What is the wavelength of this

wave?

Ȝ = 0.60 m

15.6 - Period and frequency

Period: Amount of time for a particle in a wave

to complete a cycle of motion.

Frequency: Number of wave cycles per second.

The definitions of period and frequency may look familiar from your study of simple

harmonic motion.

The period of a wave equals the amount of time required for a particle of the medium to

move through a complete cycle of motion.

At the top of this section are four time-lapse “snapshots” of a transverse wave moving

through a string. The particle marked in red moves vertically up and down. The amount

of time it takes to rise to a peak, fall to a trough and return to its initial position is the

period. Because the period is an interval of time, its unit is the second.

As the particle oscillates up and down through a full cycle of motion, the wave travels to

the right a distance of one wavelength. Frequency is the number of full cycles of motion

per second. Frequency (cycles/second) equals the reciprocal of the period

(seconds/cycle). The unit for frequency is the hertz (Hz), equal to one cycle per second.

In Concept 2, we show a graph related to the transverse wave, which is not a depiction of the wave itself, but a graph of the motion of a particle

over time. The scale of its horizontal axis is time, not position. The particle oscillates up and down in SHM, like the red particle used in the

wave illustration at the top of this section. This graph could be generated in a fashion akin to the graphs you saw in the chapter on simple

harmonic motion, where we rolled graph paper below a mass that had a “pen” attached to it. In this case, we would roll the paper under the red

circle to record its location over time.

The period of the wave itself can be measured as the difference in time between two equivalent points (such as adjacent peaks) on the graph.

The frequency of the wave is the reciprocal of the period. The particle in Concept 2 has a period of 2.0 seconds, so its frequency is 0.5 cycles

per second, and that is the frequency of the associated wave.

The example problem asks you to determine the frequency and period of another transverse wave. The transverse motion of a single particle in

this wave is graphed with time on the horizontal axis.

PeriodT of a wave

Time a particle takes to complete a

cycle of motion

Period and frequency

Period: time to complete a cycle

Frequency: number of cycles per

second

·Units: seconds (s)

·Reciprocal of period

·Units: hertz (Hz)

(^298) Copyright 2007 Kinetic Books Co. Chapter 15