Physics
Name ______________________________
The Anatomy of a Wave
Period _____
Use the following site to answer the questions below.
http://www.glenbrook.k12.il.us/gbssci/phys/Class/waves/u10l2a.html
HTTP://WWW.GLENBROOK.K12.IL.US/GBSSCI/PHYS/CLASS/WAVES/U10L2A.H
TML
Define a transverse wave .
_____________________________________________________________________
_____________________________________________________________________
The dashed line drawn through the center of the diagram represents the equilibrium or
rest position of the string.
Define the crest of a wave.
_____________________________________________________________________
_____________________________________________________________________
Define the trough of a wave.
_____________________________________________________________________
_____________________________________________________________________
Define the amplitude of a wave.
_____________________________________________________________________
_____________________________________________________________________
Define the wavelength of a wave.
_____________________________________________________________________
_____________________________________________________________________
Define a longitudinal wave.
_____________________________________________________________________
_____________________________________________________________________
Define a compression of a longitudinal wave.
_____________________________________________________________________
_____________________________________________________________________
Define a rarefaction of a longitudinal wave.
_____________________________________________________________________
_____________________________________________________________________
Consider the diagram below in order to answer questions #1-2.
1.
The wavelength of the wave in the diagram above is given by letter _______.
2.
The amplitude of the wave in the diagram above is given by letter ______.
3.
Indicate the interval which represents one full wavelength. ____________
a.
b.
c.
d.
a to c
b to d
a to g
c to g
Click on
Frequency and Period of a Wave
Define the frequency of a wave and give the correct units for measuring frequency.
_____________________________________________________________________
_____________________________________________________________________
Define a periodic event.
_____________________________________________________________________
Define the period of a wave and give the correct units for measuring frequency.
_____________________________________________________________________
_____________________________________________________________________
Mathematically, show how the period frequency are related. 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 speed of an object refers to how fast an object is moving and is usually expressed as
the distance traveled per time of travel.
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.
Show work!
2.
A fly flaps its wings back and forth 150 times each second. The period of a wing
flap is Show work!
a. 150 sec
b. 2.5 sec
c. 0.040 sec
d. 0.0067 sec
3.
A tennis coach paces back and forth along the sideline 10 times in 2 minutes. The
frequency of her pacing is ____ Show work!
a. 5.0 Hz
4.
b. 0.20 Hz
c. 0.12 Hz
d. 0.083 Hz
The frequency of rotation of a second hand on a clock is ______ Show work!
a. 1/60 Hz
b. 1/12 Hz
c. 1/2 Hz
d. 1 Hz
e. 60 Hz
5.
A kid on a playground swing makes a complete to-and-fro swing each 2 seconds.
The frequency of swing is ________ Show work!
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. Show
work!
a. 0.2
8.
b. 0.5
c. 0.02
d. 0.05
e. 0.002
A pendulum makes 40 vibrations in 20 seconds. Calculate its period?
Show work!
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 __________
a. speed
b. frequency
c. period
10.
The period of a 440 Hertz sound wave is ___________. Show work!
11.
As the frequency of a wave increases, the period of the wave ___________.
a. decreases
b. increases
c. remains the same
Click on
Energy Transport and the Amplitude of a Wave
The amount of energy carried by a wave is related to the ____________________ of the
wave. A high energy wave is characterized by high amplitude; a low energy wave is
characterized by low amplitude.
Click on
The Speed of a Wave
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. In the case of a wave, the speed is the distance
traveled by a given point on the wave (such as a crest) in a given interval of time. In
equation form,
_________________________________________
If an echo is heard one second after the holler and reflects off canyon walls which
are a distance of 170 meters away, then what is the speed of the wave?
Show work!
What variables effect the speed at which a wave travels through a medium?
Speed of a Standing Wave Lab - Sample Data
Tension
Frequency
Wavelength
Speed
Trial
(N)
(Hz)
(m)
(m/s)
1
2.0
4.05
4.00
16.2
2
2.0
8.03
2.00
16.1
3
2.0
12.30
1.33
16.4
4
2.0
16.25
1.00
16.3
5
2.0
20.25
0.800
16.2
6
5.0
12.8
2.00
25.6
7
5.0
19.3
1.33
25.7
8
5.0
25.45
1.33
25.5
________________________________________________________________________
1.
Mr. Wegley attaches a slinky to the wall and begins introducing pulses with
different amplitude. Which of the two pulses (A or B) below will reach the wall first?
Justify your answer.
________________________________________________________________________
________________________________________________________________________
2.
