We did not reach this in class but I am leaving it in because it might help some of you in solving the homework
A fascinating phenomenon occurs when two waves with
frequencies close to each other but not the same interfere: The
interference produces a wave-like amplitude modulation with the
difference wave number and frequency.
To be specific we write the sum of the
waves as such:
We see that I have a conventional traveling wave with an
amplitude which behaves like a traveling wave with the
difference spatial and temporal frequency. This type of wave is
exactly what carries your favorite AM station to your radio
receiver. The amplitude of the electromagnetic carrier wave
is modulated by the signal which is to be transmitted.
We have an experimental setup which illustrates the effect.
I have two tuning forks which each produce a traveling
harmonic sound wave. The frequency can be modified
ever so slightly by changing the mass of one of the tuning forks
by attaching a piece of putty. Our ears easily detect the
amplitude modulation as a beat frequency. We detect an amplitude
modulation with a period which I denote, 
. The period
correspond to the time in which the amplitude of the modulated waves goes from
maximum to maximum. Remembering that a maximum in amplitude
means that 
or
this means that
the beat period is related to 
by
The beat frequency
is approximately 
Hz which means that the putty
evidently changes the frequency of the tuning forks by this amount.
The beat phenomenon is useful as a tool for musicians to
tune their instruments.