Progressive waves are oscillations that travel through matter (or vacuum), transferring energy from one place to another, but not matter. In a transverse wave the oscillations are perpendicular to the direction of energy transfer (e.g.
electromagnetic waves, waves on stretched springs and s-waves). In a longitudinal wave the oscillations are parallel to the direction of energy transfer (e.g. sound waves, p-waves produced in earthquakes. When they travel through a medium, they create a series of compressions and rarefactions.
|Distance from the equilibrium position in a particular direction; a vector, so it can have either a negative or positive value
|Maximum displacement from the equilibrium position (can be positive or negative)
|Minimum distance between two points in phase on adjacent waves, e.g. peak to peak
|Period of oscillation
|Time taken for one complete oscillation or for wave to move one whole wavelength past a given point
|How far through the wave cycle a point on one wave is compared to another point on the same wave, or how “out of step” two waves are. 360° is equivalent to one complete cycle.
|Number of wavelengths passing a given point per unit time, or number of oscillations per second
|v (or c)
|Distance travelled by the wave per unit time
Using an oscilloscope to determine frequency: using a microscope, we can produce a trace on a screen. Each horizontal square on the oscilloscope trace represents a time interval (the timebase). By counting the number of oscillations per second, we can determine the frequency of the wave.
(The wave equation)
Graphical representations of transverse ad longitudinal waves:
- Displacement-distance graphs; also known as a wave profile. Used to determine wavelength and amplitude.
- Displacement-time graphs: used to determine the period and amplitude of the wave.
- Reflection: occurs when a wave changes direction at a boundary between two different media, remaining in the original medium. The law of reflection states that the angle of incidence is equal to the angle of reflection. When waves are reflected, their wavelength and frequency do not change.
- Refraction: occurs when a wave changes direction as it changes speed when it passes from one medium to another. If a wave slows down, it will refract towards the normal. If it speeds up, it will refract away from the normal. Has an effect on the wavelength of a wave, but not its frequency.
- Diffraction: the spreading out of waves as they pass through a gap or travel around an obstacle. Does not affect speed, wavelength or frequency. Diffraction effects become significant when the wavelength is comparable to the gap width.
- Polarisation: confining a wave to a single plane of oscillation such that particles oscillate in one direction only. In longitudinal waves, the oscillations are always parallel to the direction of energy transfer, so they cannot be plane polarised: by definition, the oscillations are already limited to one plane. When transverse waves reflect off a surface, they become partially polarised (horizontally). Some sunglasses contain polarising filters; these only allow light oscillating in one plane to pass through them, reducing the glare reflected off flat surfaces like lakes.
The intensity of a progressive wave is defined as the radiant power passing through a surface per unit area. It has units watts per square metre (Wm-2) and can be calculated with the equation:
I is the intensity of the wave at a surface, O s the radiant power passing through the surface and A is the cross-sectional area of the surface.
This is an inverse square relationship: if distance doubles, the intensity decreases by a factor of 4.
When intensity drops, amplitude decreases. This means a reduced average speed of the oscillating particles: at half the amplitude, particles oscillate at half the speed, so have a quarter of their original kinetic energy. Thus:
Techniques and procedures:
- Demonstrating wave effects with a ripple tank: the speed of water waves changes with water depth, enabling easy investigation of refraction (slows in shallower water).
- Observing polarising effects with microwaves and light: unpolarised electromagnetic waves can be polarised with “polarisers”. These only allow waves with a particular orientation through. This can be demonstrated with polaroid filters (plastic films that contain very long crystals) and metal grilles with microwave transmitters (receiver only picks up signal at specific orientation of grille).