Physics - OAK PARK USD
Physics 7: Waves Name __________________________
A. Wave Motion (11-7 to 11-8, 11-12 to 11-13)
1. general
a. oscillation (energy) spreads out without carrying matter
b. mechanical wave: individual particles move a short distance, transmit their energy to the next particle, and then return to their original position
c. pulses are generated by a single “bump”, which is not repeated
d. periodic wave is generated by an oscillating source
e. characteristics of a periodic wave
[pic]
1. amplitude A (m): maximum oscillation distance from midpoint
2. wavelength λ (m): distance between any two successive identical points of the wave
3. frequency f (Hz or s-1): the number of waves that pass a point per unit time
4. period T = 1/f (s): time for one wave to pass
5. velocity, vw = λ/T = λf (m/s)
2. types of waves
[pic]
a. transverse wave (a)
1. forms in solids only (guitar string)
2. disturbance Ε wave →
3. light waves (next section)
b. longitudinal wave (b)
1. forms in all states (sound)
2. disturbance Δ wave →
3. sound
a. requires a medium
b. speed of sound (in air) depends on air density
1. ↓density = ↑velocity
2. ↑humidity, ↑elevation, ↑temperature = ↓density
c. pitch is related to frequency of sound
1. human ear: 20 Hz to 20,000 Hz
2. piano range: 27.5 Hz to 4186 Hz
d. loudness, β, is measured in decibels (dB)
|dB |0 dB |60 dB |120 dB |160 dB |
|example |threshold of |normal |rock concert |ruptures |
| |hearing |conversation |(damage) |eardrum |
|loudness |20 |26 |212 |216 |
|power |100 |106 |1012 |1016 |
e. decrease of 6 dB for each doubling of distance
|distance |10 m |20 m |40 m |80 m |
|loudness |100 dB |94 dB |88 dB |82 dB |
f. high frequencies sound louder (ear is most sensitive between 2000 Hz and 4000 Hz)
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
4. Interference
a. amplitudes combine when two waves meet (superposition principle)
|constructive interference |destructive interference |
|[pic] | |
b. similar frequency produce beats: fbeat = |fB – fA|
[pic]
c. same frequency = standing wave
1. maximum displacement (constructive interference) is “antinode”
2. minimum displacement (destructive interference) is “node”
3. vibrating string (transverse wave)
a. velocity: vw = [Ft/(m/L)]½
b. harmonics (first, second, etc.)
1. all possible standing waves where nodes form at both ends
2. number of harmonic (n) = # of loops
3. λn = 2L/n and fn = nf1
λ1 = 2L/1
λ2 = 2L/2
λ3 = 2L/3
d. resonance: vibrating a structure at its natural frequency will cause amplitude magnification
5. Doppler effect
a. when source(vs) and/or observer(vo) are moving with respect to each other, the perceived frequency changes
b. frequency heard, f', compared to frequency generated, f
1. f’ = f(vw ± vo)/(vw ± vs)
2. f' > f when approaching (+ vo and/or – vs)
3. f' < f when receding (– vo and/or + vs)
c. approximation formula Δf/f ≈ v/vw
1. f’ = f + Δf when approaching
2. f’ = f – Δf when receding
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
B. Light (23-2, 23-4, 23-6, 24-2, 24-4, 24-10)
1. general properties
a. speed in a vacuum: c = 3 x 108 m/s
b. no medium is needed
c. transverse wave
d. polarization
e. Doppler shift alters frequency (red shift for receding source, blue shift for approaching source)
2. reflection
a. law of reflection θi = θr
1. angles measured from perpendicular (normal)
2. "r" for reflection, "R" for refraction
b. phase shift occurs when reflecting surface has greater n (index of refraction)
phase shift no
phase
shift
3. refraction
a. light slows when entering a transparent medium
1. atom-atom interactions
2. vn = c/n = 3 x 108/n
3. v = fλ and fn = f1 ∴ λn = λ1/n
b. rays that enter at an angle from normal
1. bend toward normal if ni < nR
2. bend away from normal if ni > nR
[pic]
c. Snell's law: n1sinθ1 = n2sinθ2
d. dispersion
1. n increases with frequency (violet > red)
2. color separation by a prism
[pic]
3. when light travels from air to glass; violet light bends toward normal more than red
4. when light travels from glass to air; violet light bends away from normal more than red
e. total reflection
1. light in glass can be trapped because the refraction angle ≥ 90o (total reflection)
2. only when ni > nR
3. critical angle θc (when θR = 90o):
sinθc = (ni/nR)
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
C. Lenses and Mirrors (23-3, 23-5, 23-7 to 23-8)
1. parallel light rays refract toward (converge) or away from (diverge) a focus F by a parabolic lens
a. distance from lens to F = focal length f
b. depends on nlens/nmedium ∴ lenses work differently under water (less refraction)
2. parallel light rays reflect off of a parabolic mirror
radius of curvature r, where f = ½r
CB bisector ∴ angles equal
isosceles Δ CBF ∴ CF = FB
BF ≈ AF ∴ CF ≈ AF
∴ AF ≈ ½AC or f = ½r
3. shape
a. convex—center is thicker than the edges
1. lens is converging in function
2. mirror is diverging in function
b. concave—center is thinner than the edges
1. lens is diverging in function
2. mirror is converging in function
4. ray tracings
a. parallel rays go toward/away from focus
mirror diverging lens
F F
mirror converging lens
b. rays through center are straight
lens mirror
F F
mirror lens
c. image forms where the two rays intersect
5. Lens/mirror equation: 1/do + 1/±di = 1/±f
