In this equation, A is the amplitude, f is the frequency, and T is the period of the
oscillation. It is useful to think of each of these quantities in terms of a graph plotting the
mass’s displacement over time.
The graph shows us an object moving back and forth withina distance of 1 m from its
equilibrium position. It reaches its equilibrium position of x = 0 at t = 0, t = 2, and t = 4.
Note that one cycle is completed not at t = 2 but at t = 4. Though the object is at the same
position, x = 0 , at t = 2 as it was at t = 0, it is moving in the opposite direction. At the
beginning of a new cycle, both the position and the velocity must be identical to the
position and velocity at the beginning of the previous cycle.
Wave Motion
Because both masses suspended on a spring and waves at the beach exhibit periodic
motion, we can use much of the same vocabulary and mathematical tools to describe
both. However, there is a significant difference: waves are extended in space, while a
mass on a spring just oscillates back and forth in one place.
The Basics
A familiar and concrete example of wave motion is the “wave” spectators create at
sporting events by standing up and sitting down at appropriate intervals. Each person
stands up just as that person’s neighbor stands up, transmitting a form of energy all the
way around the stadium. There are two things worth noting about how this works:
- Waves are transmitted through a medium: The energy and the “wave” are
both created by the successive action of people standing up and down. If there
were no people in the stadium, no wave could exist and no energy could be
transmitted. We call the people at the stadium, the water at the beach, the air
molecules transmitting sound, etc., the medium through which these waves are
transmitted. - The medium itself is not propagated: For the “wave” to work, each person
in the stadium only needs to stand up and sit back down. The “wave” travels
around the stadium, but the people do not.