Waves in air, fluids and solids

Waves may be either transverse or longitudinal.

The ripples on a water surface are an example of a transverse wave. Longitudinal waves show areas of compression and rarefaction. Sound waves travelling through air are longitudinal.

You should be able to describe the difference between longitudinal and transverse waves. The difference is the direction the particles move relative to the direction the wave travels: in a transverse wave they move at right angles to it, and in a longitudinal wave they move along the same line as it.

You should be able to describe evidence that, for both ripples on a water surface and sound waves in air, it is the wave and not the water or air itself that travels.

For water: a floating object such as a cork or a duck bobs up and down as ripples pass under it, but it does not travel along with them. If the water itself were moving forwards, the cork would be carried to the far side.

For sound: sound travels across a room, but there is no wind — the air is not moving from the speaker to your ear. If it were, a candle in front of a loudspeaker would be blown out, and the room would gradually empty of air.

What a wave transfers is energy, and information, from one place to another — not matter.

You should be able to describe wave motion in terms of their amplitude, wavelength, frequency and period.

• The amplitude of a wave is the maximum displacement of a point on a wave away from its undisturbed position. • The wavelength of a wave is the distance from a point on one wave to the equivalent point on the adjacent wave. • The frequency of a wave is the number of waves passing a point each second.

The wave speed is the speed at which the energy is transferred, or the wave moves, through the medium.

period = 1 / frequency T = 1 / f

period, T, in seconds, s; frequency, f, in hertz, Hz. This equation is given on the Physics equation sheet.

All waves obey the wave equation:

wave speed = frequency × wavelength v = f λ

wave speed, v, in metres per second, m/s; frequency, f, in hertz, Hz; wavelength, λ, in metres, m.

You should be able to recall and apply the wave equation — note the difference: v = f λ must be recalled, while T = 1 / f is given.

You should also be able to identify amplitude and wavelength from given diagrams. Amplitude is measured from the undisturbed middle line to a peak, not from a peak to a trough.

You should be able to describe a method to measure the speed of sound waves in air, and a method to measure the speed of ripples on a water surface.

Sound in air: two people stand a measured distance apart — a few hundred metres, so the time is long enough to measure. One bangs two blocks together while the other starts a stopwatch on seeing the bang and stops it on hearing it. Repeat and take a mean, then use speed = distance ÷ time. The result should be around 330 m/s.

Ripples on water: use a ripple tank with a motorised dipper. Measure the wavelength by freezing the pattern with a strobe light and measuring across ten wavelengths, then dividing by ten. Read the frequency from the dipper's setting, or count the waves passing a point in a measured time. Then use v = f λ.

Physics only students should be able to show how changes in velocity, frequency and wavelength, in transmission of sound waves from one medium to another, are inter-related.

The rule to hold on to: when a wave crosses into a different medium, the frequency does not change — it is set by the source. The speed does change. So from v = f λ, if the speed increases the wavelength must increase in proportion, and if the speed decreases the wavelength decreases.

Waves can be reflected at the boundary between two different materials. Waves can be absorbed or transmitted at the boundary between two different materials.

So three things can happen at a boundary, and usually all three happen at once in some proportion: some of the wave is reflected back, some is absorbed by the material, and some is transmitted through it.

You should be able to describe the effects of reflection, transmission and absorption of waves at material interfaces, and construct ray diagrams to illustrate the reflection of a wave at a surface.

For a ray diagram of reflection, the conventions are strict: draw the normal as a dashed line at right angles to the surface at the point where the ray hits, measure both angles from the normal rather than from the surface, and mark the direction of travel with an arrow on each ray. The angle of incidence equals the angle of reflection.

A smooth surface reflects all the rays in the same direction, giving a clear image — specular reflection. A rough surface reflects rays in many directions, because the normal at each point faces a different way, so no image forms — diffuse scattering.

Sound waves can travel through solids causing vibrations in the solid.

Within the ear, sound waves cause the ear drum and other parts to vibrate, which causes the sensation of sound. The conversion of sound waves to vibrations of solids works over a limited frequency range. This restricts the limits of human hearing.

You should know that the range of normal human hearing is from 20 Hz to 20 kHz.

You should be able to describe, with examples, processes which convert wave disturbances between sound waves and vibrations in solids — the effect of sound waves on the ear drum being the obvious example. A microphone works the same way, its diaphragm vibrating in response to the sound; a loudspeaker runs the process backwards, its cone vibrating to produce sound waves in the air.

You should also be able to explain why such processes only work over a limited frequency range, and the relevance of this to human hearing.

The explanation: the solid parts that have to vibrate — the ear drum and the small bones behind it — have a size and a stiffness, and they respond well only to a limited range of frequencies. Below about 20 Hz and above about 20 kHz they do not vibrate enough to pass the wave on, so no sensation of sound is produced. That is what sets the limits of human hearing, and it is why the upper limit falls with age as the ear becomes less flexible.

You should be able to explain in qualitative terms how the differences in velocity, absorption and reflection between different types of wave in solids and liquids can be used both for detection and exploration of structures which are hidden from direct observation.

That is the idea behind all three examples below: a wave that reaches somewhere we cannot go, and comes back changed, carries information about what it passed through.

Ultrasound waves have a frequency higher than the upper limit of hearing for humans — so above 20 kHz. Ultrasound waves are partially reflected when they meet a boundary between two different media. The time taken for the reflections to reach a detector can be used to determine how far away such a boundary is. This allows ultrasound waves to be used for both medical and industrial imaging.

Echo sounding, using high frequency sound waves, is used to detect objects in deep water and measure water depth.

The calculation in both cases uses s = v t, with one correction that is easy to forget: the wave travels to the boundary and back, so the distance found is twice the depth.

Seismic waves are produced by earthquakes.

• P-waves are longitudinal seismic waves. P-waves travel at different speeds through solids and liquids. • S-waves are transverse seismic waves. S-waves cannot travel through a liquid.

P-waves and S-waves provide evidence for the structure and size of the Earth's core.

How that becomes evidence: after an earthquake, detectors around the world record which waves arrive where. S-waves are not detected on the far side of the Earth at all, and since S-waves cannot travel through a liquid, part of the core must be liquid. P-waves are detected, but they arrive later than expected and are refracted, because they change speed on entering a different medium — and the size of that shadow zone gives the size of the core.

You should be aware that the study of seismic waves provided new evidence that led to discoveries about parts of the Earth which are not directly observable. Nobody has ever been near the core; everything known about it was inferred from waves.