a. + f for converging lens or mirror
– f for diverging lens or mirror
b. do = object distance, use + for single optic system
c. di = image distance
1. +, image is real—visible on screen
2. –, image is virtual—visible through lens/mirror
d. ho = object height, use + for upright object
e. hi = image height
1. +, image is upright
2. –, image is upside down (inverted)
f. magnification, M = hi/ho = -di/do
1. > |1|, image is larger than object
2. < |1|, image is smaller than object
3. generalizations
a. real image: inverted, form on opposite side as object for lens; same side for mirror
b. virtual image: upright, form on same side as object for lens, opposite side for mirror
c. converging lens or mirror image
1. do > 2f: real and small -1 < M < 0
2. do = 2f: real and same size M = -1
3. 2f > do > f: real and larger M < -1
4. do = f: no image
5. f > do > 0: virtual and larger M > 1
6. |M| increases as do approaches f
d. diverging lens or mirror image
1. all images are virtual and smaller
2. M increases as object approaches lens/mirror
g. small or partially covered lens reduces amount of light (brightness of image) but not size or nature
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
D. Interference (24-3, 24-5 to 24-8
1. two or more openings (slits)
a. waves of synchronized, monochromatic light traveling from different openings to a common point interfere with each other
[pic]
b. light and dark bands (fringes) on a screen
1. center antinode = 0 order bright
2. adjacent nodes = 0 order dark
3. next antinode/node = 1st order, etc
4. m = order #
c. light intensity decreases as m increases
d. angular deflection (θ) from center to band
1. tanθ = x/L
2. x = distance from center to band
3. L = distance between slits and screen
e. path length difference
1. path difference Δ = mλ, then constructive interference—bright band
2. path difference Δ = (m + ½)λ, then destructive interference—dark band
f. angular deflection vs. order
1. Constructive: sinθC = mλ/d
2. Destructive: sinθD = (m + ½)λ/d
3. d = distance between slits
g. multiple slits (grating)
1. more pronounced effect
2. d = grating space = length(m)/lines
(i.e. 500 lines/mm: d = 1E-3 m/500 = 2E-6 m)
3. atomic spectra produced by a grating
a. transitions between energy levels generate multiple wavelengths
b. constructive interference at different locations x on screen
2. one opening—W ≈ 2λL/d
spot light d width of light spot: W
L
3. partial reflection
a. interference occurs when light partially reflects off of a thin film or air space at both boundaries
incident light n1 nf n2
film
interference
T
b. path difference = 2(T) + phase shift
1. when nfilm (nf) is middle value: phase shift = 0
2. when nf is largest or smallest: phase shift = ½λ
3. constructive interference when total path difference = even-half wavelengths (2/2, 4/2, ...)
4. destructive interference when total path difference = odd-half wavelengths (1/2, 3/2, ...)
c. minimum thickness of a film, T (λf = λ1/nf)
|Interference |nf is middle value |nf is extreme value |
|Bright |T = ½λf |T = ¼λf |
|Dark |T = ¼λf |T = ½λf |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
Experiments
1. Reflection and Refraction Lab
a. Reflection: Place a plane mirror with its back along the line XY below. Stick a pin through point P from the back side of the paper. Point the ray-box so that the ray passes over R1, reflects off of the mirror and shines on the pin. Make a mark on the paper where the ray strikes the mirror. Repeat with R2 and R3. Extend the marks that you made to the line XY. Draw a line from R1 to the mark on the line XY and extend it to the top of the template. Draw a second line from P to the same mark on line XY so that you make a "V" at the XY line. Repeat with R2 and R3. Draw a perpendicular line from where the two lines intersect (this is the normal). Make a mark, P', in the middle of the intersections of the lines from R1, R2 and R3 on the opposite side of the mirror.
X Y
mirror
P• R1• R2• R3•
| |R1 |R2 |R3 |
|Angle between R and Normal θi | | | |
|Angle between P and Normal θr | | | |
|% Δ = 100|θi – θr|/½(θi + θr) | | | |
b. Index of Refraction: Place the semi-circle lens on the template below. Make sure the lens is aligned correctly by shining the ray-box along the 0o incident angle, which must refract at 0o. Move the ray-box to θ1 and mark where the light exits the lens. Repeat with θ2 and θ3. Remove the lens. Draw lines from each mark to the origin.
refracted angle 0o
place the half-circle lens here with flat side along this line
Collect the following data and calculate n for
the three values of θi and the average n.
| |θ1 |θ2 |θ3 |
|Incident angle (θi) | | | |
|refracted angle (θR) | | | |
|n = sinθi/sinθR | | | |
|Average n | |
Incident angle 0o θ1 θ2 θ3
2. Ray Tracing Lab
a. Lens: Place the pin in the acetate strip through the center of the lens (this represents the ray that passes straight through the lens). Rotate the strip so that the center line passes over each arrow head (1-6) that represent objects at different locations with respect to the focus F. Mark and number the location where the center line ray intersects with the pre-drawn parallel ray line. This is the location of the image. Draw an arrow with the head touching the pre-drawn line to represent the images 1-6.
