Physics 130 Wave Motion, Optics and Sound Final Examinationkhchow/phys130_related/p130_2011_final... · A 0.20-kg object mass attached to a massless spring whose spring constant is

Physics 130Wave Motion, Optics and Sound

Final Examination

17 December, 20119:00 AM – 12:00 PM Pavilion

All Sections (Consolidated) Course Convener: M. Heimpel

LAST NAME: FIRST NAME:

ID #

A single 8 ½” x 11” formula sheet (front and back) is permitted.

Calculators without communications features are permitted. All other electronic devices are prohibited.

The exam is 3 hours (180 minutes) in length.

Attempt ALL questions.

Answers must be clearly indicated on the answer sheet using an HB pencil.

Several sheets of scratch paper are appended in the back of the exam for rough work (you may separate these extra pages), and you may write on this exam paper. At the end of the exam, turn in your answer sheet, this exam paper, and the scratch paper (but not your formula sheet). Turn everything in to the box for your section, keeping the answer sheet separate.

Rough work will not be graded.

ON THE ANSWER SHEET ENTER:Your name (Surname followed by space then given names)

Student Identification Number

Course Section in Special Codes columns JKL:

Section Instructor Lecture Time Codes

A01 MacDonald 09:00 – 09:50 AM JKL = 111

A02 Heimpel 10:00 – 10:50 AM JKL = 222

A03 Davis 02:00 – 02:50 PM JKL = 333

A04 Samarbakhsh 03:00 – 03:50 PM JKL = 444

Grading: 1 point per question.Possibly useful constants:Gravitational acceleration: g = 9.81 m/s2 Kelvin temperature: 0ºC = 273.15 KSpeed of light in a vacuum: c = 3.00 x 108 m/s Ideal gas constant: R = 8.31 J/(K•mol)Stefan-Boltzmann constant: k = 5.67 x 10–8 J/(s•m2•K4) Threshold of human hearing: I0 = 1.0 x 10–12 W/m2

Refractive index of air: n0 = 1.000

There is only one correct answer to each question. There is no extra penalty for a wrong answer.If you believe the correct answer is not listed, choose the closest matching value.

There are 17 pages with 50 questions for a maximum total of 50 points for this exam.

IF ANYTHING IS UNCLEAR, PLEASE ASK!

1. The acceleration a(t) of a particle moving in simple harmonic motion is shown in the graph to the right. At point 4, is the velocity of the particle positive, negative, or zero?

A) positive

B) negative

C) zero

D) not enough information to tell

2. The displacement of an object oscillating on a spring is given by x(t) = xm cos(ωt + φ). At time t = 0, the object is displaced in the negative x direction, and is moving toward –xm. What is the phase constant φ?

A) between 0 and π/2 radians

B) between π/2 and π radians

C) between π and 3π/2 radians

D) between 3π/2 and 2π radians

E) none of the above (φ is exactly 0, π/2, π, or 3π/2 radians)

3. A certain massless spring stretches 9 mm when it is suspended vertically and a block of mass M is hung on it. What is the natural frequency of this mass-spring system?

A) 0.088 rad/s

B) 33 rad/s

C) 200 rad/s

D) 1140 rad/s

E) cannot be computed unless the value of M is given

4. A 0.20-kg object mass attached to a massless spring whose spring constant is 500 N/m executes simple harmonic motion. If its maximum speed is 5.0 m/s, the amplitude of its oscillation is:

A) 0.0020 m

B) 0.10 m

C) 0.20 m

D) 25 m

E) 250 m

PHYS 130 Final Exam page 2 of 17

5. Diana, Duck of Science! has strapped herself to the end of a massless spring with a spring constant of 200 N/m. Diana’s mass is 0.50 kg. She sets herself oscillating in simple harmonic motion, and determines that her spring-duck system has an energy of 12 J. What is her maximum speed?

A) 0.06 m/s

B) 0.17 m/s

C) 0.24 m/s

D) 4.9 m/s

E) 6.9 m/s

6. A Pirate is swinging with a period T from the end of a long massless rope. At one end of her swing, a Ninja grabs on; she has the same mass as the Pirate. As the two of them swing at the end of the rope, what is the period of the swing?

