WAVE LESSON 2
Properties of Waves
The Anatomy of a Wave
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, such as created in a rope if
the rope is stretched out horizontally and the end is vibrated back-and-forth in a vertical
direction.
If you froze the shape of the rope in time, then it would look like this diagram.
The dashed line drawn through the center of the diagram represents the equilibrium or
rest position of the string.
Once a disturbance is introduced into the string, the particles of the string begin to vibrate
upwards and downwards.
Vocabulary of a Wave
The crest of a wave = the maximum amount of positive or upwards displacement from
the rest position.
Which points on the diagram represent the crest? A, E and H
The trough of a wave = the maximum amount of negative or downwards displacement
from the rest position.
Which points on the diagram represent the trough? C and J
The amplitude of a wave refers to the maximum amount of displacement of a particle on
the medium from its rest position.
The amplitude is the distance from rest to crest OR rest to trough
The wavelength of a wave is simply the length of one complete wave cycle.
A wave is a repeating pattern.
The length of one repetition (known as a wave cycle) is the wavelength.
The wavelength of a wave can be measured as the distance from a point on a
wave to the corresponding point on the next cycle of the wave, such as from crest
to crest or from trough to trough.
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.
If a snapshot of such a longitudinal wave could be taken then it would look like the
following diagram.
The 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.
At which points are these? A, C and E
The 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.
At which points are these? B, D, and F
A longitudinal wave does not have crest; so how can its wavelength be determined?
The wavelength can always be determined by measuring the distance between any
two corresponding points on adjacent waves such as by measuring the distance
from a compression to the next compression or from a rarefaction to the next
rarefaction.
Frequency and Period of a Wave
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, etc.
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.
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. 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 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.
Frequency refers to how often something happens.
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 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.
A wave is a disturbance which moves along a medium from one end to the other.
If one watches an ocean wave moving along the medium (the ocean water), one
can observe that the crest of the wave is moving from one location to another over
a given interval of time. The crest is observed to cover distance.
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 the crest of an ocean wave moves a distance of 20 meters in 10 seconds, then the speed
of the ocean wave is 2 m/s.
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.
Energy Transport and the Amplitude of a Wave
As mentioned earlier, a wave is an energy transport phenomenon which transports energy
along a medium without transporting matter.
A pulse or a wave is introduced into a slinky when a person holds the first coil and gives
it a back-and-forth motion. This creates a disturbance within the medium; this
disturbance subsequently travels from coil to coil, transporting energy as it moves.
The energy is imparted to the medium by the person as he/she does work upon the
first coil to give it kinetic energy. This energy is transferred from coil to coil until
it arrives at the end of the slinky.
If you were holding the opposite end of the slinky, then you would feel the energy
as it reaches your end.
In fact, a high energy pulse would likely do some rather noticeable work upon
your hand upon reaching the end of the medium; the last coil of the medium
would displace you hand in the same direction of motion of the coil. For the same
reasons, a high energy ocean wave can do considerable damage to the rocks and
piers along the shoreline when it crashes upon it.
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.
As discussed earlier, the amplitude of a wave refers to the maximum amount of
displacement of a particle on the medium from its rest position. The logic underlying the
energy-amplitude relationship is as follows:
If a slinky is stretched out in a horizontal direction and a transverse pulse is
introduced into the slinky, the first coil is given an initial amount of displacement.
The displacement is due to the force applied by the person upon the coil to
displace it a given amount from rest.
The more energy that the person puts into the pulse, the more work which he/she
will do upon the first coil. The more work which is done upon the first coil, the
more displacement which is given to it.
The more displacement which is given to the first coil, the more amplitude which
it will have. So in the end, the amplitude of a transverse pulse is related to the
energy which that pulse transports through the medium.
Putting a lot of energy into a transverse pulse will not effect the wavelength, the
frequency or the speed of the pulse. The energy imparted to a pulse will only
effect the amplitude of that pulse.
Consider two identical slinkies into which a pulse is introduced.
If the same amount of energy is introduced into each slinky, then each pulse will
have the same amplitude.
But what if the slinkies are different? What if one is made of zinc and the other is
made of copper? Will the amplitudes now be the same or different?
If a pulse is introduced into two different slinkies by imparting the same amount
of energy, then the amplitudes of the pulses will not necessarily be the same.