(1) Converging lens
1 2 3 4 5 6
2F F F 2F
Describe how the image changes from 1 to 6.
(2) Diverging lens
1 2 3 4 5 6
2F F F 2F
Describe how the image changes from 1 to 6.
b. Mirror: Place the pin in the acetate strip through the center of the mirror (this represents the reflected ray at the center of the mirror). Rotate the strip so that the center line passes over each dashed arrow head (1-6) that represent the reflection of the object. Mark and number the location where the center line ray intersects with the pre-drawn parallel ray line. This is the location of the image. Draw an arrow with the head touching the pre-drawn line to represent the images 1-6.
(1) Converging mirror
1 2 3 4 5 6
2F F F 2F
Describe how the image changes from 1 to 6.
(2) Diverging mirror
1 2 3 4 5 6
2F F F 2F
Describe how the image changes from 1 to 6.
3. Lenses and Mirrors Lab
a. Testing f = ½r for a converging Mirror: Shine the rays from the ray-box at the converging mirror. Make sure the ray-box is aligned correctly by shining the center ray along the major axis and having it reflect straight back. Mark the intersection of the outside rays from the ray-box with the mirror. Also mark where the two reflected rays intersect the major axis; this is the focal point F. Measure the distance from the mirror to the intersection, which is the focal length f.
Exchange the 3-slit plate with the 1-slit plate. Shine the single ray at the mirror at one of the outside marks so that it reflects on itself. Mark where the ray crosses the major axis. Repeat with the other outside mark. Measure the distance from the mirror to the intersection of the two rays; this is the radius of curvature r.
|f (cm) |2f (cm) |r (cm) |% Δ between 2f and r |
| | | | |
b. Nature of converging and diverging lenses: Light the candle. Hold C-1 at arms length from your eyes. Have your lab partner slowly move the candle from a few centimeters from the lens to 50 cm from the lens. Describe how the image of the candle flame changes as the candle is moved away. Repeat with C-2. Compare the change in image for C-1 and C-2.
|Lens |Description of image as candle is moved away. |
|C-1 | |
|C-2 | |
|Comparison between C-1 and C-2 |
| |
Repeat the procedure from (b) with lenses D-1 and D-2.
|Lens |Description of image as candle is moved away. |
|D-1 | |
|D-2 | |
|Comparison between D-1 and D-2 |
| |
c. Determining f for converging lenses (method 1): Insert the C-1 lens in the lens holder and place it on the 50 cm line of the meter stick. Place the screen on the 80 cm line. Point the 0 cm side of the meter stick at a distant object. Move the screen toward the lens until a sharp, inverted, image forms on the screen. Measure the distance between the lens and screen, which is the focal length f. Repeat with the C-2 lens.
|Lens |Position |
| |Screen (S) |Lens (L) |f = S - L |
|C-1: f (cm) | |50 cm | |
|C-2: f (cm) | |50 cm | |
d. Determining f for converging lenses (method 2): Place the candle, lens and screen at the positions listed in the table below. Slowly move the screen toward the lens until a sharp, inverted image of the candle forms on the screen.
(1) Record the final location of the screen.
|Lens |Position |
| |Candle |Lens |Screen |
| |(C) |(L) | |
| | | |initial |final (S) |
|C-1 |10 cm |60 cm |95 cm | |
| |10 cm |50 cm |95 cm | |
|C-2 |10 cm |60 cm |95 cm | |
| |10 cm |50 cm |95 cm | |
(2) Calculate the following from the experiment data.
|variable |di |do |f |fav |
|formula |di = S – L |do = L – C |1/f = 1/do + |fav = Σf/2 |
| | | |1/di | |
|Lens|C-1 | | | | |
| | | | | | |
| |C-2 | | | | |
| | | | | | |
(3) Calculate the percent difference between the f from the two techniques (c and d).
|C-1 |C-2 |
| | |
4. Hydrogen Spectrum Lab
a. Determine the distance d between lines on the gratings.
|300 lines/mm | |
|600 lines/mm | |
b. Observe the hydrogen spectrum through the diffraction gratings and measure the distance x from the light source to the color band.
|Diffraction |300 lines/mm |600 lines/mm |
|Grating | | |
|x |Aqua |Red |Aqua |Red |
| | | | | |
c. Calculate the following from the data.
