 Lesson
1: The Nature of a Wave
Waves and wavelike
Motion
What is a Wave?
Categories of Waves
Lesson 2: Properties of a
Wave
The Anatomy of a Wave
Frequency and Period
Energy Transport and
Amplitude
The Speed of a Wave
The Wave Equation
Lesson 3: Behavior of
Waves
Boundary Behavior
Reflection, Refraction, and
Diffraction
Interference of Waves
Waves Generated by Moving
Sources
Lesson 4: Standing
Waves
Traveling Waves vs. Standing
Waves
Formation of Standing
Waves
Nodes and Anti-nodes
Harmonics and Patterns
Mathematics of Standing
Waves
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Lesson 2: Properties of
Waves
Frequency and Period of a
Wave
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
medium. 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. 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 Glenbrook South (non-block and non-AP) is 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 has an amplitude of 2 cm and a frequency of
12 Hz, and the distance from a crest to the nearest
trough is measured to be 5 cm. Determine the period of
such a wave.
2. A fly flaps its wings back and forth 150 times each
second. The period of a wing flap is
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a. 150 sec
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b. 2.5 sec
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c. 0.040 sec
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d. 0.0067 sec
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3. A tennis coach paces back and forth along the
sideline 10 times in 2 minutes. The frequency of her
pacing is ________.
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a. 5.0 Hz
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b. 0.20 Hz
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c. 0.12 Hz
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d. 0.083 Hz
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4. The frequency of rotation of a second hand on a
clock is _______.
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a. 1/60 Hz
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b. 1/12 Hz
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c. 1/2 Hz
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d. 1 Hz
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e. 60 Hz
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5. A kid on a playground swing makes a complete
to-and-fro swing each 2 seconds. The frequency of swing
is _________.
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a. 0.5 Hz
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b. 1 Hz
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c. 2 Hz
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6. In problem #5, the period of swing is
__________.
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a. 0.5 second
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b. 1 second
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c. 2 second
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7. A period of 5.0 seconds corresponds to a frequency
of ________ Hertz.
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a. 0.2
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b. 0.5
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c. 0.02
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d. 0.05
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e. 0.002
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8. A pendulum makes 40 vibrations in 20 seconds.
Calculate its period?
9. A child in a swing makes one complete back and
forth motion in 4.0 seconds. This statement provides
information about the child's
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a. speed
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b. frequency
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c. period
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10. The period of a 440 Hertz sound wave is
___________.
11. As the frequency of a wave increases, the period
of the wave ___________.
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a. decreases
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b. increases
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c. remains the same
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