The speed of a wave equals its frequency times its wavelength.
A displacement/time graph shows the position of one particle in the medium as the wave passes.
A displacement/distance graph shows the position of each particle along the length of the medium.
For a longitudinal wave, a compression occurs when particles are closer than normal and the pressure is higher than normal.
The particles in a compression move in the same direction as the wave.
The particle at the centre of the compression has zero displacement and is moving in the forward direction at the same speed as the wave.
For a longitudinal wave, a rarefaction occurs when particles are further apart than normal and the pressure is lower than normal.
The particles in a rarefaction move in the opposite direction to the wave.
The particle at the centre of the rarefaction has zero displacement and is moving in the reverse direction at the same speed as the wave.
The particles in a compression and rarefaction have small displacements. The pressure is large or smaller than normal because the particles on opposite sides of the compression/rarefaction have opposite displacements.
The particle where the pressure is normal, has a maximum displacement.
Waves in two dimensions
The direction of propagation is at 90 degrees to the wavefront.
The angle of incidence or reflection is the angle between the direction of propogation and the normal.
The angle of incidence or reflection is the same as the angle between the wavefront and the barrier/boundary.
2.
Circular waves that reflect from a straight barrier seem to come from a point an equal distance behind the barrier.
Circular waves generated from the focus of a parabolic barrier, reflect as straight wavefronts.
Refraction of waves.
When waves move into a medium where they travel slower, the direction of propagation refracts towards the normal.
When refraction occurs, the speed and wavelength change but the frequency remains constant.
If the frequency of waves is increased, the amount of refraction decreases slightly - less deviation.
Sound travels faster in water than in air.
Sound refracts away from the normal when it passes from air into water.
The warmer the air, the faster sound travels.
Sound refracts away from the normal when it moves into higher temperature air.
Diffraction
Diffraction is the change in direction of waves when they move past an obstacle or through an opening.
Diffraction is strong when the wavelength is equal to or greater than the size of the obstacle or opening.
Red light has a longer wavelength than violet light and diffracts more than violet light.
Interference
Constructive interference occurs when crests overlap crests and troughs overlap troughs.
Destructive interference occurs when a crest overlaps a trough.
Constructive interference occurs along an antinodal line.
Destructive interference occurs along a nodal line.
For antinodal lines, the path difference from the sources is equal to a whole number multiple of the wavelength.
For nodal lines, the path difference is equal to a half multiple of the wavelength.
Standing Waves
Standing waves are the vibrations on the spot formed by waves moving through each other from opposite directions, with the same frequency and similar amplitude.
The nodes in a standing wave pattern are separated by half the wavelength of the waves moving through each other.
A node exists at a fixed end and an antinode exists at a free end.
In an air column, an antinode is at an open end and a node is at a closed end.
Antinodes at open ends are a quarter of the tube’s diameter past the end of the tube.
In an air column, the air has zero displacement at nodes.
In an air column, the displacement of the air fluctuates between two extremes at the antinodes.
In an air column the displacement of the air is small near nodes and large near antinodes.
In an air column, air pressure fluctuates between two extremes at displacement nodes. There is normal pressure at displacement antinodes.
Resonance occurs when a string/air column is stimulated by a vibration with the same frequency as one of its standing wave modes of vibration.
When resonance occurs, the amplitude of the standing wave is very large.
3.
Loudness and Intensity
Intensity in W/m2 measures the energy of the sound passing through an area of 1 m2 each second.
The intensity of sound that can just be heard is 10-12 W/m2.
Intensity is inversely proportional to the square of the distance. At twice the distance the intensity is one quarter as much.
Unit of Loudness is the Bel. A sound that can just be heard is 0 Bel
10 deciBel equals 1 Bel
Loudness in Bel equals log to the base 10 of the intensity divided by 10-12.
When loudness changes new loudness minus old loudness equals log to the base 10 of new intensity divided by old intensity.
Different frequencies at the same intensity are not heard to be the same loudness by the ear.
The ear is most sensitive when frequency is about 5000 Hz.
Two sounds have the same subjective loudness when they are heard by the ear to be equally loud.