| |Formula |Calculation |
| |300 lines/mm Aqua |
|θ |tanθ = x/L | |
|λ |λ = dsinθ | |
| |300 lines/mm Red |
|θ |tanθ = x/L | |
|λ |λ = dsinθ | |
| |600 lines/mm Aqua |
|θ |tanθ = x/L | |
|λ |λ = dsinθ | |
| |600 lines/mm Red |
|θ |tanθ = x/L | |
|λ |λ = dsinθ | |
d. Calculate the average value for λ for the 300 lines/mm and 600 lines/mm diffraction gratings.
|Aqua | |
|Red | |
e. Calculate the percent difference between the expected wavelengths (in parentheses) and the average wavelengths.
| |True Value |% Δ |
|Aqua |4.9 x 10-7 m | |
|Red |6.6 x 10-7 m | |
Practice Problems
A. Wave Motion
Questions 1-3 Consider the following graph of a periodic wave.
wave direction
?
1. If this is a transverse wave in a steel beam, which way are the iron atoms moving?
(A) Δ (B) Ε
2. If this is a longitudinal wave in a steel beam, which way are the iron atoms moving?
(A) Δ (B) Ε
3. If this is a water wave, which way is the black dot moving?
(A) ← (B) ↑ (C) → (D) ↓
4. If you wanted to make a sound by hitting a steel beam with a hammer, which way would you strike the left side of the beam?
(A) → (B) ↓ (C) ↑ (D) →, ↓, or ↑
5. The figure shows two wave pulses that are approaching each other.
Which of the following best shows the shape of the resultant pulse when points P and Q, coincide?
(A) (B)
(C) (D)
Questions 6-8 A child swings from A to C back to A
A B C
6. Where would the child hear the highest frequency?
7. Where would the child hear the lowest frequency?
8. Where would the child hear the same frequency as the man?
9. Complete the following chart.
|Velocity |Frequency |Wavelength |
|340 m/s |510 s-1 | |
|337 m/s | |3.5 m |
| |0.067 s-1 |75 m |
10. 100-Hz and 85-Hz whistles are blown simultaneously. How many beats per second are heard?
| |
11. A guitar string 0.5-m long has a mass of 0.0125 kg and is under tension of 4 x 103 N. Determine the
a. wave velocity
| |
b. wavelength of the first harmonic
| |
c. frequency of the first harmonic
| |
12. Determine the observed frequency of sound (f’) for 600 Hz sound (f) for each of the following situations. (vw = 340 m/s)
a. The source approaches the observer at 34 m/s.
| |
b. The observer approaches the source at 34 m/s.
| |
c. The source recedes from the observer at 34 m/s.
| |
d. The observer recedes from the source at 34 m/s.
| |
13. Choice the correct word concerning sound waves in air.
|temperature increases, speed |increases |decreases |
|power increases, loudness |increases |decreases |
|distance increases, loudness |increases |decreases |
|frequency increases, sensitivity |increases |decreases |
|frequency increases, pitch |increases |decreases |
14. Two whistles are blown simultaneously. The wavelengths of the sound emitted are 9.0 m and 9.5 m, respectively. How many beats per second are heard? The speed of sound in air is 340 m/s.
| |
15. When the E-string of an old piano is sounded simultaneously with a tuning fork of frequency 660 Hz, a 2 Hz beat is heard. What are the two possible frequencies of the E-string?
| |
16. A guitar string 0.5-m long has a mass of 0.010 kg and is under tension of 4500 N.
a. What is the wave velocity?
| |
b. What is the frequency of the first harmonic?
| |
c. What tension would produce a first harmonic frequency of 600 Hz?
| |
17. The frequency of the second harmonic is 400 Hz. What is the frequency of the fourth harmonic?
| |
18. An ambulance, generating a 600 Hz sound, approaches a listener at 17 m/s. What frequency does the listener hear? (vw = 340 m/s)
| |
B. Light
19. What is the mirror image of the letter "d"?
(A) d (B) b (C) p (D) q
20. You look at your self in a full length mirror, where the bottom half of the mirror is covered. What would you see?
(A) The top half of your body
(B) The bottom half of your body
(C) Your whole body full size
(D) Your whole body half size
21. Where would the image form?
observer A
B C
(object) X mirror D
Questions 22-24 Light travels from air to glass and bends as shown in the diagram below.
22. Which side of the vertical line is the glass?
(A) left (B) right
23. Would the diagram differ if the light went from glass to air?
(A) yes (B) no
24. Would the diagram be different if the glass was under water?
(A) yes (B) no
Questions 25-27 A light ray R in medium I strikes a sphere of medium II with angle of incidence θ. The index of refraction for medium I is n1 and medium II is n2. A
B
C
D
E
25. Which path is possible if nI < nII?
26. Which path is possible if nI > nII?
27. Which path is possible if nI = nII?
Questions 28-29 You are on shore looking at a fish in a pond.
