Assignment – Interference
Reading: Chapter Sections 11 – 12; 12 – 5, 7; 24 – 1, 3 – 7
Objectives/HW
|
|
The
student will be able to: |
HW: |
|
1 |
Define,
apply, and give examples of the following concepts: superposition, constructive and destructive interference,
phase. |
1 – 2 |
|
2 |
Explain
the requirements for the creation of a standing wave. Define and identify nodes and antinodes in
standing wave patterns. Sketch the
harmonics for strings or pipes and calculate wavelength, frequency, or
velocity for any harmonic given sufficient information. |
3 – 16 |
|
3 |
Define
resonance and identify and give examples of this phenomenon. |
17 – 20 |
|
4 |
Explain
what is meant by diffraction and give examples of it. |
21 – 23 |
|
5 |
State
the relation between bright line spacing, source, separation, and wavelength
for an interference pattern and use this relation to solve related problems
involving slits or diffraction gratings. |
24 – 31 |
|
6 |
Use
the path difference concept to find regions of constructive or destructive
interference. |
32 – 34 |
Homework
Problems
1.
Suppose
two sine waves are produced – each with wavelength 10.0 m. One wave has amplitude 7.00 cm and the other
has amplitude 2.00 cm. Determine the
wavelength and amplitude of the superposition of these two waves: (a) if the
two waves are exactly in phase, and (b) if the two waves are exactly out of
phase.
2.
A
radio receiver is prone to a phenomenon known as multipath interference. In this case, the radio signal coming from a
broadcast tower reflects off of various obstacles and takes different (or
multiple) paths to the receiver’s antenna.
(a) Explain how this can result in poor reception. (b) Explain how it could possibly improve
reception.
3.
How
could a standing wave be created with the light coming from a red laser. Would it be possible to see the nodes and
antinodes of such a pattern? Explain.
4.
Explain
what is happening at a node in a standing wave produced in a guitar
string.
5.
An
organ pipe involves standing waves that occur in the air inside it. What would happen to the pitch of the pipe
if the temperature of the air increases?
Explain!
6.
An
organ pipe that is covered at one end produces a certain note. If the cover is removed from the end what
will happen to the pipe’s pitch?
Explain!
7.
A
standing wave is produced in a thin strip of metal at a frequency of 125
Hz. The nodes in the pattern are 5.00
cm apart. For the waves in the metal strip find the following: (a) wavelength, and (b) speed.
8.
A
certain skyscraper is 440 m tall and is found to sway back and forth with a
period of 10.0 seconds. A simple model
of this phenomenon would be to assume the building is like a huge standing wave
where the base of the building is like a node and the top of the building is
like an anitnode. If this is the case
what is the speed of waves traveling up and down the building?
9.
A
string 45.0 cm long is fixed at both ends to a musical instrument. Waves in the string travel at speed 520
m/s. Sketch the standing wave, find the
frequency and wavelength for each of the following: (a) the fundamental, (b) the 2nd harmonic, (c) the 3rd
harmonic.
10.
A
12.0 cm pipe is open at both ends.
Sketch the standing wave, find the frequency and wavelength for each of
the following: (a) the 2nd
harmonic, (b) the 3rd harmonic.
11.
A
violin string is 25.4 cm long and produces a fundamental frequency of 440.0 Hz
(an A). The violinist frets the string
to change the length of the string.
This changes the fundamental.
(a) What is the speed of waves in the string? (b) What change in length is required to produce a frequency of
523 Hz (a C)? (c) At its new length
what wavelength of sound is produced by the violin?
12.
A
0.560 m pipe is closed at one end.
Sketch the standing wave, find the frequency and wavelength for each of
the following: (a) the fundamental, (b)
the next possible harmonic.
13.
A
slide whistle has a length of 27 cm. If
you want to play a note one octave higher (twice the frequency), the whistle
should be how long?
14.
If
you hold a 1.2 m aluminum rod in the center and hit one end with a hammer, it
will oscillate like an open pipe. The
speed of sound in aluminum is 5150 m/s.
What would be the lowest frequency at which the rod will vibrate when it
is hit?
15.
A
flute acts like an open pipe and sounds a note with a 370 Hz pitch. What are the frequencies of the four lowest
pitched harmonics that the flute makes?
16.
A
clarinet sounds the same note as in the previous problem, 370 Hz. It, however, behaves the same as a pipe that
is closed off at one end. What are the
frequencies of the four lowest pitched harmonics that the clarinet makes?
17.
An
opera singer can cause a crystal glass to shatter just by the sound of her
voice. However this only works if the
singer hits a certain note and not other notes.
(a) Explain why the glass shatters at a certain note. (b) Explain why the glass
does not shatter at other notes that are just as loud.
18.
I
drive an old, kind of pathetic, cheap car.
