Waves

Definitions

Wavelength is the distance between equivalent points on two consecutive waves e.g. peak to peak.
Amplitude is the maximum displacement of a point on the wave from its undisturbed (equilibrium) position.
Frequency is the number of complete waves passing a given point per second (in ).
Time period is the time taken for a complete wave cycle to pass through a point. This is the reciprocal of frequency.
Phase of a wave refers to the stage of the wave cycle. Two waves are in phase when they have phase difference. They are in antiphase when they have phase difference.
Coherence is where waves have the same frequency and a constant phase difference.
Path difference is the difference between the distance travelled by two waves when they meet. A path difference of produces waves meeting in phase, while a path difference of produces waves meeting in antiphase.

Standing waves

Formation of a standing wave:

A progressive wave travels through the medium.
The progressive wave reflects off a boundary e.g. the end of the medium.
The two progressive waves travelling in opposite directions interfere to produce a standing wave pattern.
Where waves meet in phase, constructive interference occurs, causing antinodes of maximum displacement to form.
Where waves meet in antiphase, destructive interference occurs, causing nodes of minimum displacement to form.

When standing waves form in tubes and strings, antinodes always form at open ends, and nodes always form at closed ends (or where a string is held down).

Practical

Use a resonance tube partially submerged in water
Hold a tuning fork over the top and move the tube until resonance occurs.
Measure the length for the first and second resonance frequencies.

Refraction

Refraction occurs waves move between two mediums that have different wave speeds, causing the wave to change speed and bend. If the wave travels faster in the new medium, it bends away from the normal, else if it travels slower, it bends towards the normal.

Refractive index

The refractive index is the ratio of the speed of light in two media. The absolute refractive index is the ratio of speed of light in a vacuum to that of the material.

Snell's law

Huygen's wavelet model

A wave of light is made up of many smaller wavelets. As the wave reaches a boundary at an angle, the wavelets which reach first, slow down first, causing the wave to bend towards the slower wavelets.

Diffraction

Diffraction is the spreading out of waves as they pass through an aperture with a width on the same order of magnitude as their wavelength.

Double slit diffraction

The waves from each slit interfere with each other, producing a pattern of bright and dark fringes.