28. You want to spear the fish, where would you aim?
(A) directly at (B) behind (C) ahead
29. Where would you aim a laser light on a fish under water?
(A) directly at (B) behind (C) ahead
30. 600-nm light (in air) enters glass (n = 1.50). Determine the
a. frequency in glass.
| |
b. wavelength in glass.
| |
c. speed of light in glass.
| |
31. The rays of the sun strike the surface of a lake at an angle of 65o with the vertical. At what angle, measured from the vertical, is the refracted ray in the water (n = 1.33)?
| |
32. Determine the critical angle for light passing from diamond (n = 2.42) into air (n = 1.00).
| |
33. What is the index of refraction of glass for which the critical angle at the glass-air interface is 37o?
| |
34. Light of wavelength 450 nm passes from a vacuum into water (n = 1.33). Determine the following in water
|velocity |wavelength |
| | |
35. Light strikes a flat piece of glass (n = 1.50) at an incident angle of 70o. Some of the light is reflected and some light passes out of the glass on the opposite side.
a. What is the angle of reflection?
| |
b. What is the angle of refraction inside the glass?
| |
c. With what angle does light exit the glass?
| |
36. What is the critical angle for glass (n = 1.50) in water (1.33)?
| |
C. Lenses and Mirrors
37. A mirror with 10-cm radius of curvature, has a focal length of
| |
38. State whether the lens or mirror is converge or diverge.
| |Lens |Mirror |
|Concave | | |
|Convex | | |
39. Convex-converging lens: Draw the two ray tracings.
| | |
| | |
| | |
| | |
40. Concave-diverging lens: Draw the ray tracings.
| | |
| | |
41. What is the + and – case for each of the following?
| |f |di |h |
|positive | | | |
|negative | | | |
42. What does it mean to have a magnification that is
|greater than 1 | |
|negative | |
43. Concave-converging mirror: Draw the two ray tracings.
| | |
| | |
| | |
| | |
44. Convex-diverging mirror: Draw the ray tracings.
| | |
| | |
45. A 1.5-cm-high diamond ring is placed 20 cm from a concave mirror (r = 30 cm). Determine
a. the position of the image di.
| |
b. the height of the image hi.
| |
46. Which type of mirror is the following
|make-up mirror | |
|passenger side mirror | |
47. Indicate the nature of the image when the object position (do) is in the following ranges.
|do |real/virtual |inverted/upright ||M| |
|do > 2f | | | |
|do = 2f | | | |
|2f > do > f | | | |
|do = f | | | |
|0 < do < f | | | |
48. An object 2.0 cm high is placed 20 cm from a convex lens of focal length 10 cm.
a. Draw a ray diagram and locate the position of the image formed. Draw in the image.
| | | |
| | | |
c. Circle the correct descriptions of the image.
|real |virtual |inverted |
| | | |
c. Circle the correct descriptions of the image.
|real |virtual |inverted |
| | | |
c. Circle the correct descriptions of the image.
|real |virtual |
|Which side could be used as a make-up mirror? | |
|Which side could be used as a side mirror in a car? | |
|Which point is closest to focus? | |
b. Where would an object be placed to produce
|an upright magnified image? | |
|an inverted unmagnified image? | |
|an inverted image that is smaller than the object? | |
|no image at all | |
|an upright image that is smaller than the object? | |
|an inverted image that is larger than the object? | |
52. A converging lens (f = 10 cm) is used to examine object A that is held 6 cm from the lens.
a. Draw rays that show the position and size of the image.
[pic]
b. Is the image real or virtual. Explain your reasoning.
| |
c. Calculate the distance of the image from the lens.
| |
d. Calculate the ratio of the image size to the object size.
| |
e. The object A is moved to 20 cm. Describe the image position, size, and orientation.
| |
D. Interference
53. Consider the diagram of a light wave.
D
A B ? E
C
a. Which position(s) are in phase with the dot?
| |
b. Which position(s) are ½λ out of phase with the dot?
| |
c. Which position(s) are ¼λ out of phase with the dot?
| |
54. Triangles S1RS2 and QPoP1 are nearly similar. Therefore, the angles, θ, are equal.
[pic]
a. Complete the trig function: _______θ = x/L.
b. Complete the trig function: _______θ = λ/d.
c. Determine the sin and tan of the following angles.
|θo |1 |
|tanθ = x/L and sinθ = (m + ½)λ/d |x = |
55. Consider the Young's double slit experiment below, which demonstrated the wave nature of light.
a. Fill in the order for each bright and dark band.
b. Fill in the path difference Δ between the rays.
Order Δ
____ ____
____ ____
____ ____
____ ____
____ ____
____ ____
____ ____
56. The diagram shows the relative intensity for each band.
What generalization can you say about the intensity as m increases?
| |
57. A 600 nm (600 x 10-9 m) laser beam is incident on a pair of slits 0.500 mm (0.50 x 10-3 m) apart. Determine the angular deflection, θ, for the following.
a. Second-order bright band?
| |
b. Zero-order dark band?
| |
c. Determine the distance from the center bright band to the zero order dark band (x) on a screen 2.0 m away.
(1) Use the angular deflection from part b.
| |
(2) Use the formula derived in 59e(2).
| |
d. What is the width of the center bright band?
(Distance between the zero order dark bands.)
| |
e. One slit is covered, so that the light only passes through one slit which is 0.500 mm wide and 1.00 mm tall.
