Questions and answers on Wave
CONCEPTUAL QUESTIONS ON WAVE
Traveling Waves
1. Give one example of a transverse wave and one
example of a longitudinal wave, being careful to note the
relative directions of the disturbance and wave propagation
in each.
position
2. A sinusoidal transverse wave has a wavelength of 2.80
m. It takes 0.10 s for a portion of the string at
x to move from a maximum position of y = 0.03 m to
the equilibrium position y = 0. What are the period,
frequency, and wave speed of the wave?
3. What is the difference between propagation speed and
the frequency of a mechanical wave? Does ane or both
affect wavelength? If so, how?
4. Consider a stretched spring, such as a slinky. The
stretched spring can support longitudinal waves and
transverse waves. How can you produce transverse waves
on the spring? How can you produce longitudinal waves on
the spring?
5. Consider a wave produced on a stretched spring by
holding one end and shaking it up and down. Does the
wavelength depend on the distance you move your hand up
and down?
6. A sinusoidal, transverse wave is produced on a
stretched spring, having a period T. Each section of the
spring moves perpendicular to the direction of propagation
of the wave, in simple harmonic motion with an amplitude
A. Does each section oscillate with the same period as
the wave or a different period? If the amplitude of the
transverse wave were doubled but the period stays the
same, would your answer be the same?
7. An electromagnetic wave, such as light, does not
require a medium. Can you think of an example that would
support this claim?
16.2 Mathematics of Waves
8. If you were to shake the end of a taut spring up and
down 10 times a second, what would be the frequency and
the period of the sinusoidal wave produced on the spring?
9. If you shake the end of a stretched spring up and down
with a frequency f. you can produce a sinusoidal, transverse
wave propagating down the spring. Does the wave number
depend on the frequency you are shaking the spring?
10. Does the vertical speed of a segment of a horizontal
taut string through which a sinusoidal, transverse wave is
propagating depend on the wave speed of the transverse
wave?
11. In this section, we have considered waves that move at
a constant wave speed. Does the medium accelerate?
12. If you drop a pebble in a pond you may notice that
several concentric ripples are produced, not just a single
ripple. Why do you think that is?
16.3 Wave Speed on a Stretched String
13. If the tension in a string were increased by a factor of
four, by what factor would the wave speed of a wave on the
string increase?
14. Does a sound wave move faster in seawater or fresh
water, if both the sea water and fresh water are at the same
temperature and the sound wave moves near the surface?
( pₘ≈ 100 kg/m³, pₛ ≈ 1030 kg/m³,
Bₘ= 2.15 X 10⁹ pa
Bₛ = 2.34 X 10⁹pa
15. Guitars have strings of different linear mass density. If
the lowest density string and the highest density string are
under the same tension, which string would support waves
with
16. Shown below are three waves that were sent down a
string at different times. The tension in the string remains
constant. (a) Rank the waves from the smallest wavelength
to the largest wavelength. (b) Rank the waves from the
lowest frequency to the highest frequency.
Y₂
∞ +
17. Electrical power lines connected by two utility poles
are sometimes heard to hum when driven into oscillation
by the wind. The speed of the waves on the power lines
depend on the tension. What provides the tension in the
power lines?
Chapter 16 | Waves
student holding each end. Each student gives the end a flip
sending one wavelength of a sinusoidal wave down the
spring in opposite directions. When the waves meet in the
middle, what does the wave look like?
18. Two strings, one with a low mass density and one
with a high linear density are spliced together. The higher
density end is tied to a lab post and a student holds the
free end of the low-mass density string. The student gives
the string a flip and sends a pulse down the strings. If the
tension is the same in both strings, does the pulse travel at
the same wave velocity in both strings? If not, where does
it travel faster, in the low density string or the high density
string?
16.4 Energy and Power of a Wave
19. Consider a string with under tension with a constant
linear mass density. A sinusoidal wave with an angular
frequency and amplitude produced by some external
driving force. If the frequency of the driving force is
decreased to half of the original frequency, how is the time
averaged power of the wave affected? If the amplitude of
the driving force is decreased by half, how is the time
averaged power affected? Explain your answer.
18. Two strings, one with a low mass density and one
with a high linear density are spliced together. The higher
density end is tied to a lab post and a student holds the
free end of the low-mass density string. The student gives
the string a flip and sends a pulse down the strings. If the
tension is the same in both strings, does the pulse travel at
the same wave velocity in both strings? If not, where does
it travel faster, in the low density string or the high density
string?
