Section 15.12 Due: 10:00am on Tuesday, August 11, 2015 You will receive no credit for items you complete after the assignment is due. Grading Policy Wave and Particle Velocity Vector Drawing A long string is stretched and its left end is oscillated upward and downward. Two points on the string are labeled A and B. Part A Points A and B are indicated on the string. Orient the two vectors, and , to correctly represent the direction of the wave velocity at points A and B. Rotate the given vectors to indicate the direction of the wave velocity at the indicated points. Hint 1. Distinguishing between wave velocity and particle velocity A wave is a collective disturbance that, typically, travels through some medium, in this case along a string. The velocity of the individual particles of the medium are quite distinct from the velocity of the wave as it passes through the medium. In fact, in a transverse wave such as a wave on a string, the wave velocity and particle velocities are perpendicular. Hint 2. Wave velocity A wave on a stretched string travels away from the source of the wave along the length of the string. ANSWER:
Transcript
Section 15.12Due: 10:00am on Tuesday, August 11, 2015
You will receive no credit for items you complete after the assignment is due. Grading Policy
Wave and Particle Velocity Vector Drawing
A long string is stretched and its left end is oscillated upward and downward. Two pointson the string are labeled A and B.
Part A
Points A and B are indicated on the string. Orient the two vectors, and , tocorrectly represent the direction of the wave velocity at points A and B.
Rotate the given vectors to indicate the direction of the wave velocity at theindicated points.
Hint 1. Distinguishing between wave velocity and particle velocity
A wave is a collective disturbance that, typically, travels through somemedium, in this case along a string. The velocity of the individual particles ofthe medium are quite distinct from the velocity of the wave as it passesthrough the medium. In fact, in a transverse wave such as a wave on a string,the wave velocity and particle velocities are perpendicular.
Hint 2. Wave velocity
A wave on a stretched string travels away from the source of the wave alongthe length of the string.
ANSWER:
v A v B
Correct
Part B
At the instant shown, orient the given vectors and to correctly represent thedirection of the velocity of points A and B.
At each of the points A and B, rotate the given vector to indicate the directionof the velocity.
Hint 1. Distinguishing between wave velocity and particle velocity
A wave is a collective disturbance that, typically, travels through somemedium, in this case along a string. The velocity of the individual particles ofthe medium are quite distinct from the velocity of the wave as it passesthrough the medium. In fact, in a transverse wave such as a wave on a string,
v A v B
the wave velocity and particle velocities are perpendicular.
Hint 2. Determining velocity from a snapshot
The diagram represents the position of a small portion of the string at aspecific instant of time: a snapshot of the string at this time. Based on only asnapshot, you cannot determine the velocity of an object, such as a point onthe string. However, you also know that the left end of the string is the sourceof the wave disturbance. From this information you can deduce what is aboutto happen to point A’s position, and from this change in position deduce thedirection of point A’s velocity (and similarly for point B).
Hint 3. Find the change in point A’s position
Based on the location of the source of the wave (the left end of the string), willthe wave crest to the immediate left of point A soon raise or lower point A’sposition?
ANSWER:
Hint 4. Find the change in point B’s position
Based on the location of the source of the wave (the left end of the string), willthe wave trough to the immediate left of point B soon raise or lower point B’sposition?
ANSWER:
ANSWER:
raise
lower
raise
lower
Correct
Properties of Ocean Waves
A fisherman notices that his boat is moving up and down periodically without anyhorizontal motion, owing to waves on the surface of the water. It takes a time of 2.90 forthe boat to travel from its highest point to its lowest, a total distance of 0.670 . Thefisherman sees that the wave crests are spaced a horizontal distance of 6.40 apart.
Part A
How fast are the waves traveling?
Express the speed in meters per second using three significant figures.
smm
v
Hint 1. How to approach the problem
Calculate the period of the ocean waves, using the fisherman's observations.Then, use the period and wavelength to calculate the speed of the waves.
Hint 2. Calculate the period of the waves
Calculate the period of the ocean waves.
Express your answer in seconds using three significant figures.
Hint 1. Definition of period
The period of a wave is the time it takes for one full wavelength to passa particular point. This is also the time it takes to go from one crest tothe next, or from one trough to the next.
ANSWER:
Hint 3. Equation for the speed of a wave
The speed of a wave is given by , where is the frequency of thewaves and = 6.40 is the wavelength. The frequency is simply thereciprocal of the period, or .
ANSWER:
Correct
Part B
What is the amplitude of each wave?
T
= 5.80 T s
v = fλ fλ m
f = 1/T
= 1.10 v m/s
A
Express your answer in meters using three significant figures.
Hint 1. Definition of amplitude
The amplitude of a wave is the vertical distance from the top of the crest to theneutral position, halfway between the crest and trough. Equivalently, theamplitude is the vertical distance from the bottom of the trough to the neutralposition.
ANSWER:
Correct
The fisherman does not simply move up and down as the waves pass by. In fact,the motion of the fisherman will be roughly circular with both upward and forwardcomponents (with respect to the direction of the wave) as the wave rises anddownward and backward components as the wave falls. The water thatcomprises the ocean wave itself moves in this same way. Thus, an ocean waveis not a purely transverse wave; it also has a longitudinal component.