(1) What is the width of the light spot?
| |
(2) What is the length of the light spot?
| |
(3) The slit is longer than it is wide. How would you describe the shape of the spot light?
| |
58. A 500 lines/mm diffraction grating is used to observe mercury light. The first-order green band is 28.4 cm away from the light when the grating is 1.00-meter from the light.
a. What is the angle of deflection for the green band?
| |
b. What is the spacing between each groove on the diffraction grating (d)?
| |
c. Determine the wavelength of the green band.
| |
d. Use the formula derived in 59e(1) to determine λ.
| |
e. Which answer, part c or d, is correct? Explain.
| |
59. 500 nm light does not reflect off of a film (n = 1.25) that is on a piece of glass (n = 1.5) viewed in air (n = 1).
a. What is the wavelength of light in the film?
| |
b. What is the minimum thickness of the film?
| |
c. Would this coating work under water? Explain.
| |
60. A soap bubble appears blue (λ = 450 nm) in sunlight.
a. What is the wavelength in the soap film (n = 1.35)?
| |
b. What is the minimum thickness for a soap bubble?
| |
61. A laser beam is incident on two slits separated by 0.5 mm. The interference pattern is formed on a screen 1 m from the slits and the first bright fringe is found to be 0.12 cm to the right of the central maximum. Determine the
a. angular deflection of the first bright fringe.
| |
b. wavelength of light in nanometers.
| |
c. distance from the center to the zero order dark fringe.
| |
d. width of the zero order bright fringe.
| |
e. Would the width of the zero order bright fringe increase or decrease if 700 nm light is used?
| |
62. The hydrogen spectrum is analyzed using a 600 lines/mm diffraction grating, which is 1.00 m away from the light source. An aqua line appears at 30.5 cm and a red line appears at 42.8 cm to the right of the light source. Determine the
a. wavelength of aqua light.
| |
b. wavelength of red light.
| |
63. What is the minimum thickness for a soap bubble that appears red (λ = 750 nm, n = 1.35)?
| |
64. What is the thickness of a coating (n = 1.22) on glass
(n = 1.50) that will eliminate 550 nm light?
| |
Practice Multiple Choice
Briefly explain why the answer is correct in the space provided.
Questions 1-3 The diagram represents a transverse wave traveling in a string.
6 m
1. Which pair points is half a wavelength apart?
(A) A and D (B) D and F (C) B and F (D) D and H
| | |
2. What is the wavelength?
(A) 1 m (B) 6 m (C) 2 m (D) 3 m
| | |
3. What is the speed of the wave if its frequency is 9 Hz?
(A) 0.3 m/s (B) 1 m/s (C) 3 m/s (D) 27 m/s
| | |
4. If the amplitude of a transverse wave traveling in a rope is doubled, the speed of the wave in the rope will
(A) decrease (B) increase (C) remain the same
| | |
Question 5-6 Use the graph wavelength versus frequency of waves to answer the questions.
[pic]
5. What is the wavelength when the frequency is 2.0 Hz?
(A) 5.0 m (B) 2.5 m (C) 2.0 m (D) 1.0 m
| | |
6. What is the speed of the waves generated in the spring?
(A) 2 m/s (B) 5 m/s (C) 7 m/s (D) 10 m/s
| | |
7. Sound in air can best be described as which of the following types of waves?
(A) Longitudinal (B) Transverse
(C) Gravitational (D) Electromagnetic
| | |
8. Maximum destructive interference will occur when two waves having the same amplitude and frequency
(A) meet crest to crest (B) meet crest to trough
| | |
9. The motion of the individual particles in the medium compared to the direction of the transverse wave, is
(A) perpendicular (B) parallel
| | |
Questions 10-12 A standing wave of frequency 5 Hz is set up on a string 2 m long with nodes at both ends and in the center.
[pic]
10. What is the harmonic of this standing wave?
(A) first (B) second (C) third (D) fourth
| | |
11. The speed at which waves propagate on the string is
(A) 0.4 m/s (B) 2.5 m/s (C) 5 m/s (D) 10 m/s
| | |
12. The first harmonic of vibration of the string is
(A) 1 Hz (B) 2.5 Hz (C) 5 Hz (D) 7.5 Hz
| | |
13. The frequencies of the third harmonics of a vibrating string is f. What is the fundamental frequency of this string?
(A) f/3 (B) f/2 (C) f (D) 2f
| | |
14. A ringing bell is located in an airless chamber. The bell be seen vibrating but not be heard because
(A) Light can travel through a vacuum, but sound cannot.
(B) Sound waves have greater amplitude than light waves.
(C) Light waves travel slower than sound waves.
(D) Sound waves have higher frequencies than light waves.
| | |
15. Resonance occurs when a vibrating object transfers energy to another object causing it to vibrate. The energy transfer is most efficient when the two objects have the same
(A) frequency (B) amplitude
(C) loudness (D) speed
| | |
16. In the Doppler effect for sound waves, factors that affect the frequency that the observer hears include which of the following?