Mr. Wegley then begins introducing pulses with a different wavelength. Which of
the two pulses (C or D) will reach the wall first? Justify your answer.
________________________________________________________________________
________________________________________________________________________
3.
The time required for the waves (v = 340 m/s) to travel from the tuning fork to
point P is
a.
b.
c.
d.
0.020 sec.
0.059 sec.
0.59 sec.
2.9 sec.
Show work!
4.
Two waves are traveling through the same container of nitrogen gas. Wave A has
a wavelength of 1.5 m. Wave B has a wavelength of 4.5 m. The speed of wave B must be
________ the speed of wave A.
a.
b.
c.
d.
one-ninth
one-third
the same as
three times larger than
5.
An automatic focus camera is able to focus on objects by use of an ultrasonic
sound wave. The camera sends out sound waves which reflect off distant objects and
return to the camera. A sensor detects the time it takes for the waves to return and then
determines the distance an object is from the camera. If a sound wave (speed = 340 m/s)
returns to the camera 0.150 seconds after leaving the camera, how far away is the object?
Show work!
6.
Doubling the frequency of a wave source doubles the speed of the waves.
a. True
b. False
7.
While hiking through a canyon, Noah Formula lets out a scream. An echo
(reflection of the scream off a nearby canyon wall) is heard 1.6 seconds after the scream.
The speed of the sound wave in air is 345 m/s. Calculate the distance from Noah to the
nearby canyon wall.
Show work!
8.
Mac and Tosh are resting on top of the water near the end of the pool when Mac
creates a surface wave. The wave travels the length of the pool and back in 25 seconds.
The pool is 25 meters long. Determine the speed of the wave.
Show work!
9.
The water waves below are traveling with a speed of 2 m/s and splashing
periodically against the Wilbert's perch. Each adjacent crest is 4 meters apart and splashes
Wilberts feet upon reaching his perch. How much time passes between each successive
drenching? Answer and explain using complete sentences. Show work!
Click on
The Wave Equation
Give an equation relating speed of a wave to the frequency and the wavelength of the
wave.
_____________________________________
The above equation is known as the wave equation. It states the mathematical
relationship between the speed (v) of a wave and its wavelength ( ) and frequency (f).
Using the symbols v, , and f, the equation can be rewritten as
_____________________________________
1.
Two waves on identical strings have frequencies in a ratio of 2 to 1. If their wave
speeds are the same, then how do their wavelengths compare? Explain!
a. 2:1
b. 1:2
c. 4:1
d. 1:4
_______________________________________________________________________
_______________________________________________________________________
2.
A transverse wave is found to have a distance of 4 cm from a trough to a crest (up
and down), a frequency of 12 Hz, and a distance of 5 cm from a crest to the nearest
trough (left right). Determine the amplitude, period, wavelength and speed of such a
wave.
Show work!
3.
Dawn and Aram have stretched a slinky between them and begin experimenting
with waves. As the frequency of the waves is doubled, Explain
a.
b.
c.
d.
the wavelength is halved and the speed remains constant
the wavelength remains constant and the speed is doubled
both the wavelength and the speed are halved.
both the wavelength and the speed remain constant.
_______________________________________________________________________
4.
The annoying sound from a mosquito is produced when it beats its wings at the
average rate of 600 wing beats per second.
a. What is the frequency in Hertz of the sound wave?
Show work!
b. Assuming the sound wave moves with a velocity of 340 m/s, what is the wavelength of
the wave?
Show work!
5.
A marine weather station reports waves along the shore that are 2 meters high, 8
meters long, and reach the station 8 seconds apart. Determine the frequency and the speed
of these waves.
Show work!
6.
Two boats are anchored 4 meters apart. They bob up and down every 3 seconds,
but when one is up the other is down. There are never any wave crests between the boats.
Calculate the speed of the waves.
Show work!
Physics
Name __________Key____________
The Anatomy of a Wave
Period _____
Use the following site to answer the questions below.
http://www.glenbrook.k12.il.us/gbssci/phys/Class/waves/u10l2a.html
HTTP://WWW.GLENBROOK.K12.IL.US/GBSSCI/PHYS/CLASS/WAVES/U10L2A.H
TML
A transverse wave is a wave in which the particles of the medium are displaced in a
direction perpendicular to the direction of energy transport.
The dashed line drawn through the center of the diagram represents the equilibrium or
rest position of the string.
The crest of a wave is the point on the medium which exhibits the maximum amount of
positive or upwards displacement from the rest position.
The trough of a wave is the point on the medium which exhibits the maximum amount of
negative or downwards displacement from the rest position.
