Wave motion differs in three important ways from the motion of material objects:
(1) Waves obey the principle of superposition. When two waves collide, they simply add
together.
(2) The medium is not transported along with the wave. The motion of any given point in
the medium is a vibration about its equilibrium location, not a steady forward motion.
(3) The velocity of a wave depends on the medium, not on the amount of energy in the
wave. (For some types of waves, notably water waves, the velocity may also depend on
the shape of the wave.)
Sound waves consist of increases and decreases (typically very small ones) in the density of the air. Light
is a wave, but it is a vibration of electric and magnetic fields, not of any physical medium. Light can travel
through a vacuum.
A periodic wave is one that creates a periodic motion in a receiver as it passes it. Such a wave has a welldefined
period and frequency, and it will also have a wavelength, which is the distance in space between
repetitions of the wave pattern. The velocity, frequency, and wavelength of a periodic wave are related by the
equation
v = f λ .
A wave emitted by a moving source will be shifted in wavelength and frequency. The shifted wavelength is
given by the equation
where v is the velocity of the waves and v
_{s} is the velocity of the source, taken to be positive or negative so as
to produce a Doppler-lengthened wavelength if the source is receding and a Doppler-shortened one if it
approaches. A similar shift occurs if the observer is moving, and in general the Doppler shift depends approximately
only on the relative motion of the source and observer if their velocities are both small compared to the
waves' velocity. (This is not just approximately but exactly true for light waves, and this fact forms the basis of
Einstein's Theory of Relativity.) |