Assignment – Waves
Objectives/HW
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The
student will be able to: |
HW: |
|
1 |
Define,
apply, and give examples of the following concepts: wave, pulse vs. continuous wave, source,
medium, longitudinal wave, transverse wave, surface wave, crest, trough,
compression, rarefaction. |
1 – 3 |
|
2 |
Define,
apply and give examples of the following wave parameters: speed, wavelength, frequency, period, and
amplitude and state the influence of source and medium on each wave
parameter. |
4 – 11 |
|
3 |
State
the wave type and medium of EMR and sound and identify the speed of
each. State and recognize the
different types of electromagnetic radiation (EMR): radio, microwave,
infrared, light, ultraviolet, x-ray, gamma.
State the relation between speed, wavelength, and frequency for a
wave, and use this relation to solve related problems. |
12 – 27 |
|
4 |
Create
the two wave graphs given a wave’s parameters and/or determine a wave’s
parameters given the two graphs. |
28 – 31 |
Homework
Problems
1. What are the differences and
similarities among transverse, longitudinal, and surface waves?
2. Suppose an astronaut
standing on the Moon rings a metal bell.
Would that astronaut hear the bell?
How about any other astronauts in the vicinity?
Explain.
3. Suppose an earthquake occurs
in California. The resulting seismic
waves are recorded by special equipment (seismographs) in laboratories all over
the world (not just in California). (a)
What is the source of seismic waves? (b)
What is the medium of seismic waves? (c)
Scientists use measurements of seismic waves to map out and determine the
properties of the Earth’s interior – explain how the Earth’s interior might
affect the seismic waves.
4. What is the difference
between wave frequency and wave velocity?
5. Suppose you produce a
transverse wave by shaking one end of a spring back and forth. How does the frequency of your hand moving
back and forth compare with the frequency of the wave that travels down the
spring?
6. A physics teacher creates
waves that travel along a spring that is stretched across the room. (a) Without changing the length of the
spring, can the teacher change the speed of the waves in the spring? Explain.
(b) Can the teacher change the frequency of the waves in the
spring? Explain. (c) Can the teacher change the wavelength of
the waves in the spring? Explain.
7. When a sound wave goes from
water to air its speed and wavelength change, but its frequency does not. Explain why the frequency is constant.
8. Suppose a wave enters a
medium where its speed is decreased as a result. Explain what will happen to this wave’s
wavelength and frequency.
9. In the last century, people
put their ears to a railroad track to get an early warning of an approaching
train. Why did this work?
10. Suppose you hear the sound
made by a certain tuning fork. And then
you hear the sound made by the same tuning fork but the room’s temperature is
higher than before. How do the speed, wavelength, and frequency of this sound
at higher temperature compare to the speed, wavelength, and frequency at lower
temperature?
11. What happens to the
wavelength of a radio signal as its frequency is increased?
12. An ocean wave has a length
of 10.0 m. A wave passes a fixed
location every 2.0 s. What is the speed
of the wave?
13. Water waves in a shallow
dish have troughs that are 6.0 cm apart.
At one point in the dish the water is observed to undergo 4.8
oscillations up and down every second.
(a) What is the speed of these waves?
(b) What is the period of these waves?
14. Water waves in a lake travel
4.4 m in 1.8 s. The period of the
oscillation is 1.2 s.
(a) What is the speed of these waves?
(b) What is the wavelength?
15. The frequency of yellow
light is 5.0 ´ 1014 Hz. Find the wavelength.
16. A group of swimmers is
resting in the sun on a raft. They
estimate that 3.0 m separates a trough and an adjacent crest of surface waves
on the lake (these must be physics students!).
They count 14 crests that pass by the raft in 20.0 s. How fast are the waves moving?
17. Compare and contrast
mechanical waves and electromagnetic waves – noting similarities and
differences.
18. (a) AM radio signals are broadcast
at frequencies between 550 kHz and 1600 kHz.
What is the range of wavelengths for these signals? (b) Repeat for FM, which ranges from 88 MHz
to 108 MHz.
19. A sonar signal of frequency
1.00 MHz has a wavelength of 1.50 mm in water.
(a) What is the speed of the signal in water? (b) What is its period in water? (c) What is its wavelength in air?
20. A sound wave of wavelength
70.0 cm and velocity 330 m/s is produced by a tuning fork that vibrates
for 0.500 s. (a) What is the frequency
of the tuning fork? (b) How many
complete waves are emitted from the tuning fork in this time interval? (c) For this group of waves, how far is the
front wave from the back wave?
