General properties of waves

Key points

What a wave does

• A wave carries energy from one place to another. It does not carry matter with it.
• Example: a plastic bottle floating on the sea moves up and down as each wave passes. The waves move on towards the beach, but the bottle stays in about the same place.
• Rope: move one end of a long rope up and down. A wave travels along the rope. Each part of the rope only moves up and down. The shape of the wave moves along.
• Spring: a long, loose spring (a “slinky”) can show two kinds of wave.
  • Move one end from side to side. The wave travels along the spring, and the coils move from side to side.
  • Push and pull one end along the length of the spring. The coils bunch up and spread out, and these regions travel along the spring. The coils move backwards and forwards (see 3.4).
• Water waves: dip a finger or a bar into water again and again. Waves spread out across the surface. The energy comes from the vibrating source.

Describing a wave

• A crest (also called a peak) is a highest point of a wave. A trough is a lowest point.
• A wavefront is a line that joins points on a wave that are moving in step, for example a line along one crest. In diagrams of water waves, each line is usually a crest.
• The wavelength, λ, is the distance from one point on a wave to the same point on the next wave. Example: from one crest to the next crest. It is also the distance between two neighbouring wavefronts. Unit: metre (m).
• The amplitude is the largest distance a point moves from its rest position. On a diagram, measure it from the rest line (the middle line) up to a crest. It is not the distance from a crest to a trough.
• The frequency, f, is the number of waves that pass a point each second. It is also the number of vibrations the source makes each second. Unit: hertz (Hz). 1 Hz = one wave per second.
• The wave speed, v, is the distance a wavefront travels each second. Unit: m/s.
• v = fλ. Reason: each second, f waves pass a point, and each wave is λ long. So the wave travels f × λ metres each second.
• The frequency of a wave is set by its source. It does not change when the wave moves into a different material or a different depth of water.

Transverse and longitudinal waves

• The direction of propagation is the direction in which the wave travels. Energy is carried in this direction.
• In a transverse wave, the vibrations are at right angles (90°) to the direction of propagation.
• These can be modelled as transverse waves:
  • all electromagnetic radiation, including light and radio waves (see 3.3)
  • water waves
  • seismic S-waves (secondary waves). Seismic waves are waves made by an earthquake. They travel through the Earth.
• In a longitudinal wave, the vibrations are parallel to the direction of propagation. The particles move backwards and forwards along the line in which the wave travels.
• These can be modelled as longitudinal waves:
  • sound waves (see 3.4)
  • seismic P-waves (primary waves).
• Memory aid: S for S-wave and Sideways (transverse); P for P-wave and Push–pull (longitudinal).

Reflection, refraction and diffraction

• Reflection: a wave bounces back when it hits a flat (plane) surface. The waves leave the surface at the same angle as they arrived. The speed, wavelength and frequency do not change.
• Refraction: a change in the direction of a wave caused by a change in its speed. It happens when the wave passes into a different material, or into water of a different depth.
• When a wave slows down, its frequency stays the same, so its wavelength gets shorter (from v = fλ).
• If a wave meets the boundary at an angle, refraction changes its direction. If the wavefronts are parallel to the boundary, the speed and wavelength change but the direction does not.
• Diffraction: waves spread out as they pass through a narrow gap or go past an edge. Diffraction does not change the speed, wavelength or frequency.
• Example: sea waves spread out after they pass through a gap in a breakwater. They also bend round the end of a breakwater into the calm water behind it.

The ripple tank

• A ripple tank is a shallow glass-bottomed tray of water used to study water waves.
• A motor makes a bar (the dipper) vibrate up and down in the water. A straight bar makes straight wavefronts. A small ball on the bar makes circular wavefronts.
• A lamp above the tank shines down through the water. Each crest acts like a lens and makes a bright line on a screen or paper below. So the bright lines show the wavefronts.
• To see the waves more easily, a flashing light (a stroboscope) can make the waves seem to stand still.
• (a) Reflection at a plane surface: put a straight metal barrier in the tank. The wavefronts reflect from it. They leave the barrier at the same angle as they arrived.
• (b) Refraction: put a glass or plastic plate on the bottom of part of the tank. This makes a region of shallow water. Waves travel more slowly in shallow water. Over the plate, the wavefronts are closer together (shorter wavelength). If the edge of the plate is at an angle to the wavefronts, the waves change direction as they cross it.
• (c) Diffraction due to a gap: put two barriers in a line with a gap between them. The wavefronts curve and spread out after they pass through the gap.
• (d) Diffraction due to an edge: put one barrier in the water. The waves bend round its end into the region behind the barrier.

How much diffraction?

• Diffraction through a gap depends on the size of the gap compared with the wavelength. Extended
• Gap much wider than the wavelength: the waves pass through almost straight. Only the ends of the wavefronts curve a little. There is little diffraction. Extended
• Gap about one wavelength wide, or smaller: the waves spread out a lot. The wavefronts become almost semicircles. The spreading is very noticeable. Extended
• So, for the same wavelength, a narrower gap gives more spreading. For the same gap, a longer wavelength gives more spreading. Extended
• At an edge, waves with a longer wavelength bend round the edge more than waves with a shorter wavelength. Extended
• Example: you can hear a person talking in the next room through an open door, but you cannot see them. Many sounds have a wavelength similar to the width of a door, so they diffract a lot. Light has a very short wavelength compared with the door, so it hardly diffracts at all. Extended

Common mistakes

• Students measure the amplitude from a crest down to a trough. / The mark scheme wants: from the rest position to a crest (or to a trough). This is half the crest-to-trough height.
• Students measure the wavelength from a crest to the next trough. / The mark scheme wants: one whole wave, for example crest to crest.
• Students write that the water moves along with the wave. / The mark scheme wants: waves transfer energy without transferring matter.
• Students write that the frequency changes when a wave refracts. / The mark scheme wants: the speed and wavelength change; the frequency stays the same.
• Students mix up the seismic waves. / The mark scheme wants: S-waves are transverse; P-waves are longitudinal.
• Students write that a wider gap gives more diffraction. / The mark scheme wants: a narrower gap gives more spreading. The spreading is very noticeable when the gap is about one wavelength wide or smaller. Extended

Exam tips

• Define each wave word in one short sentence. Give the unit for wavelength (m), frequency (Hz) and wave speed (m/s).
• On a wave diagram, draw the wavelength from crest to crest and the amplitude from the rest line to a crest. Use a double-headed arrow for each.
• Calculate: write v = fλ, substitute, then give the answer with a unit. Change cm to m and kHz to Hz first.
• Draw reflected wavefronts with the same spacing as the incoming ones.
• Draw refracted wavefronts in shallow water closer together, because the wave is slower and the wavelength is shorter.
• Draw diffracted wavefronts with the same spacing after the gap. Diffraction does not change the wavelength.
• Describe diffraction by comparing the gap with the wavelength. Use the words “gap”, “wavelength” and “spreads out”. Extended
• A typical 1-mark answer: “In a transverse wave, the vibrations are at right angles to the direction the wave travels.”
• A typical 2-mark answer to “How does a ripple tank show refraction?”: “Place a glass plate in the tank to make shallow water (1). The waves slow down over the plate, so the wavefronts get closer together and change direction (1).”
• A typical 3-mark answer to “Describe how diffraction depends on gap size”: “Waves spread out after passing through a gap (1). A narrower gap gives more spreading; it is very noticeable when the gap is about one wavelength wide or smaller (1). A gap much wider than the wavelength gives very little spreading (1).” Extended