave is transverse and travels at about \(3.5\,\text{km/s}\). So a seismograph always records the P-wave first. The longer the gap between the two, the farther away the earthquake was. The National Centre for Seismology in New Delhi reads these gaps from many stations to find where an earthquake started.
A seismograph records the P-wave of an earthquake \(10\,\text{s}\) before the S-wave. The P-wave travels at \(6\,\text{km/s}\) and the S-wave at \(3.5\,\text{km/s}\). How far away was the earthquake, in km?
- Thinking that sound can cross empty space because light can.Light is electromagnetic and needs no medium. Sound is mechanical and needs one.
- Judging the kind of wave by the shape of the medium.Look at the motion of one particle. Across the direction of travel means transverse; along it means longitudinal.
- Thinking that the particles of a longitudinal wave travel with the compressions.The compressions travel. Each particle only oscillates back and forth about its own place.