I. The speed of the source
II. The speed of the observer
III. The loudness of the sound
(A) I only (B) II only (C) III only (D) I and II
| | |
17. A train whistle has a frequency of 100 Hz as heard by the engineer on the train. Assume that the velocity of sound in air is 330 m/s. If the train is approaching the station at a velocity of 30 m/s, the whistle frequency that a stationary listener at the station hears is most nearly
(A) 90 Hz (B) 110 Hz (C) 120 Hz (D) 240 Hz
| | |
18. The product of a wave's frequency and its period is
(A) one (B) its velocity
(C) its wavelength (D) Plank's constant
| | |
19. The figure shows two waves that are approaching each other.
[pic]
Which of the following best shows the shape of the resultant pulse when points P and Q, coincide?
(A) (B)
(C) (D)
| | |
20. A sound wave has a wavelength of 5.5 m as it travels through air, where the velocity of sound is 330 m/s. What is the wavelength of this sound in a medium where its speed is 1320 m/s?
(A) 1.4 m (B) 2.2 m (C) 14 m (D) 22 m
| | |
21. A cord of fixed length and uniform density, when held between two fixed points under tension T, vibrates with a fundamental frequency f. If the tension is doubled, the fundamental frequency is
(A) 2f (B) √2f (C) f (D) f/√2
| | |
Questions 22-23 An object, slanted at an angle of 45°, is placed in front of a vertical plane mirror. mirror
• A
• B
• C
⎛ • D
22. Which of the labeled points is the position of the image?
| | |
23. Which of shows the orientation of the object's image?
(A) ∑ (B) ⎛ (C) ⎜ (D) ⎝
| | |
Questions 24-26 A ray of light (λ = 6 x 10-7 m) in air (n = 1) is incident on quartz glass (n = 2).
Air
Quartz glass
24. What is the angle of reflection measured from normal?
(A) 35o (B) 55o (C) 22o (D) 33o
| | |
25. The angle of refraction measured from normal is closest to
(A) 25o (B) 35o (C) 55o (D) 75o
| | |
26. Which is correct about the light in quartz glass is correct?
(A) v = 3 x 108 m/s (B) λ = 6 x 10-7 m
(C) v = 1.5 x 108 m/s (D) λ = 1.2 x 10-6 m
| | |
Question 27-31 A curved surface, with a 10-cm focal length is mirrored on both sides.
A B C D
| | |
10 cm 10 cm 20 cm
27. Which location would you place an object to form a virtual image that is smaller than the object?
| | |
28. Which location would you place light source in order to produce parallel rays of reflected light?
| | |
29. Which location would you place an object to form a real image?
| | |
30. Which location would you place an object to form a virtual image that is larger than the object?
| | |
31. Which location is the radius of curvature for this mirror?
| | |
32. The critical angle for a transparent material in air is 30°. The index of refraction is most nearly
(A) 0.33 (B) 0.50 (C) 1.0 (D) 2.0
| | |
33. Light leaves a source at X and travels to Y along the path.
[pic]
Which of the following statements is correct?
(A) n1 = n2 (B) n1 > n2 (C) v1 > v2 (D) f1 > f2
| | |
34. Which statement is correct about lenses and mirrors?
(A) Converging lenses are thinnest in the middle.
(B) Convex mirrors are curved inward.
(C) A real image formed by a convex lens is dimmed when half of the lens is covered.
(D) A diverging lens or mirror can make a real or virtual image depending on where the object is placed.
| | |
35. Two plane mirrors are positioned perpendicular to each other as shown. A ray of light is incident on mirror 1 at an angle of 55°. This ray is reflected from mirror 1 and then strikes mirror 2.
55o
35o
90o 35o
55o
Which is correct?
I. The incident ray for mirror 2 is 55o measured from normal.
II. The reflected ray for mirror 2 is 35o measured from normal.
III. The reflected ray for mirror 2 is parallel to incident ray for mirror 1.
(A) I only (B) II only (C) I and III (D) II and III
| | |
36. A thin film with index of refraction nf separates two materials, each of which has an index of refraction less than nf. A monochromatic beam of light is incident normally on the film.
If the light has wavelength λ in air, maximum constructive interference between the incident beam and the reflected beam occurs for which of the following film thicknesses?
(A) 2λ/nf (B) λ/nf (C) λ/2nf (D) λ/4nf
| | |
37. 600-nm light passes through two slits. The first-order interference maximum appears at 6°. What is the separation of the slits? (sin6o = 0.10)
(A) 1500 nm (B) 4500 nm (C) 3000 nm (D) 6000 nm
| | |
38. How are electromagnetic waves that are produced by oscillating charges and sound waves in air that are produced by oscillating tuning fork similar?
(A) Both have the same frequency as their respective sources.
(B) Both require a matter medium for propagation.
(C) Both are longitudinal waves.