A) T/2

B) T/√2

C) T

D) (√2)•T

E) 2T

7. A damped harmonic oscillator consists of a block (m = 2.00 kg), a massless spring (k = 12.0 N/m), and a damping force (F = –bv) with a damping constant b = 0.060 kg/s. Initially, it oscillates with an amplitude of 24.0 cm. How many oscillations does it take for the amplitude to fall to 18.0 cm?

A) 0.509

B) 3.25

C) 7.48

D) 19.2

E) 47.0


8. A 40-cm long string, with both ends clamped, is vibrating in its fundamental standing wave mode. If the wave speed is 320 cm/s, what is the frequency?

A) 4 Hz

B) 8 Hz

C) 16 Hz

D) 32 Hz

E) 64 Hz

9. In the diagram to the right, wave 1 consists of a rectangular peak of height 4 units and width d, and a rectangular valley of depth 2 units and width d. The wave travels rightward along an x axis. One of the other waves will be sent leftward along the same axis, to interfere with wave 1. Which of the choices will result in a flat line (for an instant)?

A) wave 2

B) wave 3

C) wave 4

D) none of the above

10. A transverse traveling sinusoidal wave on a string has a frequency of 100 Hz, a wavelength of 0.040 m and an amplitude of 2.0 mm. What is the maximum velocity of any point on the string?

A) 0.2 m/s

B) 1.3 m/s

C) 4 m/s

D) 15 m/s

E) 25 m/s


11. Two identical but separate strings, with the same tension, carry sinusoidal waves with the same amplitude. Wave A has a frequency that is twice that of wave B. How does the rate that wave A transmits energy compare to that of wave B?

A) one-fourth the rate of wave B

B) half the rate of wave B

C) twice the rate of wave B

D) four times the rate of wave B

E) eight times the rate of wave B

12. Strings A and B have identical lengths and linear densities, but string B is under greater tension than string A. The figure to the right shows four situations, (a) through (d), in which standing wave patterns exist on the two strings. In which situation is there the possibility that strings A and B are oscillating at the same resonant frequency?

A) a

B) b

C) c

D) d

E) none of the above

13. The figure at the right shows the pressure of a single-frequency sound wave traveling at 319 m/s through air. The air temperature is −20 ℃ and its uniform density is 1.39 kg/m3.

Take Δps = 3.60 mPa. Which function below best represents the displacement function of the wave?

A) y (x,t) = (2.58 nm) cos[(9.85 m−1)x−(3140 s−1)t]

B) y (x,t) = (2.58 nm) cos[(19.7 m−1)x−(6280 s−1)t]

C) y (x,t) = (2.58 nm) cos[(9.16 m−1)x−(3140 s−1)t]

D) y (x,t) = (5.17 nm) cos[(9.85 m−1)x−(3140 s−1)t]

E) y (x,t) = (5.17 nm) cos[(19.7 m−1)x−(6280 s−1)t]

(a)

(b)

(c)

(d)


14. Two in-phase coherent sources emitting harmonic waves of 4-m wavelength are separated by a distance d. What is the minimum value of d for which destructive interference occurs everywhere along the line that passes through the locations of the two sources?

A) 0 m

B) 1 m

C) 2 m

D) 4 m

E) 8 m

15. The sound level measured 300 m from a jet plane is 120 dB. What is the sound level from the jet at 3000 m?

A) 100 dB

B) 110 dB

C) 120 dB

D) 130 dB

E) 140 dB

16. A 660-Hz tone has an intensity level of 54 dB. The velocity of sound in air is 345 m/s. The bulk modulus of air is 142 kPa. What is the pressure amplitude of the sound waves?

A) 1.4 × 10−3 Pa

B) 2.9 × 10−3 Pa

C) 7.2 × 10−3 Pa

D) 1.4 × 10−2 Pa

E) 2.9 × 10−2 Pa


17. An open pipe is made to go into resonance at frequency fo. Next one end of the pipe is covered, and it is again made to go into resonance, this time at frequency fc. If both resonances are first harmonics (that is, fundamental modes), how do these two resonance frequencies compare?

