Figure 9.1: Wave motion at a fixed timet. Ais the wave amplitude,ıis the phase constant, is the
wavelength, and D2= is the wave number.
This looks similar to the equation for simple harmonic motion, only it involvesbothpositionxand timet.
Hereyis the displacement of the wave at positionxand timet,Ais the wave amplitude,!is the angular
frequency of the wave, andıis the phase constant that is determined from the initial conditions. The variable
is called thewave number, and is defined as
D
2
; (9.2)
where , called thewavelengthof the wave, is the distance between successive wave crests.^2 Fig. 9.1 shows
a “snapshot” of a harmonic wave at an instant in time, withA,ı, and illustrated. As time increases, you
would see this wave move to the right. (This analysis applies equally to transverse and longitudinal waves.)
9.2 Wave Speed
The speed of a wave may be thought of as the speed of a single wave crest as it propagates through the
medium. Since the wave moves by one wavelength in a time equal to the periodT, the wave speed is
(^2) Some physicists define the wave number as1=.