In a situation such as this, the actual amplitude assumed by the pulse is dependent
upon two types of factors: an inertial factor and an elastic factor.
Two different materials have different mass densities. The imparting of energy to
the first coil of a slinky is done by the application of a force to this coil. More
massive slinkies have a greater inertia and thus tend to resist the force; this
increased resistance by the greater mass tends to cause a reduction in the
amplitude of the pulse.
Different materials also have differing degrees of springiness or elasticity. A more
elastic medium will tend to offer less resistance to the force and allow a greater
amplitude pulse to travel through it; being less rigid (and therefore more elastic),
the same force causes a greater amplitude.
The energy transported by a wave is directly proportional to the square of the amplitude
of the wave. This energy-amplitude relationship is sometimes expressed in the following
manner.
This means that a doubling of the amplitude of a wave is indicative of a
quadrupling of the energy transported by the wave. A quadrupling of the
amplitude of a wave is indicative of a _____________increase in the
amount of energy transported by the wave (16-fold).
Reflection
Sometimes a wave encounters the end of a medium and the presence of a
different medium.
For example, a wave introduced by a person into one end of a slinky will travel
through the slinky and eventually reach the end of the slinky and the presence of
the hand of a second person.
One behavior which waves undergo at the end of a medium is reflection.
The wave will reflect or bounce off the person's hand. When a wave undergoes
reflection, it remains within the medium and merely reverses its direction of
travel.
Reflection phenomenon are commonly observed with sound waves. When you let out a
holler within a canyon, you often hear the echo of the holler. The sound wave travels
through the medium (air in this case), reflects off the canyon wall and returns to its origin
(you).
The result is that you hear the echo (the reflected sound wave) of
your holler.
A classic physics problem goes like this:
Noah stands 170 meters away from a steep canyon wall.
He shouts and hears the echo of his voice one second
later. What is the speed of the wave?
In this instance, the sound wave travels 340 meters in 1 second, so the speed of the wave
is 340 m/s. Remember, when there is a reflection, the wave doubles its distance. In other
words, the distance traveled by the sound wave in 1 second is equivalent to the 170
meters down to the canyon wall plus the 170 meters back from the canyon wall.
Variables Affecting Wave Speed
What variables affect the speed at which a wave travels through a medium?
Does the frequency or wavelength of the wave affect its speed?
Does the amplitude of the wave affect its speed?
Or are other variables such as the mass density of the medium or the elasticity of the
medium responsible for affecting the speed of the wave?
Suppose a wave generator is used to produce several waves within a rope of a measurable
tension.
The wavelength, frequency and speed are determined.
Then the frequency of vibration of the generator is changed to investigate the
affect of frequency upon wave speed.
Finally, the tension of the rope is altered to investigate the affect of tension upon
wave speed.
Sample data for the experiment are shown below.
Speed of a 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
16.2
1.00
16.2
5
2.0
20.2
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
25.5
1.00
25.5
1.
In the first five trials, the tension of the rope was held constant and the frequency
was systematically changed. What do you notice?
A change in the frequency of a wave does not affect the speed of the wave.
2.
The last three trials involved the same procedure with a different rope tension.
What do you notice?
The speed of the waves was significantly higher at higher tensions. Waves travel
through tighter ropes at higher speeds.
So while the frequency did not affect the speed of the wave, the tension in the
medium (the rope) did. The speed of the wave is dependent upon the properties
of the medium such as the tension of the rope.
One theme of this unit has been that "a wave is a disturbance moving through a medium."
There are two distinct objects in this phrase - the "wave" and the "medium."
The medium could be water, air, or a slinky. These media are distinguished by
their properties - the material they are made of and the physical properties of that
material such as the density, the temperature, the elasticity, etc. Such physical
properties describe the material itself, not the wave.
On the other hand, waves are distinguished from each other by their properties amplitude, wavelength, frequency, etc. These properties describe the wave, not the
material through which the wave is moving.
The lab activity described above is that wave speed depends upon the medium through
which the wave is moving. Only an alteration in the properties of the medium will
cause a change in the speed.
WAVE LESSON 2 HOMEWORK
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. A to C
b. B to D
c. A to G
d. C to G
4. The wavelength is the distance from crest to crest, trough to trough, or from a point on
one wave cycle to the corresponding point on the next adjacent wave cycle.