21. The speed of sound in water
is 1498 m/s. A sonar signal is sent from
a ship at a point just below the water surface and 1.80 s later the reflected
signal is detected. How deep is the
ocean beneath the ship?
22. A bolt of lightning occurs
5.00 km away from you. This bolt emits
light with wavelength 450 nm and sound with frequency 35.0 Hz. (a) What is the frequency of the light? (b) What is the wavelength of the sound? (c) What amount of time elapses between
seeing and hearing the bolt?
23. The velocity of the
transverse waves produced by an earthquake is 8.9 km/s, while that of the
longitudinal waves is 5.1 km/s. A
seismograph records the arrival of the transverse waves 73 s before that of the
longitudinal waves. How far away is the
earthquake that produced the two types of waves?
24. The velocity of a wave on a
string depends on how hard the string is stretched, and on the mass per unit
length of the string. If T is the
tension in the string, and m is the mass/unit length,
then the speed, v, is related by the following equation: v2 = T/m. A
piece of string 5.30 m long has a mass of 15.0 grams. What must the tension of the string be to
make the wavelength of a 125 Hz wave equal 120.0 cm?
25. The time needed for a water
wave to change from the equilibrium level to the crest is 0.18 s. (a) What fraction of a cycle is this? (b) What is the period of the wave?
(c) What is the frequency of the wave?
26. A sound wave with period
80.0 ms goes from air to water. The speed of sound in water is 1498 m/s. (a) Find the change in the wavelength. (b) Find the frequency of sound heard by an
underwater listener.
27. A marine radar operating at a
frequency of 9400 MHz emits groups of radio waves 80.0 ns in duration. (The time needed for reflections of these
groups to return indicates the distance of the target.) Radio waves are EMR. (a) Find the wavelength of these waves. (b) Find the length of each wave group, which
is indicative of the precision with which the radar can measure distance. (c) Find the number of complete cycles in the
group.
28. A certain sound wave is
described by the following two graphs:
y(x) = 2.00 sin(72.0 x) + sin(120 x)
y(t) = 2.00 sin(27000 t) + sin(45000 t)
x = distance in meters, t = time in seconds, y =
disturbance level in Pascals
Set your graphing calculator to Degree mode and graph the above equations one
at a time. You will need to adjust your
viewing window for each graph. (a) Make
a sketch of the distance graph showing the wave’s shape. (b) Make a sketch of the time graph
showing the wave’s shape. (These do not
have to be graphed on graph paper.)
29. Use the tracing features of
your calculator and any necessary calculations to determine the following
parameters for the sound wave of the previous problem:
(a) Wavelength, (b) Period, (c) Frequency, (d) Amplitude, (e)
Speed.
30. On graph paper construct the
two graphs necessary to completely describe a sinusoidal sound wave with
frequency 5.00 kHz and amplitude 1.20 Pa.
You may wish to graph these first on your calculator and then transfer
some points to graph paper. (a) Make a
time graph and on the graph label the period and amplitude.
(b) Make a distance graph and label wavelength and amplitude.
31. (a) through
(d) – Turn in the 4 pairs of graphs that were done (or started) in class. For each pair of graphs you should indicate A, l, T, f, and v. For A, l, and T, you should label how you
found the values on the graphs. For f
and v, you should show the calculations you made to find them.
1.
2.
3.a.
b.
c.
4.
5.
6. a.
b.
c.
7.
8.
9.
10.
11.
12.
5.0 m/s
13.
a. 0.29 m/s
b. 0.21 s
14.
a. 2.4 m/s
b. 2.9 m
15.
600 nm
16.
4.2 m/s
17.
18.
a. 190 m – 550 m
b. 2.8 m – 3.4 m
19. a. 1.50 km/s
b. 1.00 ms
c. 0.343 mm
20.
a. 471 Hz
b. 236 waves
c. 165 m
21.
1350 m
22.
a. 6.67 ´ 1014 Hz
b. 9.80 m
c. 14.6 s
23.
870 km
24.
63.7 N
25.
a. ¼
b. 0.72 s
c. 1.4 Hz
26.
a. 9.24 cm
b. 12.5 kHz
27.
a. 3.19 cm
b. 24.0 m
c. 752
28.
a. sketch
b. sketch
29.
a. 15.0 m
b. 0.0400 s
c. 25.0 Hz
d. 2.77 m
e. 375 m/s
30.
a. graph
b. graph
31.
a. graph with A, l, T, f, v
b. graph with A,
l, T, f, v
c. graph with A,
l, T, f, v
d. graph with A,
l, T, f, v