Summary
For traveling waves, in which the peaks and valleys visibly move along the
length of a rope, the displacement y of each point depends also on x and t.
In the point of view in which x varies, and t does not, we “freeze time” and
see the points at which the wave crosses the horizontal, the maximum vertical
displacement above the horizontal (crests), and the maximum vertical
displacement below the horizontal (the troughs).
In the point of view in which t varies, and x does not, you designate one
position x along the rope to watch as time varies. The point on the rope will
oscillate vertically and the wave propagates, or travels, horizontally.
The five most important characteristics of a traveling wave are its wavelength,
amplitude, period, frequency, and speed.
The equation to determine wave speed on a stretched string is v =.
Superposition of waves is the concept that when two or more waves meet, the
displacement at any point of the medium is equal to the sum of the
displacements due to the individual waves. When waves meet and overlap
(interfere) the displacement of the string is equal to the sum of the individual
displacements.
Constructive interference creates a combined wave of greater magnitude than
either individual wave. Destructive interference results in a combined
waveform that has a displacement of a smaller magnitude than either
individual wave.
Standing waves are seen when two oppositely traveling waves that have the
same frequency, amplitude, and wavelength oscillate vertically and remain
fixed. The crests and troughs do not appear to travel down the length of the
string.
Sound waves are produced by the vibration of an object. The vibrations cause
pressure variations in the conducting medium: Compressions are where the
molecules are bunched together (the pressure is above normal). Rarefactions