A wave is introduced into a thin wire held tight at each end. It has an amplitude of 3.80
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.
5. Frieda the fly flaps its wings back and forth 121 times each second. The period of the
wing flapping is ____ sec.
6. 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
7. 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
d. 1
b. 1/12
e. 60
c. 1/2
8. 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
9. In problem #5, the period of swing is __________.
a. 0.5 second
b. 1 second
c. 2 second
10. A period of 5.0 seconds corresponds to a frequency of ________ Hertz.
a. 0.2
d. 0.05
b. 0.5
e. 0.002
c. 0.02
11. 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 ______.
12. 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
13. The period of the sound wave produced by a 440 Hertz tuning fork is ___________.
14. As the frequency of a wave increases, the period of the wave ___________.
a. decreases
b. increases
c. remains the same
15. Mac and Tosh stand 8 meters apart and demonstrate the motion of a transverse wave
on a snakey. The wave e can be described as having a vertical distance of 32 cm from a
trough to a crest, a frequency of 2.4 Hz, and a horizontal distance of 48 cm from a crest to
the nearest trough. Determine the amplitude, period, and wavelength of such a wave.
16. An ocean wave has an amplitude of 2.5 m. Weather conditions suddenly change such
that the wave has an amplitude of 5.0 m. The amount of energy transported by the wave
is __________.
a. halved
b. doubled
c. quadrupled
d. remains the same
17. Two waves are traveling through a container of an inert gas. Wave A has an
amplitude of .1 cm. Wave B has an amplitude of .2 cm. The energy transported by wave
B must be __________ the energy transported by wave A.
a. one-fourth
b. one-half
c. two times larger than
d. four times larger than
18. A teacher attaches a slinky to the wall and begins introducing pulses with different
amplitudes. Which of the two pulses (A or B) below will travel from the hand to the wall
in the least amount of time? Justify your answer.
19. The teacher then begins introducing pulses with a different wavelength. Which of the
two pulses (C or D) will travel from the hand to the wall in the least amount of time ?
Justify your answer.
20. The time required for the sound waves (v = 340 m/s) to travel from the tuning fork to
point A is ____ .
a. 0.020 second
c. 0.59 second
b. 0.059 second
d. 2.9 second
21. 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. one-ninth
c. the same as
b. one-third
d. three times larger than
22. 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. The camera lens then focuses at that distance.
Now that's a smart camera! In a subsequent life, you might have to be a camera; so try
this problem for practice:
If a sound wave (speed = 340 m/s) returns to the camera 0.150 seconds
after leaving the camera, then how far away is the object?
23. TRUE or FALSE:
Doubling the frequency of a wave source doubles the speed of the waves.
24. While hiking through a canyon, Noah Formula lets out a scream. An echo (reflection
of the scream off a nearby canyon wall) is heard 0.82 seconds after the scream. The speed
of the sound wave in air is 342 m/s. Calculate the distance from Noah to the nearby
canyon wall.
25. 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.
26. The water waves below are traveling along the surface of the ocean at a speed of 2.5
m/s and splashing periodically against Wilbert's perch. Each adjacent crest is 5 meters
apart. The crests splash Wilbert's feet upon reaching his perch. How much time passes
between each successive drenching? Answer and explain using complete sentences.
HOMEWORK KEY
1. A
2. D
3. D
4. 0.0195 s
5. 0.00826 s
6. D
7. A
8. A
9. C
10. A
11. 0.33 s
12. B and C
13. 0.0023 s
14. A
15. Amplitude 16 m, Wavelength 96 m, Period 0.42 s
16. C
17. D
18. At same time
19. At same time
20. B
21. C
22. 26 m
23. F
24. 140 m
25. 2.0 m/s
26. Every 2.0 s
WAVE LESSON 2 HOMEWORK
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 ______.
Answer: A
The wavelength is the distance from crest to crest (or from trough to trough) (or between
any two corresponding points on adjacent waves).
2. The amplitude of the wave in the diagram above is given by letter _____.
Answer: D
The amplitude is the distance from rest to crest or from rest to trough.
3. Indicate the interval which represents one full wavelength.
a. A to C
b. B to D
c. A to G
d. C to G
Answer: D
4. The wavelength is the distance from crest to crest, trough to trough, or from a point on
one wave cycle to the corresponding point on the next adjacent wave cycle.
