The nature of a wave was
discussed in Lesson 1 of this unit. In that lesson, it was
mentioned that a wave is created in a slinky by the periodic
and repeating vibration of the first coil of the slinky.
This vibration creates a disturbance which moves through the
slinky and transports energy from the first coil to the last
coil. A single back-and-forth vibration of the first coil of
a slinky introduces a pulse into the slinky. But the act of
continually vibrating the first coil with a back-and-forth
motion in periodic fashion introduces a wave into the
slinky.

Suppose that a hand holding the first coil
of a slinky is moved back-and-forth two complete cycles in
one second. The rate of the hand's motion would be 2
cycles/second. The first coil, being attached to the hand,
in turn would vibrate at a rate of 2 cycles/second. The
second coil, being attached to the first coil, would vibrate
at a
rate of 2 cycles/second. The third coil, being attached to
the second coil, would vibrate at a rate of 2 cycles/second.
In fact, every coil of the slinky would vibrate at this rate
of 2 cycles/second. This rate of 2 cycles/second is referred
to as the frequency of the wave. The
frequency of a wave
refers to how often the particles of the medium vibrate when
a wave passes through the medium. Frequency is a part of our
common, everyday language. For example, it is not uncommon
to hear a question like "How frequently do you mow
the lawn during the summer months?" Of course the question
is an inquiry about how often the lawn is mowed and
the answer is usually given in the form of "1 time per
week." In mathematical terms, the frequency is the number of
complete vibrational cycles of a medium per a given amount
of time. Given this definition, it is reasonable that the
quantity frequency would have units of cycles/second,
waves/second, vibrations/second, or something/second.
Another unit for frequency is the
Hertz (abbreviated Hz)
where 1 Hz is equivalent to 1 cycle/second. If a coil of
slinky makes 2 vibrational cycles in one second, then the
frequency is 2 Hz. If a coil of slinky makes 3 vibrational
cycles in one second, then the frequency is 3 Hz. And if a
coil makes 8 vibrational cycles in 4 seconds, then the
frequency is 2 Hz (8 cycles/4 s = 2 cycles/s).

The quantity frequency
is often confused with the quantity period.
Period refers to the time which
it takes to do something. When an event occurs repeatedly,
then we say that the event is
periodic and refer to
the time for the event to repeat itself as the period. The
period of a wave is the
time for a particle on a medium to make one complete
vibrational cycle. Period, being a time, is measured in
units of time such as seconds, hours, days or years. The
period of orbit for the Earth around the Sun is
approximately 365 days; it takes 365 days for the Earth to
complete a cycle. The period of a typical class at a high
school might be 55 minutes; every 55 minutes a class cycle
begins (50 minutes for class and 5 minutes for passing time
means that a class begins every 55 minutes). The period for
the minute hand on a clock is 3600 seconds (60 minutes); it
takes the minute hand 3600 seconds to complete one cycle
around the clock. When a physics teacher is regular
with his stools, the period of the stools is 24 hours. That
doesn't mean he spends 24 hours on the stool, it merely
means that it takes 24 hours before he must return to the
stools to repeat the daily cycle. (Of course, this assumes
that a trip to the stools is a periodic event for that
teacher.)

Frequency and period
are distinctly different, yet related, quantities. Frequency
refers to how often something happens. Period refers to the
time it takes something to happen. Frequency is a rate
quantity. Period is a time quantity. Frequency is the
cycles/second. Period is the seconds/cycle. As an example of
the distinction and the relatedness of frequency and period,
consider a woodpecker that drums upon a tree at a periodic
rate. If the woodpecker drums upon a tree 2 times in one
second, then the frequency is 2 Hz. Each drum must endure
for one-half a second, so the period is 0.5 s. If the
woodpecker drums upon a tree 4 times in one second, then the
frequency is 4 Hz; each drum must endure for one-fourth a
second, so the period is 0.25 s. If the woodpecker drums
upon a tree 5 times in one second, then the frequency is 5
Hz; each drum must endure for one-fifth a second, so the
period is 0.2 s. Do you observe the relationship?
Mathematically, the period is the reciprocal of the
frequency and vice versa. In equation form, this is
expressed as follows.

Since the symbol
f is used for frequency
and the symbol T is used
for period, these equations are also expressed as:

The
quantity frequency is also confused with the quantity speed.
The speed of an object
refers to how fast an object is moving and is usually
expressed as the distance traveled per time of travel. For a
wave, the speed is the distance traveled by a given point on
the wave (such as a crest) in a given period of time. So
while wave frequency refers to the number of cycles
occurring per second, wave speed refers to the meters
traveled per second. A wave can vibrate back and forth very
frequently, yet have a small speed; and a wave can vibrate
back and forth with a low frequency, yet have a high speed.
Frequency and speed are distinctly different quantities.
Wave speed will be discussed in more detail later
in this lesson.

Check
Your Understanding

Throughout this unit, internalize the meaning of terms
such as period, frequency, and wavelength. Utilize the
meaning of these terms to answer conceptual questions; avoid
a formula fixation.

1. A wave is introduced into a thin wire held tight at
each end. It has an amplitude of 3.8 cm, a frequency of 51.2
Hz and a distance from a crest to the neighboring trough of
12.8 cm. Determine the period of such a wave.

2. Frieda the fly flaps its wings back and forth 121
times each second. The period of the wing flapping is ____
sec.

3. A tennis coach paces back and forth along the sideline
10 times in 2 minutes. The frequency of her pacing is
________ Hz.

a. 5.0

b. 0.20

c. 0.12

d. 0.083

4. Non-digital clocks (which are becoming more rare) have
a second hand which rotates around in a regular and
repeating fashion. The frequency of rotation of a second
hand on a clock is _______ Hz.

a. 1/60

b. 1/12

c. 1/2

d. 1

e. 60

5. Olive Udadi accompanies her father to the park for an
afternoon of fun. While there, she hops on the swing and
begins a motion characterized by a complete back-and-forth
cycle every 2 seconds. The frequency of swing is
_________.

a. 0.5 Hz

b. 1 Hz

c. 2 Hz

6. In problem #5, the period of swing is __________.

a. 0.5 second

b. 1 second

c. 2 second

7. A period of 5.0 seconds corresponds to a frequency of
________ Hertz.

a. 0.2

b. 0.5

c. 0.02

d. 0.05

e. 0.002

8. A common physics lab involves the study of the
oscillations of a pendulum. If a pendulum makes 33 complete
back-and-forth cycles of vibration in 11 seconds, then its
period is ______.

9. A child in a swing makes one complete back and forth
motion in 3.2 seconds. This statement provides information
about the child's

a. speed

b. frequency

c. period

10. The period of the sound wave produced by a 440 Hertz
tuning fork is ___________.

11. As the frequency of a wave increases, the period of
the wave ___________.