Exercise 15.4
Ultrasound is the name given to frequencies above the human range of hearing, which isabout 20000 . Waves above this frequency can be used to penetrate the body and toproduce images by reflecting from surfaces. In a typical ultrasound scan, the waves travelwith a speed of 1500 . For a good detailed image, the wavelength should be no morethan 1.0 .
Part A
What frequency is required?
ANSWER:
= 0.335 A m
Hz
m/smm
= 1.50×106 f Hz
Correct
Exercise 15.5
Part A
Audible wavelengths. The range of audible frequencies is from about 20.0 to2.00×104 . What is range of the wavelengths of audible sound in air?
ANSWER:
Correct
Part B
Visible light. The range of visible light extends from 400 to 700 . What is therange of visible frequencies of light?
ANSWER:
Correct
Part C
Brain surgery. Surgeons can remove brain tumors by using a cavitron ultrasonicsurgical aspirator, which produces sound waves of frequency 23.0 . What is thewavelength of these waves in air?
ANSWER:
HzHz
= 1.72×10−2,17.2 ,λmin λmax m
nm nm
= 4.29×1014,7.50×1014 ,fmin fmax Hz
kHz
Correct
Part D
Sound in the body. What would be the wavelength of the sound in part C in bodilyfluids in which the speed of sound is 1480 , but the frequency is unchanged?
ANSWER:
Correct
Exercise 15.6
A fisherman notices that his boat is moving up and down periodically, owing to waves onthe surface of the water. It takes 2.90 for the boat to travel from its highest point to itslowest, a total distance of 0.670 . The fisherman sees that the wave crests are spaced7.60 apart.
Part A
How fast are the waves traveling?
ANSWER:
Correct
Part B
= 1.50 λs cm
m/s
= 6.43 λs cm
sm
m
= 1.31 v m/s
What is the amplitude of each wave?
ANSWER:
Correct
Part C
If the total vertical distance traveled by the boat were 0.400 , but the other dataremained the same, how fast are the waves traveling ?
ANSWER:
Correct
Part D
If the total vertical distance traveled by the boat were 0.400 , but the other dataremained the same, what is the amplitude of each wave?
ANSWER:
Correct
Exercise 15.1
The speed of sound in air at 20 is 344 .
= 0.335 A m
m
= 1.31 v′ m/s
m
= 0.200 A′ m
C∘ m/s
Part A
What is the wavelength of a sound wave with a frequency of 784 , correspondingto the note on a piano?
ANSWER:
Correct
Part B
How many milliseconds does each vibration take?
ANSWER:
Correct
Part C
What is the wavelength of a sound wave one octave higher than the note in part A?
ANSWER:
Correct
Exercise 15.2
Provided the amplitude is sufficiently great, the human ear can respond to longitudinalwaves over a range of frequencies from about 20.0 to about 20.0 .
HzG5
= 0.439 λ m
= 1.28 T ms
= 0.219 λ m
Hz kHz
Part A
If you were to mark the beginning of each complete wave pattern with a red dot forthe longwavelength sound, how far apart would the red dots be?
ANSWER:
Correct
Part B
If you were to mark the beginning of each complete wave pattern with a blue dot forthe shortwavelength sound, how far apart would the blue dots be?
ANSWER:
Correct
Part C
In reality would adjacent red dots be far enough apart for you to easily measure theirseparation with a meterstick?
ANSWER:
Correct
Part D
= 17.2 λ m
= 1.72 λ cm
Yes
No
In reality would adjacent blue dots be far enough apart for you to easily measure theirseparation with a meterstick?
ANSWER:
Correct
Part E
Suppose you repeated part A in water, where sound travels at 1480 . How farapart would the red dots be ?
ANSWER:
Correct
Part F
Suppose you repeated part A in water, where sound travels at 1480 . How farapart would the blue dots be ?
ANSWER:
Correct
Part G
Could you readily measure their separation with a meterstick?
Yes
No
m/s
= 74.0 λ m
m/s
= 7.40 λ cm
ANSWER:
Correct
Exercise 15.3
On December 26, 2004, a great earthquake occurred off the coast of Sumatra andtriggered immense waves (tsunami) that killed some 200000 people. Satellites observingthese waves from space measured 800 from one wave crest to the next and a periodbetween waves of 1.0 hour.
Part A
What was the speed of these waves in ?
Express your answer using two significant figures.
ANSWER:
Correct
Part B
What was the speed of these waves in ?
Express your answer using two significant figures.
ANSWER:
Yes
No
km
m/s
= 220 v m/s
km/h
= 800 v km/h
Correct
Part C
How does your answer help you understand why the waves caused suchdevastation?
ANSWER:
Submitted, grade pending
Score Summary:Your score on this assignment is 99.9%.You received 5.99 out of a possible total of 6 points.
3646 Character(s) remaining
we cannot judge these waves like an earthquake. The wave comes at such a high speed and with such transferred energy that it causes surprising devastation