A wave is introduced into a thin wire held tight at each end. It has an amplitude of 3.80
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.
Answer: 0.0195 sec
Here is an example of a problem with a lot of extraneous information. The period is
simply the reciprocal of the frequency. In this case, the period is 1/(51.2 Hz) which is
0.0195 seconds.
Know your physics concepts to weed through the extra information.
5. Frieda the fly flaps its wings back and forth 121 times each second. The period of the
wing flapping is ____ sec.
Answer: 0.00826 seconds
The quantity 121 times/second is the frequency. The period is the reciprocal of the
frequency.
T=1/(121 Hz) = 0.00826 s
6. 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
Answer: D
Frequency refers to the number of occurrences of a periodic event per time and is
measured in cycles/second. In this case, there are 10 cycles per 2 minutes (also known as
10 cycles per 120 seconds). So the frequency is
f =10 cycles / 120 s = 0.0833 cycles/s
7. 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
d. 1
Answer: A
b. 1/12
e. 60
c. 1/2
Frequency refers to the number of occurrences of a periodic event per time and is
measured in cycles/second. In this case, there is 1 cycle per 60 seconds. So the frequency
is
f = 1 cycle / (60 s) = (1 / 60) Hz
8. 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
Answer: A
Frequency refers to the number of occurrences of a periodic event per time and is
measured in cycles/second. In this case, there is 1 cycle per 2 seconds. So the frequency
is 1 cycles/2 s = 0.5 Hz.
9. In problem #5, the period of swing is __________.
a. 0.5 second
b. 1 second
c. 2 second
Answer: C
Period refers to the time for something to happen. In this case, the period is the time for
one complete swing - given as 2 seconds.
10. A period of 5.0 seconds corresponds to a frequency of ________ Hertz.
a. 0.2
d. 0.05
b. 0.5
e. 0.002
c. 0.02
Answer: A
Frequency is the reciprocal of the period. The period is 5 seconds, so the frequency is
1/(5 s) = 0.20 Hz.
11. 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 ______.
Answer: 0.33 second
Period refers to the time for something to happen and is measured in seconds/cycle. In
this case, there are 11 seconds per 33 vibrational cycles. Thus the period is (11 s) / (33
cycles) = 0.33 seconds.
12. 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
Answer: B and C
We now know that the period is 3.2 seconds and that the frequency is 0.31 Hz.
13. The period of the sound wave produced by a 440 Hertz tuning fork is ___________.
Answer: 0.0023 seconds
GIVEN: f = 440 Hz
Find T
T = 1 / f = 1 / (440 HZ) = 0.00227 s
14. As the frequency of a wave increases, the period of the wave ___________.
a. decreases
b. increases
c. remains the same
Answer: A
Period is the reciprocal of the frequency. So as f increases, 1 / f decreases.
15. Mac and Tosh stand 8 meters apart and demonstrate the motion of a transverse wave
on a snakey. The wave e can be described as having a vertical distance of 32 cm from a
trough to a crest, a frequency of 2.4 Hz, and a horizontal distance of 48 cm from a crest to
the nearest trough. Determine the amplitude, period, and wavelength of such a wave.
Answer: Amplitude 16 m, Wavelength 96 m, Period 0.42 s
Amplitude = 16 cm
(Amplitude is the distance from the rest position to the crest position
which is half the vertical distance from a trough to a crest.)
Wavelength = 96 cm
(Wavelength is the distance from crest to crest, which is twice the
horizontal distance from crest to nearest trough.)
Period = 0.42 s
(The period is the reciprocal of the frequency. T = 1 / f)
16. An ocean wave has an amplitude of 2.5 m. Weather conditions suddenly change such
that the wave has an amplitude of 5.0 m. The amount of energy transported by the wave
is __________.
a. halved
b. doubled
c. quadrupled
d. remains the same
Answer: C (quadrupled)
The energy transported by a wave is directly proportional to the square of the amplitude.
So whatever change occurs in the amplitude, the square of that affect impacts the energy.
This means that a doubling of the amplitude results in a quadrupling of the energy.
Equations are guides to thinking about how a variation in one variable affects another
variable.