A) fo =12fc

B) fo =23fc

C) fo = fc

D) fo =32fc

E) fo = 2 fc

18. The figure below shows a standing wave in a 85-cm pipe:

If the frequency of this mode is 930 Hz, what is the speed of sound in the pipe?

A) 180 m/s

B) 330 m/s

C) 350 m/s

D) 700 m/s

E) 3200 m/s

19. A sound wave is traveling under water of density 1025 kg/m3 and bulk modulus 2.31×109 Pa. The wavelength of this sound is 3.35 m. Another sound wave is produced by striking a tuning fork underwater so that it vibrates at a 440-Hz frequency. What would be the beat frequency heard by an underwater swimmer?

A) 2 Hz

B) 8 Hz

C) 12 Hz

D) 16 Hz

E) 24 Hz


20. Two cars, A and B, are moving at equal ground speeds in opposite directions away from each other on a straight highway. The driver of car A blows a horn with a 366-Hz frequency. The driver of car B perceived the frequency emitted from car A as being 342 Hz. Take the speed of sound equal to 343 m/s. If there is no wind, what is the ground speed of each car?

A) 11.6 m/s

B) 22.5 m/s

C) 24.1 m/s

D) 343 m/s

E) not enough information to tell

21. A jet plane passes over you at a speed of Mach 1.6. The speed of sound is 330 m/s. If the shock wave reaches you 9.4 s after the jet passed directly overhead, then what is the jet’s altitude?

A) 2480 m

B) 3100 m

C) 3970 m

D) 5280 m

E) 6200 m

22. In the figure at the right, unpolarized light is sent into the system of three polarizing sheets, where the polarizing directions of the first and third sheets are at angles θ1 = 57o (counterclockwise) and θ3 = 34o (clockwise). What fraction of the initial light intensity emerges from the system?

A) 0.060

B) 0.080

C) 0.110

D) 0.150

E) 0.220

θ1

θ3


23. If the electric field in a plane electromagnetic wave propagating in the vacuum is given by E(t) = Em sin[(3 × 106 m–1)x – ωt)], in SI units, what is the value of ω?

A) 0.01 rad/s

B) 10 rad/s

C) 100 rad/s

D) 9 × 1014 rad/s

E) 9 × 1016 rad/s

24. A ray of light passes through three media as shown in the figure to the right. How are the speeds of light in these media related?

A) v1 > v2 > v3

B) v3 > v2 > v1

C) v3 > v1 > v2

D) v2 > v1 > v3

E) v1 > v3 > v2

25. The illustration to the right shows total internal reflection taking place in a piece of glass. What is the index of refraction of this glass?

A) at least 2.0

B) at most 2.0

C) at least 1.15

D) at most 1.15

E) cannot be calculated from the given data

26. A hollow lens is made of thin glass as shown to the right. It can be filled with air, water (n = 1.3) or CS2 (n = 1.6). How can it be made to diverge a beam of parallel light?

A) fill it with air and immerse it in air

B) fill it with air and immerse it in water

C) fill it with water and immerse it in CS2

D) fill it with CS2 and immerse it in water

E) fill it with CS2 and immerse it in CS2

light, least to greatest.

3, 1, 4, 2

2, 4, 3, 1

1, 2, 3, 4

4, 2, 1, 3

2, 4, 1, 3

7. Test Bank, Question 67

A ray of light passes through three media as shown. The speeds of light in these media obey:

v1 > v

2 > v

3

v3 > v

2 > v

1

v3 > v

1 > v

2

v2 > v

1 > v

3

v1 > v

3 > v

2


The illustration shows total internal reflection taking place in a piece of glass. The index of refraction of this

Print Assignment: E1 :: http://edugen.wileyplus.com/edugen/shared/assignment/test/agpr...