16.4 Energy and Power of a Wave
19. Consider a string with under tension with a constant
linear mass density. A sinusoidal wave with an angular
frequency and amplitude produced by some external
driving force. If the frequency of the driving force is
decreased to half of the original frequency, how is the time
averaged power of the wave affected? If the amplitude of
the driving force is decreased by half, how is time
averaged power affected? Explain your answer.
20. Circular water waves decrease in amplitude as they
move away from where a rock is dropped. Explain why.
21. In a transverse wave on a string, the motion of the
string is perpendicular to the motion of the wave. If this is
so, how is possible to move energy along the length of the
string?
22. The energy from the sun warms the portion of the earth
facing the sun during the daylight hours. Why are the North
and South Poles cold while the equator is quite warm?
23. The intensity of a spherical waves decreases as the
wave moves away from the source. If the intensity of the
wave at the source is le, how far from the source will the
intensity decrease by a factor of nine?
16.5 Interference of Waves
24. An incident sinusoidal wave is sent along a string that
is fixed to the wall with a wave speed of v. The wave
reflects off the end of the string. Describe the reflected
wave.
25. A string of a length of 2.00 m with a linear mass
density of = 0.006 kg/ m is attached to the end of a
2.00-m-long string with a linear mass density of
μ = 0.012 kg/ m. The free end of the higher-density string
is fixed the wall, and a student holds the free end of
the low-density string, keeping the tension constant in both
strings. The student sends a pulse down the string. Describe
what happens at the interface between the two strings.
26. A long, tight spring is held by two students, one
student holding each end. Each student gives the end a flip
sending one wavelength of a sinusoidal wave down the
spring in opposite directions. When the waves meet in the
middle, what does the wave look like?
27. Many of the topics discussed in this chapter are useful
beyond the topics of mechanical waves. It is hard to
conceive of a mechanical wave with sharp corners, but
you could encounter such a wave form in your digital
electronics class, as shown below. This could be a signal
from a device known as an analog to digital converter,
in which a continuous voltage signal is converted into a
discrete signal or a digital recording of sound. What is the
result of the superposition of the two signals?
28. A string of a constant linear mass density is held taut
by two students, each holding one end. The tension in the
string constant. The students each send waves down the
string by wiggling the string. (a) Is it possible for the waves
to have different wave speeds? (b) Is it possible for the
waves to have different frequencies? (c) Is it possible for
the waves to have different wavelengths?
16.6 Standing Waves and Resonance
29. A truck manufacturer finds that a strut in the engine is
failing prematurely. A sound engineer determines that the
strut resonates at the frequency of the engine and suspects
that this could be the problem. What are two possible
characteristics of the strut can be modified to correct the
problem?
30. Why do roofs of gymnasiums and churches seem to
fail more than family homes when an earthquake occurs?
ChapTh16 | Waves
31. Wine glasses can be set into resonance by moistening
your finger and rubbing it around the rim of the glass.
Why?
32. Air conditioning units are sometimes placed on the
roof of homes in the city. Occasionally, the air conditioners.
cause an undesirable hum throughout the upper floors of
the homes. Why does this happen? What can be done to
reduce the hum?
. Consider a standing wave modeled as
y (x, t) = 4.00 cm sin (3 m-¹x) cos (4 s-¹1) Is there a
node or an antinode at x = 0,00 m? W
standing wave model
y (x, t) = 4.00 cm sin (3 mx + cos
HINT
a node or an antinode at the x = 0.00 m
PROBLEMS
to the right of a person, whose ears are approximately 18
16.1 Traveling Waves cm apart, and the speed of sound generated is 340 m/ s. How
34. Storms in the South Pacific can create waves that long is the interval between when the sound arrives at the
travel all the way to the California coast, 12,000 km away. right ear and the sound arrives at the left ear? (b) Assume
How long does it take them to travel this distance if they the same person was scuba diving and a low-frequency
travel at 15.0 m/ s? sound source was to the right of the scuba diver. How long
is the interval between when the sound arrives at the right
ear and the sound arrives at the left ear, if the speed of
35. Waves on a swimming pool propagate at 0.75 m/ s. You
sound in water is 1500 m/ s? (c) What is significant about
splash the water at one end of the pool and observe the
the time interval of the two situations?
wave go to the opposite end, reflect, and return in 30.00 s.
How far away is the other end of the pool?