The amplitude of a wave refers to the maximum amount of displacement of a particle on
the medium from its rest position.
The wavelength of a wave is simply the length of one complete wave cycle.
A longitudinal wave is a wave in which the particles of the medium are displaced in a
direction parallel to the direction of energy transport.
A region where the coils are pressed together in a small amount of space is known as a
compression. A compression is a point on a medium through which a longitudinal wave
is traveling which has the maximum density.
A region where the coils are spread apart, thus maximizing the distance between coils, is
known as a rarefaction. A rarefaction is a point on a medium through which a
longitudinal wave is traveling which has the minimum density
As discussed above, the wavelength of a wave is the length of one complete cycle of a
wave.
Consider the diagram below in order to answer questions #1-2.
1.
The wavelength of the wave in the diagram above is given by letter (A).
2.
The amplitude of the wave in the diagram above is given by letter (D).
3.
Indicate the interval which represents one full wavelength. (d. c to g)
e.
f.
g.
h.
a to c
b to d
a to g
c to g
Click on
Frequency and Period of a Wave
The frequency of a wave refers to how often the particles of the medium vibrate when a
wave passes through the medium. The unit for frequency is the Hertz (abbreviated Hz)
where 1 Hz is equivalent to 1 cycle/second.
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 vibration cycle. Period, being a time, is
measured in units of time such as seconds, hours, days or years.
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 speed of an object refers to how fast an object is moving and is usually expressed as
the distance traveled per time of travel.
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.
(1/12 of a second or 0.083 s) Show work!
2.
A fly flaps its wings back and forth 150 times each second. The period of a wing
flap is (d) Show work!
a. 150 sec
b. 2.5 sec
c. 0.040 sec
d. 0.0067 sec
3.
A tennis coach paces back and forth along the sideline 10 times in 2 minutes. The
frequency of her pacing is (d). Show work!
a. 5.0 Hz
4.
b. 0.20 Hz
c. 0.12 Hz
d. 0.083 Hz
The frequency of rotation of a second hand on a clock is (a). Show work!
a. 1/60 Hz
b. 1/12 Hz
c. 1/2 Hz
d. 1 Hz
e. 60 Hz
5.
A kid on a playground swing makes a complete to-and-fro swing each 2 seconds.
The frequency of swing is (a). Show work!
a. 0.5 Hz
6.
b. 1 Hz
c. 2 Hz
In problem #5, the period of swing is (c) .
a. 0.5 second
b. 1 second
c. 2 second
7.
A period of 5.0 seconds corresponds to a frequency of _(a)_ Hertz. Show work!
a. 0.2
8.
b. 0.5
c. 0.02
d. 0.05
e. 0.002
A pendulum makes 40 vibrations in 20 seconds. Calculate its period? (0.5 s)
Show work!
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 (b and c)
a. speed
10.
b. frequency
c. period
The period of a 440 Hertz sound wave is ___________. (0.00227 s)
Show work!
11.
As the frequency of a wave increases, the period of the wave ___________. (a.)
a. decreases
Click on
b. increases
c. remains the same
Energy Transport and the Amplitude of a Wave
The amount of energy carried by a wave is related to the amplitude of the wave. A high
energy wave is characterized by a high amplitude; a low energy wave is characterized by
a low amplitude.
Click on
The Speed of a Wave
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. In the case of a wave, the speed is the distance
traveled by a given point on the wave (such as a crest) in a given interval of time. In
equation form,
If an echo is heard one second after the holler and reflects off canyon walls which
are a distance of 170 meters away, then what is the speed of the wave?
Show work!
What variables effect the speed at which a wave travels through a medium? Does the
frequency or wavelength of the wave effect its speed? Does the amplitude of the wave
effect its speed? Or are other variables such as the mass density of the medium or the
elasticity of the medium responsible for effecting the speed of the wave? These questions
were investigated in the Speed of a Standing Wave Lab performed in class. A wave
generator was used to produce several waves within a rope of a measurable tension. The
wavelength, frequency and speed were determined. Then the frequency of vibration of
the generator was systematically changed to investigate the effect of frequency upon
wave speed. Finally, the tension of the rope was altered to investigate the effect of
tension upon wave speed. Sample data for the experiment are shown below.
Speed of a Standing Wave Lab - Sample Data
Tension
Frequency
Wavelength
Speed
Trial
(N)
(Hz)
(m)
(m/s)
1
2.0
4.05
4.00
16.2
2
2.0
8.03
2.00
16.1
3
2.0
12.30
1.33
16.4
4
2.0
16.25
1.00
16.3
5
2.0
20.25
0.800
16.2
6
5.0
12.8
2.00
25.6
7
5.0
19.3
1.33
25.7
8
5.0
25.45
1.33
25.5
Only an alteration in the properties of the medium will cause a change in the speed.
