Transverse and longitudinal waves
What does a wave carry?
Drop a pebble into a still pond. Circular ripples spread outwards across the water.
Now watch a leaf floating on the surface. As the ripples pass, it bobs up and down, but it does not ride outwards with them.
So the water is not flowing outwards. What travels is a pattern of disturbance, and with it, energy.
Think of a Mexican wave in a cricket stadium. Each spectator only stands up and sits down, yet the wave races all the way round the ground.
That is a wave: a disturbance that moves through a medium and carries energy from one place to another, while each part of the medium only moves about its own position.
How is the disturbance passed on? Picture the medium as a row of balls joined by springs. Pull the first ball, and its spring tugs on the next one, which tugs on the next.
Two properties make this work. Elasticity gives a restoring force that pulls each part back. Inertia makes each part overshoot, so the motion keeps going.
Waves like these, which need a material medium such as water, air, a string or rock, are called mechanical waves. Newton’s laws govern them.
Watch an electric bell ringing inside a glass jar. As we pump out the air, the hammer keeps striking, but the sound fades away. Sound cannot travel through a vacuum.
Light from the Sun does cross empty space, because it is an electromagnetic wave, which needs no medium. In this chapter, we study mechanical waves.
Two ways to wave
Tie one end of a long rope to a pole. Jerk the free end up and down once. A single pulse runs along the rope.
Now shake your hand up and down steadily. A train of crests and troughs travels along. Each bit of rope moves up and down, at right angles to the direction the wave travels.
A wave in which the particles of the medium move perpendicular to the direction of travel is called a transverse wave.
Now take a slinky. Push and pull one end along its length. The coils bunch together in compressions and spread apart in rarefactions, and these move along the spring.
Here each coil moves back and forth along the same line as the wave travels. This is a longitudinal wave.
Sound in air is longitudinal. A tabla skin pushes the air next to it, making a compression. As it moves back, it leaves a rarefaction. The layers of air pass these on to your ear.
Which media carry which waves? A transverse wave needs a medium that resists a change of shape, a shear. Solids and stretched strings can do this. Liquids and gases cannot.
A longitudinal wave needs a medium that resists being squeezed. Solids, liquids and gases all do. So a steel rail can carry both kinds of wave, but air carries only longitudinal waves.
Earthquakes show this beautifully. The longitudinal P waves pass through the whole Earth. The transverse S waves cannot cross its liquid outer core.
Ripples on water are a mixture. Each bit of water near the surface moves both up and down and back and forth. In every case, the medium only oscillates. The energy is what travels.
Try it: transverse and longitudinal
- Follow the amber particle. It moves up and down, but never travels along with the wave.
- Switch to Longitudinal: now the same particle moves back and forth along the wave’s direction.
- In the longitudinal view, look for the crowded compressions and the spread-out rarefactions moving along.
- Its graph against time looks the same in both views: every particle just oscillates about its own position.
Waves in air
Which kind of mechanical wave can travel through the air in a room?
- Both transverse and longitudinal waves
- Only transverse waves
- Only longitudinal waves
- Neither: air is too thin to carry a wave
Answer
C. A transverse wave needs the medium to resist a change of shape (shear). Air, like any fluid, cannot, so it carries only longitudinal waves: compressions and rarefactions. That is exactly what sound in air is. A solid such as steel can carry both kinds.
The bobbing cork
Ripples on a pond have crests 2 m apart. A floating cork bobs up and down 3 times every second. How far along the pond does the cork travel in 10 s?
- 0 m
- 6 m
- 20 m
- 60 m
Answer
A. The cork only oscillates about its own position, so it travels 0 m. What does travel is the wave: each time the cork bobs once, the pattern moves on by one crest gap, so the crests move 2 m × 3 = 6 m every second, or 60 m in 10 s. The energy moves; the water stays where it is.
Summary
- Transverse wave:
particles move ⟂ to the direction of travel - Longitudinal wave:
particles move ∥ to the direction of travel
- A wave is a travelling disturbance. It carries energy, but the medium only oscillates about its mean position.
- Mechanical waves need a material medium with elasticity and inertia. Sound cannot cross a vacuum; electromagnetic waves can.
- Transverse waves (crests and troughs) need a medium that resists shear: solids and stretched strings.
- Longitudinal waves (compressions and rarefactions) travel in solids, liquids and gases. Sound in air is longitudinal.
- Water surface ripples are a mixture: particles move both up and down and to and fro.