When I accelerate various things will rattle. For example the sun visors might start buzzing when I hit 30 mph. But then when I get to 35 mph the visors
will stop buzzing and the glove box will start rattling. And then when I get to 40 mph the glove box
stops rattling and some mysterious piece of loose metal somewhere hidden deep
behind the dash will start humming. And
so on. Explain what is going on here in
terms of a source of vibration, standing waves, and resonance. (And be happy if your car doesn’t do this!)
19.
A
kid plays around with a 76 cm tube of wrapping paper pretending that it is a
horn or a megaphone. However, in
reality, the tube can actually serve to amplify the sound of the kids
voice. Determine two frequencies at
which the tube will resonate.
20.
An
open vertical tube is filled with water and a tuning fork vibrates over its
mouth. As the water level is lowered in
the tube, resonance is heard when the water level has dropped 17 cm and again
after 51 cm of distance exists from the water to the top of the tube. What is the frequency of the tuning
fork?
21.
Diffraction
is typically more prominent for waves with longer wavelengths. How does this help explain the fact that AM
radio stations can often be received behind a hill or mountain while FM radio
stations cannot?
22.
Suppose
you are listening to some people talk and they are out of sight around the
corner of a building. The sound waves
from their voices are reaching your ears and yet the light waves reflecting off
their bodies are not reaching your eyes.
Explain.
23.
Explain
why diffraction is a problem for telescopes and microscopes.
24.
Light
falls on a pair of slits 0.00190 cm apart.
The slits are 80.0 cm from the screen.
The first-order bright line is 1.90 cm from the central bright
line. What is the wavelength of the
light?
25.
Light
of wavelength 542 nm falls on a double slit.
First order bright bands appear 4.00 cm from the central bright
line. The screen is 1.20 m from the
slits. How far apart are the slits?
26.
A
lecturer is demonstrating interference with sound waves. Two speakers are used, sitting 4.0 m apart
on a stage in front of the room. The
sound frequency is 325 Hz. Students sit
in the front row of seats 4.5 m away from the stage. What is the spacing between the regions of destructive
interference in the front row?
27.
Monochromatic
light of wavelength 455 nm illuminates two slits separated by a distance of
1.79 mm.
Find the angle between the antinodal lines of the first and second-order
images.
28.
An
illuminated grating with 4850 lines/cm gives a second-order image at an angle
of 37.4°. Calculate the wavelength of the light.
29.
A
certain diffraction grating has 2500 lines/cm.
What is the distance between two lines in the grating?
30.
Using
a grating with lines that are 4.00 mm apart, a red line appears
16.5 cm from the central line on a screen.
The screen is 100.0 cm from the grating. What is the wavelength of the red light?
31.
A
spectrometer uses a grating with 12000 lines/cm. Find the angles at which red light, 632 nm,
and blue light, 421 nm, have the first order bright bands.
32.
Two
speakers emit in phase a sound with a frequency of 550 Hz. Up to what maximum distance can the speakers
be separated without destructive interference occurring?
33.
A
radio station uses two antennas and broadcasts at 600 kHz. The antennas broadcast the same signal in
phase. Determine the type of
interference that would occur at the following three homes where radio receivers
are tuned to that station: (a) Home A
is 17.75 km from one tower and 19.25 km from the other. (b) Home B is 5.00 km from one tower and
5.75 km from the other. (c) Home C is
8.70 km from one tower and 8.80 km from the other.
34.
Suppose
you are listening to a stereo system.
You are located 2.50 m away from the left speaker and 1.75 m away from
the right speaker. Assume the speakers
are in phase with one another. (a) At
what frequencies would you experience constructive interference? (b) At what frequencies would you experience
destructive interference?
1.
a.
b.
2.
a.
b.
3.
4.
5.
6.
7.
a. 10.0 cm
b. 12.5 m/s
8. 176 m/s
9.
a. 578 Hz, 0.900 m
b. 1160 Hz, 0.450 m
c. 1730 Hz, 0.300 m
10.
a. 2860 Hz, 0.120 m
b. 4290 Hz, 0.080 m
11.
a. 224 m/s
b. – 4.0 cm
c. 65.6 cm
12.
a. 153 Hz, 2.24 m
b. 459 Hz, 0.747 m
13. 13.5 cm
14. 2100 Hz
15. 370 Hz, 740 Hz, 1110 Hz, 1480 Hz
16. 370 Hz, 1110 Hz, 1850 Hz, 2590 Hz
17.
a.
b.
18.
19. any two multiples of 226 Hz
20. 500 Hz
21.
22.
23.
24. 451 nm
25.
16.3 mm
26. 1.2 m
27. 15.8°
28. 626 nm
29. 4.00 mm
30. 651 nm
31. red:
49.3°; blue: 30.3°
32. 31 cm
33.
a.
b.
c.
34.
a. 457 Hz, 915 Hz, 1370 Hz, . . .
b. 229 Hz, 686 Hz, 1140 Hz, . . .