4 of 7 11-12-01 5:23 AM

glass:

at least 2.0

at most 2.0

at least 1.15

at most 1.15

cannot be calculated from the given data


A light bulb burns in front of the center of a 40-cm wide mirror that is hung vertically on a wall. A man walks infront of the mirror along a line that is parallel to the mirror and twice as far from it as the bulb. The greatestdistance he can walk and still see the image of the bulb is:

20 cm

40 cm

60 cm

80 cm

120 cm


A candle C sits between two parallel mirrors, a distance 0.2d from mirror 1. Here d is the distance between themirrors. Multiple images of the candle appear in both mirrors. How far behind mirror 1 are the nearest threeimages of the candle in that mirror?

0.2d, 0.8d, 1.4d


5 of 7 11-12-01 5:23 AM

air and immersed in air

air and immersed in water

water and immersed in CS2

CS2 and immersed in water

CS2 and immersed in CS

2


A plano-convex glass (n = 1.5) lens has a curved side whose radius is 50 cm. If the image size is to be thesame as the object size, the object should be placed at a distance from the lens of:

50 cm

100 cm

200 cm

400 cm

340 cm


In a cinema, a picture 2.5 cm wide on the film is projected to an image 3.0 m wide on a screen which is 18 maway. The focal length of the lens is about:

7.5 cm

10 cm

12.5 cm

15 cm

20 cm


7 of 7 11-12-01 5:23 AM


27. You sight along the rim of a opaque glass with vertical sides so that the top rim is lined up with the opposite edge of the bottom (figure a). The glass is a thin-walled, hollow cylinder 16.0 cm high with a top and bottom of the glass diameter of 8.0 cm. While you keep your eye in the same position, a friend fills the glass with a transparent liquid, and you then see a dime that is lying at the center of the bottom of the glass (figure b). What is the index of refraction of the liquid?

A) 1.69

B) 1.74

C) 1.79

D) 1.84

E) 1.89

28. A horizontal cylindrical tank 2.20 m in diameter is half full of water (refractive index 1.33). The space above the water is filled with a pressurized gas of unknown refractive index. A small laser can move along the curved bottom of the water and aims a light beam toward the center of the water surface. You observe that when the laser has moved a distance S = 1.09 m or more (measured along the curved surface) from the lowest point in the water, no light enters the gas. What is the index of refraction of the gas?

A) 1.08

B) 1.11

C) 1.14

D) 1.17

E) 1.20

29. Figure shows an object and its image formed by a thin lens.• What is the absolute value of the focal length of the lens?• Is the lens converging or diverging?• Is the image real or virtual?

A) | f | = 5.5 cm, Converging lens, Virtual image

B) | f | = 5.5 cm, Converging lens, Real image

C) | f | = 5.5 cm, Diverging lens, Real image

D) | f | = 4.8 cm, Converging lens, Real image

E) | f | = 4.8 cm, Diverging lens, Virtual image

(a) (b)

16.0 cm

8.0 cm

Gas

laser

S

objectimage

optic axis

lens

6.50 mm

5.00 cm

3.00 cm

?


30. As shown in the figure, the candle is at the center of curvature of the concave mirror, whose focal length is 10.0 cm. The converging lens has a focal length of 32.0 cm and is 85.0 cm to the right of the candle. The candle is viewed looking through the lens from the right. The lens forms two images of the candle. The first is formed by light passing directly through the lens. The second image is formed from the light that goes from the candle to the mirror, is reflected, and then passes through the lens. What is the distance along the optical axis between these two images produced by the lens?

A) 0.0 cm

B) 10.0 cm

C) 20.0 cm

D) 51.3 cm

E) 85.0 cm

31. One end of a long glass rod is ground to a convex hemispherical shape. This glass has an index of refraction 1.55. When an object is placed 20.0 cm in front of the spherical surface along the optic axis, an image is formed inside the glass 9.12 cm from the spherical surface. Where would the image be formed if the glass were now immersed in water (refractive index 1.33) but nothing else were changed?