1.
Mr. Wegley attaches a slinky to the wall and begins introducing pulses with
different amplitude. Which of the two pulses (A or B) below will reach the wall first?
Justify your answer.
(Neither, the medium does not change.)
2.
Mr. Wegley then begins introducing pulses with a different wavelength. Which of
the two pulses (C or D) will reach the wall first? Justify your answer.
(Neither, the medium does not change.)
3.
The time required for the waves (v = 340 m/s) to travel from the tuning fork to
point P is
e.
f.
g.
h.
(b.)
0.020 sec.
0.059 sec.
0.59 sec.
2.9 sec.
Show work!
4.
Two waves are traveling through the same container of nitrogen gas. Wave A has
a wavelength of 1.5 m. Wave B has a wavelength of 4.5 m. The speed of wave B must be
________ the speed of wave A.
e.
f.
g.
h.
one-ninth
one-third
the same as
three times larger than
(c.)
5.
An automatic focus camera is able to focus on objects by use of an ultrasonic
sound wave. The camera sends out sound waves which reflect off distant objects and
return to the camera. A sensor detects the time it takes for the waves to return and then
determines the distance an object is from the camera. If a sound wave (speed = 340 m/s)
returns to the camera 0.150 seconds after leaving the camera, how far away is the object?
Show work!
6.
(25.5 m)
Doubling the frequency of a wave source doubles the speed of the waves.
c. True
d. False
(b)
7.
While hiking through a canyon, Noah Formula lets out a scream. An echo
(reflection of the scream off a nearby canyon wall) is heard 1.6 seconds after the scream.
The speed of the sound wave in air is 345 m/s. Calculate the distance from Noah to the
nearby canyon wall.
Show work!
(276 m)
8.
Mac and Tosh are resting on top of the water near the end of the pool when Mac
creates a surface wave. The wave travels the length of the pool and back in 25 seconds.
The pool is 25 meters long. Determine the speed of the wave.
Show work!
(2 m/s)
9.
The water waves below are traveling with a speed of 2 m/s and splashing
periodically against the Wilbert's perch. Each adjacent crest is 4 meters apart and splashes
Wilberts feet upon reaching his perch. How much time passes between each successive
drenching? Answer and explain using complete sentences.
Show work!
Click on
(2 s)
The Wave Equation
Speed = Wavelength * Frequency
The above equation is known as the wave equation. It states the mathematical
relationship between the speed (v) of a wave and its wavelength ( ) and frequency (f).
Using the symbols v, , and f, the equation can be rewritten as
v=f*
1.
Two waves on identical strings have frequencies in a ratio of 2 to 1. If their wave
speeds are the same, then how do their wavelengths compare? (b) Explain!
a. 2:1
b. 1:2
c. 4:1
d. 1:4
2.
A transverse wave is found to have a distance of 4 cm from a trough to a crest (up
and down), a frequency of 12 Hz, and a distance of 5 cm from a crest to the nearest
trough (left right). Determine the amplitude, period, wavelength and speed of such a
wave.
Show work!
(2 cm amplitude, 1/12 second or 0.083 s for the period, 10 cm
for wavelength, and 120 cm/s speed)
3.
Dawn and Aram have stretched a slinky between them and begin experimenting
with waves. As the frequency of the waves is doubled, (a) Explain
e.
f.
g.
h.
the wavelength is halved and the speed remains constant
the wavelength remains constant and the speed is doubled
both the wavelength and the speed are halved.
both the wavelength and the speed remain constant.
4.
The annoying sound from a mosquito is produced when it beats its wings at the
average rate of 600 wing beats per second.
a. What is the frequency in Hertz of the sound wave?
Show work!
(600 Hz)
b. Assuming the sound wave moves with a velocity of 340 m/s, what is the wavelength of
the wave?
Show work!
(0.57 m)
5.
A marine weather station reports waves along the shore that are 2 meters high, 8
meters long, and reach the station 8 seconds apart. Determine the frequency and the speed
of these waves.
Show work!
(1/8 or 0.125 hz frequency, and 1 m/s speed)
6.
Two boats are anchored 4 meters apart. They bob up and down every 3 seconds,
but when one is up the other is down. There are never any wave crests between the boats.
Calculate the speed of the waves.
Show work!
(2.7 m/s)