43. (a) Seismographs measure the arrival times of
earthquakes with a precision of 0.100 s. To get the distance
36. Wind gusts create ripples on the ocean that have a
to epicenter of the quake, geologists compare the arrival
wavelength of 5.00 cm and propagate at 2.00 m/ s. What is
their frequency? times of S- and P-waves, which travel at different speeds. If
S- and P-waves travel at 4.00 and 7.20 km/ s, respectively.
in the region considered, how precisely can the distance to
37. How many times a minute does a boat bob up and the source of the earthquake be determined? (b) Seismic
down on ocean waves that have a wavelength of 40.0 m and waves from underground detonations of nuclear bombs can
a propagation speed of 5.00 m/ s? be used to locate the test site and detect violations of test
bans. Discuss whether your answer to (a) implies a serious
38. Scouts at a camp shake the rope bridge they have limit to such detection. (Note also that the uncertainty is
just crossed and observe the wave crests to be 8.00 m greater if there is an uncertainty in the propagation speeds
apart. If they shake the bridge twice per second, what is the of the S- and P-waves.)
propagation speed of the waves?
44. A Girl Scout is taking a 10.00-km hike to earn a merit
39. What is the wavelength of the waves you create in a badge. While on the hike, she sees a cliff some distance
swimming pool if you splash your hand at a rate of 2.00 Hz away. She wishes to estimate the time required to walk
and the waves propagate at a wave speed of 0.800 m/ s? to the cliff. She knows that the speed of sound is
approximately 343 meters per second. She yells and finds
40. What is the wavelength of an earthquake that shakes that the echo returns after approximately 2.00 seconds. If
you with a frequency of 10.0 Hz and gets to another city she can hike 1.00 km in 10 minutes, how long would it take
84.0 km away in 12.0 s? her to reach the cliff?
41. Radio waves transmitted through empty space at the 45. A quality assurance engineer at a frying pan company
speed of light (v = c = 3.00 x 10³ m/ s) by the Voyager is asked to qualify a new line of nonstick-coated frying
pans. The coating needs to be 1.00 mm thick. One method
spacecraft have a wavelength of 0.120 m. What is their to test the thickness is for the engineer to pick a percentage
frequency? of the pans manufactured, strip off the coating, and measure
the thickness using a micrometer. This method is a
42. Your ear is capable of differentiating sounds that arrive destructive testing method. Instead, the engineer decides
at each ear just 0.34 ms apart, which is useful in that every frying pan will be tested using a nondestructive
determining where low frequency sound is originating method. An ultrasonic transducer is used that produces
from. (a) Suppose a low-frequency sound source is placed sound waves with a frequency of f = 25 kHz. The sound
838
Chapter 16 | Waves
waves are sent through the coating and are reflected by the frequency, (d) wave speed, (e) phase shift, (f) wavelength,
interface between the coating and the metal pan, and the and (g) period of the wave.
time is recorded. The wavelength of the ultrasonic waves in
the coating is 0.076 m. What should be the time recorded if
52. A surface ocean wave has an amplitude of 0.60 m and
the coating is the correct thickness (1.00 mm)?
the distance from trough to trough is 8.00 m. It moves at a
constant wave speed of 1.50 m/ s propagating in the positive
x-direction. At t = 0, the water displacement at x = 0
16.2 Mathematics of Waves
is zero, and vy is positive. (a) Assuming the wave can be
46. A pulse can be described as a single wave disturbance
modeled as a sine wave, write a wave function to model
that moves through a medium. Consider a pulse that is
defined at time t = 0.00 s by the equation the wave. (b) Use a spreadsheet to plot the wave function at
times t = 0.00s and 1 = 2.00 s on the same graph. Verify
y (x) = -6.00 m³
+2.00 m² centered around x = 0.00 m. The that the wave moves 3.00 m in those 2.00 s.
pulse moves with a velocity of v = 3.00 m/ s in the 53. A wave is modeled by the wave function
positive x-direction. (a) What is the amplitude of the pulse?
y (x, t) = (0.30 m) sin 14.50 36 (-18.00) What are
(b) What is the equation of the pulse as a function of
position and time? (c) Where is the pulse centered at time the amplitude, wavelength, wave
1 = 5.00 s? speed, period, and
cy of the wave?
47. A transverse wave on a string is modeled with the 54. A transverse wave on a string is d
wave function wave
y (x, t) = (0.20 cm) sin (2.00m-¹x-3.00s¹1 +) y (x, 1) = (0.50 cm) sin (1.57 m ~ ¹ x-6. HINT
What is the height of the string with respect to the What is the wave velocity of the wave?
equilibrium position at a position x = 4.00 m and a time magnitude of the maximum velocity
= 10.00 s? perpendicular to the direction of the motion?
55. A swimmer in the ocean observes one day that the
Consider the wave function ocean surface waves are periodic and resemble a sine wave.
Comments
Post a Comment