Mechanical Waves: Pulses, Media and Energy Transfer

The wave that never leaves its seat

At a hockey game, someone starts "the wave". One section of fans stands up and sits down, then the next section, then the next. In a few seconds the wave has gone all the way around the arena. But think about it: did anybody actually move around the arena? No. Every fan stayed in their own seat. They just stood up and sat down at the right moment.

That is the big idea of this whole unit. A wave carries a disturbance, and energy, from place to place. The material itself stays (roughly) where it is.

What is a mechanical wave?

A wave is a disturbance that transfers energy from one place to another without transferring matter.

A mechanical wave needs a material to travel through. That material is called the medium. Examples:

• a wave on a guitar string (medium: the string)
• a ripple on a pond (medium: water)
• sound (medium: usually air, but also water and solids)
• an earthquake wave (medium: rock)

Every mechanical wave needs two things: a source that vibrates (something that starts the disturbance) and a medium whose particles are linked to each other, so that each particle can push or pull on its neighbour. That is why sound cannot travel through the vacuum of space: there are no particles to pass the disturbance along.

Pulses and periodic waves

Flick one end of a rope once and a single bump runs along it. That is a pulse. Keep shaking the end up and down at a steady rate and you make a periodic wave: a train of identical pulses, one after another. A tuning fork, a vibrating guitar string and your vocal cords all make periodic waves.

Two ways particles can move

Watch one tiny piece of the medium (a dot of tape on a rope, one coil of a Slinky) as a wave passes. It moves back and forth around its rest position (equilibrium position), then settles back. How it moves sorts waves into two families.

Transverse waves: the particles vibrate perpendicular (at 90°) to the direction the wave travels. Shake a rope up and down: the wave moves along the rope, but each bit of rope moves up and down. The high points are crests and the low points are troughs.

Longitudinal waves: the particles vibrate parallel to the direction the wave travels: forward and back along the same line. Push and pull one end of a stretched Slinky along its length and you see regions where the coils are bunched together (compressions) and regions where they are spread out (rarefactions). These regions travel along the Slinky. Sound is a longitudinal wave: air molecules are pushed together and spread apart along the direction the sound is going.

Why can't transverse waves travel through air?

For a transverse wave, each particle has to drag its neighbour sideways. Particles in a solid are held tightly together, so they can do that. In a liquid or gas the particles slide past each other, so a sideways tug is not passed on. A push (compression) is passed on in any state of matter. That is why sound, which is longitudinal, can travel through air, water and steel.

Earthquakes show this beautifully. An earthquake sends out P-waves (primary, longitudinal) and S-waves (secondary, transverse). P-waves travel through solid and liquid rock, and they arrive first because they are faster. S-waves cannot pass through liquid. Seismologists found that S-waves do not get through Earth's outer core, which is how they worked out that the outer core is liquid.

Water waves: a bit of both

A water particle at the surface of a lake moves in a roughly circular path as a wave passes: up and forward, then down and back. So surface water waves are a mix of transverse and longitudinal motion. A floating leaf bobs in little loops and stays almost in the same place.

What controls the speed of a wave?

This surprises many people: the speed of a wave depends on the medium, not on the source. Shaking the rope harder makes taller waves (more energy), and shaking it faster makes more waves per second, but the waves still travel along that rope at the same speed. To change the speed you must change the medium: a tighter rope, a lighter rope, a different material, or a different temperature.

The energy a wave carries does depend on the source. For a mechanical wave, the energy grows with the square of the amplitude: double the amplitude and the wave carries four times the energy. This is why a tsunami a few metres tall can be so destructive.