(D) Both are transverse waves.
| | |
39. When observed from Earth, the wavelengths of light emitted by a star are shifted toward the red end of the spectrum. This red shift occurs because the star is
(A) at rest relative to earth
(B) moving away from earth
(C) moving toward earth at decreasing speed
(D) moving toward earth at increasing speed
| | |
40. Parallel wave fronts incident on an opening in a barrier are diffracted. For which combination of wavelength and size of opening will diffraction effects be greatest?
(A) short wavelength and narrow opening
(B) short wavelength and wide opening
(C) long wavelength and narrow opening
(D) long wavelength and wide opening
| | |
Question 41-44 Consider a converging lens with focal length, f.
[pic]
41. Where is the image formed for an object that is placed on the left at 3/2f?
(A) On the right at 3f. (B) On the left at 3f.
(C) On the right at ⅓f. (D) On the left at f.
| | |
42. Where is the image formed for an object that is placed on the left at ½f?
(A) On the right at 3f. (B) On the left at 3f.
(C) On the right at ⅓f. (D) On the left at f.
| | |
43. Where would the object be placed in order to produce an upright image that is larger than the object?
(A) at 2f (B) between 2f and f
(C) at f (D) between f and the lens
| | |
44. Where would the object be placed in order to produce an inverted image that has a magnification of 2?
(A) 2f (B) 3/2f (C) 4/3f (D) 5/4f
| | |
45. Which is true of a single-slit diffraction pattern?
(A) It has equally spaced fringes of equal intensity.
(B) It has a relatively strong central maximum.
(C) It can be produced only if the slit width is less than one wavelength.
(D) It can be produced only if the slit width is exactly one wavelength.
| | |
Questions 46-48 A light ray R in medium I strikes a sphere of medium II with angle of incidence θ. The index of refraction for medium I is n1 and medium 2 is n2.
46. Which path is possible if n1 < n2?
| | |
47. Which path is possible if n1 > n2?
| | |
48. Which path is possible if n1 = n2?
(A) A or B (B) C or D (C) All (D) None
| | |
49. A beam of white light is incident on a triangular glass prism (n = 1.5) for visible light, producing a spectrum. Initially, the prism is in an aquarium filled with air.
[pic]
Which is true if the aquarium is filled with water (n = 1.3)?
(A) No spectrum is produced.
(B) The positions of red and violet are reversed.
(C) The spectrum produced has greater separation between red and violet than that produced in air.
(D) The spectrum produced has less separation between red and violet than that produced in air.
| | |
Practice Free Response
1. The figure shows a converging mirror, focal point F, center of curvature C, and an object represented by the arrow.
a. Draw a ray diagram showing two rays and the image.
[pic]
b. Is the image real or virtual? Justify your answer.
| |
c. The focal length of this mirror is 6.0 cm, and the object is located 8.0 cm away from the mirror. Calculate the position of the image formed by the mirror.
| |
Suppose that the converging mirror is replaced by a diverging mirror with the same radius of curvature that is the same distance from the object, as shown below.
d. Draw a ray diagram showing two rays and the image.
e. For this mirror, determine
(1) the image distance from the mirror.
| |
(2) the magnification.
| |
2. A diffraction grating with 600 lines/mm is used to study the line spectrum of the light produced by a hydrogen discharge tube. The grating is 1.0 m from the source (a hole at the center of the meter stick). An observer sees the first-order red line at a distance yr = 428 mm (0.428 m) from the hole.
Determine
a. the angular deflection.
| |
b. the wavelength of the red light.
| |
The 600 line/mm grating is replaced by a 800 lines/mm grating. Determine
c. the angular deflection.
| |
d. the distance, yr, where the observer sees the first-order red line.
| |
3. A beam of red light of wavelength 6.65 x 10-7 m in air is incident on a glass prism at an angle θ1. The glass has index of refraction n = 1.65 for the red light. When θ1 = 40o, the beam emerges on the other side at θ4 = 84o.
[pic]
a. Calculate the angle of refraction θ2.
| |
b. What minimum angle θ3 would result in total internal reflection (θ4 = 90o)?
| |
c. Would the incident angle θ1 be greater than or less than 40o in order to produce total internal reflection?
| |
d. The glass is coated with a thin film that has an index of refraction nf = 1.38 to reduce the partial reflection.
(1) Determine the wavelength of the red light in the film.
| |
(2) Determine the minimum thickness of the film.
| |
4. To demonstrate standing waves, one end of a string is attached to a tuning fork with frequency 120 Hz. The other end of the string passes over a pulley and is connected to a suspended mass M as shown in the figure. The value of M is such that the standing wave pattern has four "loops." The length of the string from the tuning fork to the point where the string touches the top of the pulley is 1.20 m. The linear density of the string is 1.0 x 10-4 kg/m, and remains constant throughout the experiment.
[pic]
a. Determine the wavelength of the standing wave.
| |
b. Determine the speed of transverse waves along the string.
| |
c. The speed of waves along the string increases with increasing tension in the string. Indicate whether the value of M should be increased or decreased in order to double the number of loops in the standing wave pattern. Justify your answer.
| |
d. If a point on the string at an antinode moves a total vertical distance of 4 cm during one complete cycle, what is the amplitude of the standing wave?
| |
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.