A) 6.86 cm from the spherical surface, inside the glass

B) 12.1 cm from the spherical surface, inside the glass

C) 18.8 cm from the spherical surface, inside the glass

D) 25.6 cm from the spherical surface, inside the glass

E) 72.1 cm from the spherical surface, inside the glass

32. Rays from a lens are converging toward a point image P located to the right of the lens. What thickness t of glass with index of refraction 1.60 must be interposed between the lens and P for the image to be formed at P ’, located 0.30 cm to the right of P. The distance between the lens and the left side of the glass is 5.60 cm. Assume the angles between rays and optical axis are small enough that sin(θ) = θ is correct. (Hint: draw a ray as it continues on to pass through the glass. You may not need to use all the data given to you in this problem.)

A) 0.70 cm

B) 0.80 cm

C) 0.90 cm

D) 1.00 cm

E) 1.10 cm

85.0 cmC

candle


33. An FM radio transmitter, operating at a frequency of 120 MHz, is atop a 100-m tower. An airplane is in flight over the ocean at an altitude of 2000 m. Radio waves reach the airplane directly from the transmitter and by reflection from the surface of the ocean, as shown in the figure. When the airplane is 86 km from the tower, the pilot observes that radio reception has faded due to partially destructive interference of the waves in the two paths. Assume the wave reflected from the ocean surface has undergone a half-wave phase shift. The waves of the reflected path arrive at the airplane delayed, with respect to the direct path. How long is this delay?

A) 16 ns

B) 13 ns

C) 19 ns

D) 22 ns

E) 25 ns

34. A pair of narrow slits, separated by 1.8 mm, is illuminated by a monochromatic light source. Light waves arrive at the two slits in phase. A fringe pattern is observed on a screen 4.8 m from the slits. Monochromatic light of 450-nm wavelength is used. What is the angular separation between adjacent dark fringes?

A) 0.125 mrad

B) 0.200 mrad

C) 0.250 mrad

D) 0.300 mrad

E) 0.375 mrad

35. One beam of coherent light travels path P1 in arriving at point Q and another coherent beam travels path P2 in arriving at the same point. If these two beams are to interfere destructively, what is the path difference P1 – P2?

A) an odd number of half-wavelengths.

B) an even number of half-wavelengths.

C) zero.

D) a whole number of wavelengths.

E) a whole number of half-wavelengths.


36. Light from a small region of an ordinary incandescent bulb is passed through a yellow filter and then serves as the source for a Young's double-slit experiment. Which of the following changes would cause the interference pattern to be more closely spaced?

A) Use slits that are closer together

B) Use a light source of lower intensity

C) Use a light source of higher intensity

D) Use a blue filter instead of a yellow filter

E) Move the light source further away from the slits

37. In a Young's double-slit experiment, a thin sheet of mica is placed over one of the two slits. As a result, the center of the fringe pattern (on the screen) shifts by an amount corresponding to 30 dark bands. The wavelength of the light in this experiment is 480 nm and the refraction index of the mica is 1.60. What is the thickness of the mica?

A) 0.090 mm

B) 0.012 mm

C) 0.014 mm

D) 0.024 mm

E) 0.062 mm

38. Yellow light is viewed by reflection from a thin vertical soap film, giving the pattern shown in the figure. Let λ be the wavelength of the light within the film. Why is there a large dark space at the top of the film?

A) no light is transmitted through this part of the film

B) the film thickness there is λ/4

C) the light reflected from exactly one of the two surfaces undergoes a 180° phase change

D) the film is too thick in this region for thin film formulas to apply

E) the reflected light is in the infrared


39. A liquid of refractive index n = 4/3 replaces the air in a wedge formed from two glass plates. What happens to the spacing between adjacent dark bands in the interference pattern?

A) increases by a factor of 4/3

B) increases by a factor of 3

C) remains the same

D) decreases to 3/4 of its original value

E) decreases to 1/3 of its original value

40. A lens with a refractive index of 1.5 is coated with a material of refractive index 1.2 in order to minimize reflection. If λ denotes the wavelength of the incident light in air, what is the thinnest possible such coating?

A) 0.500 λ

B) 0.416 λ

C) 0.300 λ

D) 0.208 λ

E) 0.250 λ

41. In a thin film experiment, a wedge of air is used between two glass plates. If the wavelength of the incident light in air is 480 nm, how much thicker is the air wedge at the 16th dark fringe than it is at the 6th?

