BASIC WAVE MOTION

Exercise 2.1: Consider the functions

and

where both k and w are larger than 0. Show that the first represents a wave moving to the right and the second a wave moving to the left! Determine the speed of the wave propagation.

An additional angle a in the expression  is called a phase term. Show that a phase term does not affect the wavelength L, the period T, or the propagation direction of the wave.
 
 

Exercise 2.2: Show that if we allow w and k to be negative and arbitrary phase terms to be included, all functions

may be written  for appropriate choices of  the constants
 

Exercise 2.3: The phase velocity for light waves is equal to 300 000 km/s. The periods for FM-band broadcasting range from s to s. What are the wavelengths of such waves?