A ball being bounced is a good example of a repeating system. In physics, repeating systems are described by special terms. When the ball repeatedly returns to a previous position and velocity, each repeat is called a cycle. A system that repeats is also known as an oscillating system.
The duration in time for one cycle is called a period τ. Period is often calculated by timing many cycles. Divide the time by the number of cycles to get the period. The units for period are seconds per cycle.
The mathematical reciprocal, dividing the number of cycles by the time, is called the frequency f. The units for frequency are cycles per second. Cycles per second has a special name: Hertz. One Hertz is one cycle per second.
If the distance the ball is dribbled is small (short), the then frequency f is high.
If the distance the ball is dribbled is large (long), the then frequency f is low.
Instructional note: Demonstrate using a stop watch, timing ten to twenty cycles (dribbles). Calculate both the period and frequency.
In the diagram above:
Amplitude and wavelength are measures of space. Waves have a time component as well. The time component of a wave is the frequency.
When time and space combine linearily, the result may be a velocity. Waves have a velocity. The velocity v for a wave is calculated by multiplying the wavelength λ by the frequency f.
Velocity of a water wave in shallow water where g is the acceleration of gravity and d is the depth of the water.
Instructional notes: Using a meter stick and stopwatch demonstrate the relationships between frequency f and wavelength λ. Diagram the wavelength and amplitude on the board. Calculate the velocity v of a wave on a chain. Cover the connections to sound waves, water waves.