A) 2400 nm

B) 4800 nm

C) 240 nm

D) 480 nm

E) none of these


42. Diffraction effects due to radio waves that interact with large objects such as buildings are noticeable, whereas light is not noticeably diffracted. Why is this?

A) Radio waves are unpolarized, whereas light is plane polarized.

B) The wavelength of light is much smaller than the wavelength of radio waves.

C) The wavelength of light is much greater than the wavelength of radio waves.

D) Radio waves are coherent and light is usually not coherent.

E) Light is coherent and radio waves are usually not coherent.

43. If the lens diameter is doubled, what happens to the resolvable angle of images produced at fixed wavelength?

A) The angle decreases by a factor of two.

B) The angle increases by a factor of two.

C) The angle decreases by a factor of four.

D) The angle increases by a factor of four.

E) The angle stays the same.

44. A single slit, which is 0.050 mm wide, is illuminated by light of 550 nm wavelength. What is the angular separation (in degrees) between the first two minima on either side of the central maximum?

A) 0.36°

B) 0.47°

C) 0.54°

D) 0.63°

E) 0.73°

45. A slit of width 2.0 μm is used in a single slit experiment with light of wavelength 650 nm. If the intensity at the central maximum is Im, what is the intensity 10° from the center?

A) 0.03 Im

B) 0.35 Im

C) 0.43 Im

D) 0.50 Im

E) 0.53 Im


46. A diffraction grating has 5000 lines per cm. The angle between the central maximum and the fourth order maximum is 47.2°. What is the wavelength of the light?

A) 138 nm

B) 183 nm

C) 367 nm

D) 452 nm

E) 637 nm

47. At the first minimum in the diffraction pattern, what is the phase difference between the ray from the top of the slit and the ray from the bottom of the slit?

A) π/2 rad

B) π rad

C) 3π/2 rad

D) 2π rad

E) 5π/2 rad

48. A double-slit diffraction pattern is formed using with a certain wavelength of light. What happens if we increase the wavelength of the light?

A) The width of the central diffraction peak increases and the number of bright fringes within the central peak increases.

B) The width of the central diffraction peak increases and the number of bright fringes within the central peak stays the same.

C) The width of the central diffraction peak decreases and the number of bright fringes within the central peak decreases.

D) The width of the central diffraction peak increases and the number of bright fringes within the central peak decreases.

E) The width of the central diffraction peak decreases and the number of bright fringes within the central peak increases.


49. Light of wavelength is normally incident on a diffraction grating G, as shown in the figure. On the screen S, the central line is at P and the first order line is at Q, as shown. What is the distance between adjacent slits in the grating?

A) 3λ/5

B) 3λ/4

C) 4λ/5

D) 5λ/4

E) 5λ/3

50. A mixture of 450-nm and 900-nm light is incident on a multiple-slit system. Which of the following is true?

A) All lines of the 450-nm light exactly overlap lines of the 900-nm light.

B) All lines of the 900-nm light exactly overlap lines of the 450-nm light.

C) Half of the lines of the 900-nm light exactly overlap lines of the 450-nm light.

D) None of the lines of the 450-nm light exactly overlap lines of the 900-nm light.


An N-slit system has slit separation d and slit width a. Plane waves with intensity I and wavelength are

incident normally on it. The angular separation of the lines depends only on:

a and N

a and

N and

d and

I and N


A light spectrum is formed on a screen using a diffraction grating. The entire apparatus (source, gratingand screen) is now immersed in a liquid of index 1.33. As a result, the pattern on the screen:

remains the same

spreads out

crowds together

becomes reversed, with the previously blue end becoming red

disappears because the index isn't an integer


Light of wavelength is normally incident on a diffraction grating G. On the screen S, the central line is at

P and the first order line is at Q, as shown. The distance between adjacent slits in the grating is:

3 /5

3 /4

4 /5

5 /4

5 /3


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Physics 130 Wave Motion, Optics and Sound Final Examinationkhchow/phys130_related/p130_2011_final... · A 0.20-kg object mass attached to a massless spring whose spring constant is