17. Two waves are traveling through a container of an inert gas. Wave A has an
amplitude of .1 cm. Wave B has an amplitude of .2 cm. The energy transported by wave
B must be __________ the energy transported by wave A.
a. one-fourth
b. one-half
c. two times larger than
d. four times larger than
Answer: D (four times larger)
The energy transported by a wave is directly proportional to the square of the amplitude.
So whatever change occurs in the amplitude, the square of that affect impacts the energy.
This means that a doubling of the amplitude results in a quadrupling of the energy.
Equations are guides to thinking about how a variation in one variable affects another
variable.
18. A teacher attaches a slinky to the wall and begins introducing pulses with different
amplitudes. Which of the two pulses (A or B) below will travel from the hand to the wall
in the least amount of time? Justify your answer.
Answer: At the same time.
They reach the wall at the same time. Don't be fooled! The amplitude of a wave does
not affect the speed at which the wave travels. Both Wave A and Wave B travel at the
same speed. The speed of a wave is only altered by alterations in the properties of the
medium through which it travels.
19. The teacher then begins introducing pulses with a different wavelength. Which of the
two pulses (C or D) will travel from the hand to the wall in the least amount of time ?
Justify your answer.
Answer: at the same time.
They reach the wall at the same time. Don't be fooled! The wavelength of a wave does
not affect the speed at which the wave travels. Both Wave C and Wave D travel at the
same speed. The speed of a wave is only altered by alterations in the properties of the
medium through which it travels.
20. The time required for the sound waves (v = 340 m/s) to travel from the tuning fork to
point A is ____ .
a. 0.020 second
c. 0.59 second
b. 0.059 second
d. 2.9 second
Answer: B
GIVEN: v = 340 m/s, d = 20 m and f = 1000 Hz
Find time
Use v = d / t and rearrange to t = d / v
Substitute and solve.
21. 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. one-ninth
c. the same as
b. one-third
d. three times larger than
Answer: C
The medium is the same for both of these waves ("the same container of nitrogen gas").
Thus, the speed of the wave will be the same. Alterations in a property of a wave (such as
wavelength) will not affect the speed of the wave. Two different waves travel with the
same speed when present in the same medium.
22. 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. The camera lens then focuses at that distance.
Now that's a smart camera! In a subsequent life, you might have to be a camera; so try
this problem for practice:
If a sound wave (speed = 340 m/s) returns to the camera 0.150 seconds
after leaving the camera, then how far away is the object?
Answer: 26 m
GIVEN: v = 340 m/s, t = 0.150 s (down and back time)
Find d (1-way)
If it takes 0.150 s to travel to the object and back, then it takes 0.075 s to travel the oneway distance to the object. Now solve for time using the equation d = v • t.
d = v • t = (340 m/s) • (0.075 s) = 26 m
23. TRUE or FALSE:
Doubling the frequency of a wave source doubles the speed of the waves.
Answer: FALSE!
The speed of a wave is unaffected by changes in the frequency.
24. While hiking through a canyon, Noah Formula lets out a scream. An echo (reflection
of the scream off a nearby canyon wall) is heard 0.82 seconds after the scream. The speed
of the sound wave in air is 342 m/s. Calculate the distance from Noah to the nearby
canyon wall.
Answer: 140 m
GIVEN: v = 342 m/s, t = 0.82 s (2-way)
Find d (1-way)
If it takes 0.82 s to travel to the canyon wall and back (a down-and-back time), then it
takes 0.41 s to travel the one-way distance to the wall. Now use d = v • t
d = v • t = (342 m/s) • (0.41 s) = 140 m
25. 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.
Answer: 2.0 m/s
GIVEN: d (1-way) =25 m, t (2-way)=25 s
Find v.
If the pool is 25 meters long, then the back-and-forth distance is 50 meters. The wave
covers this distance in 25 seconds. Now use v = d / t.
v = d / t = (50 m) / (25 s) = 2.0 m/s
26. The water waves below are traveling along the surface of the ocean at a speed of 2.5
m/s and splashing periodically against Wilbert's perch. Each adjacent crest is 5 meters
apart. The crests splash Wilbert's feet upon reaching his perch. How much time passes
between each successive drenching? Answer and explain using complete sentences.
Answer: Every 2.0 seconds.
If the wave travels 2.5 meters in one second then it will travel 5.0 meters in 2.0 seconds.
If Wilbert gets drenched every time the wave has traveled 5.0 meters, then he will get
drenched every 2.0 seconds.