Physics 7E Final Exam 1

Transcription

1 Physics 7E Final Exam 1 MULTIPLE CHOICE PROBLEMS. There are 15 multiple choice problems. Each is worth 2 points. There is no penalty for wrong answers. In each, choose the best answer; only one answer is correct. Be sure to transfer your answers to the front of the exam. 1. When two sinusoidal waves y 1 = A sin(kx ωt) and y 2 = A sin(kx ωt + 1 π) are superposed, 3 the result is a sinusoidal wave with amplitude (A) 0. (B) A (C) 2A (D) 3A (E) 2A 2. Which of the following will cause the maxima in a two-slit interference pattern to move closer to each other? (A) Decreasing the wavelength of the light. (B) Decreasing the distance to the screen. (C) Increasing the separation of the slits. (D) Two or more of the above. (E) None of the above. 3. A buzzer moves with velocity v directly away from a person. The person is at rest and hears a frequency f 1. A little later, the buzzer is at rest. The person moves with the same velocity v directly away from the buzzer and hears a frequency f 2. At all times the air is perfectly still. Which of the following is true? (A) f 1 < f 2. (B) f 1 = f 2. (C) f 1 > f 2. (D) Any of the first three answers could be true it depends on the velocity v. (E) Any of the first three answers could be true it depends on the distance between the buzzer and the person. 4. A source creates a sinusoidal sound wave, which produces an intensity I at a point P. If the frequency of the sound wave is doubled while the amplitude is reduced to half of its original value. The intensity at point P becomes (A) I (B) 2I

2 Physics 7E Final Exam 2 (C) 4I (D) 1 2 I (E) 1 4 I 5. An underwater scuba diver swimming in 20 C fresh water sees the Sun at an apparent elevation angle of 60 o above the horizon. What is the actual elevation angle of the Sun above the horizon? (A) 55 o (B) 48 o (C) 42 o (D) 35 o (E) This is impossible light at this angle would undergo total internal reflection. 6. A long tube contains a compressible gas. A piston on one end moves in simple harmonic motion and creates a sound wave in the tube. Which of the following statements is true? (A) If the amplitude of the pistons motion is increased, the velocity of the sound wave will not change. (B) If the frequency of the pistons motion is increased, the velocity of the sound wave will increase. (C) If the amplitude of the pistons motion is doubled, the intensity of the sound wave will double. (D) Two or more of the above are true. (E) None of the above is true. 7. A transverse wave on a string is described by the wave function y = (2.00m) sin(kx+ωt). When is the earliest time after t = 0 that the point of the string at x = 0 reaches its maximum positive transverse velocity? (A) π 2ω. (B) π ω. (C) 3π 2ω. (D) 2π ω. (E) 4π ω.

3 Physics 7E Final Exam 3 8. What are the approximate dimensions of the smallest object on Earth that astronauts can resolve by eye when they are orbiting 500 km above the Earth? Assume that the wavelength of light is 500 nm and the pupils of the astronauts eyes have diameter 5.0 mm. (A) 3.0 m (B) 12 m (C) 30 m (D) 61 m (E) 122 m 9. Which of the following is a true statement about historical attempts to understand the nature of light? (A) The double slit experiment, the successes of Huygens principle, and the photoelectric effect all favored the wave interpretation of light. (B) The double slit experiment and the successes of Huygens principle favored the wave interpretation of light, and the photoelectric effect favored the particle interpretation. (C) The double slit experiment, the successes of Huygens principle, and the photoelectric effect all favored the particle interpretation of light. (D) The successes of Huygens principle favored the wave interpretation of light, and the double slit experiment and the photoelectric effect favored the particle interpretation. (E) The successes of Huygens principle favored the particle interpretation of light, and the double slit experiment and the photoelectric effect favored the wave interpretation. 10. A fish tank, open at the top and filled with water, develops a small hole in its side at a point 4.00 m below the waters surface. What is the velocity of the water leaving through the hole? Free-fall acceleration is g = 9.80m/s 2. (A) 3.13 m/s (B) 4.43 m/s (C) 6.26 m/s (D) 8.85 m/s (E) m/s 11. A trumpet and a clarinet playing the same musical tone at the same volume (A) are indistinguishable. (B) are distinguishable because they create sound waves with different velocities. (C) are distinguishable because they create sound waves with different waveforms.

4 Physics 7E Final Exam 4 (D) are distinguishable because they create sound waves with different frequencies. (E) are distinguishable because they create sound waves with different amplitudes. 12. Light passes through a thin slit and diverges from its initial direction. This is an example of (A) dispersion. (B) diffraction. (C) reflection. (D) refraction. (E) rarefaction. 13. A source of unpolarized light is initially viewed through two ideal polarizers, one with transmission axis in the ˆx direction, and one with transmission axis in the ŷ direction. Later a third ideal polarizer with transmission axis in the 1 2 (ˆx + ŷ) direction is placed between the first two polarizers. Which of the following statements is true? (A) Initially some light passes through the first two polarizers, and some light passes through after the third polarizer is inserted. (B) Initially no light passes through the first two polarizers, and no light passes through after the third polarizer is inserted. (C) Initially some light passes through the first two polarizers, but no light passes through after the third polarizer is inserted. (D) Initially no light passes through the first two polarizers, but some light passes through after the third polarizer is inserted. (E) There is not enough information to determine the answer. 14. A cm guitar string has linear mass density g/cm. What tension must it have so that its fundamental frequency is 100 Hz? (A) 100 N. (B) 200 N. (C) 400 N. (D) 800 N. (E) 1600 N.

5 Physics 7E Final Exam When light goes from a transparent medium with one index of refraction to another transparent medium with a different index of refraction, (A) its wavelength changes. (B) its velocity changes. (C) its frequency changes. (D) Both A and B are true. (E) Both B and C are true.

6 Physics 7E Final Exam 6 FREE RESPONSE QUESTIONS. There are six free response problems, each worth 10 points. Do all problems and show all work for full credit. 1. A camera lens is made of glass with index of refraction n 1 = A thin film of a material with index of refraction n 2 = 2 is used to coat the lens so that light incident on the lens is minimally reflected. Assume that the light is traveling perpendicular to the lens surface and has wavelength λ = 600 nm in vacuum. (A) What is the minimal thickness of the thin film? Be sure to explain the phase change of light as it is reflected from the relevant boundaries. (5 pts) (B) Now suppose that the thin film is instead made of a material with index of refraction n 3 =1.38. What is the minimal thickness of the thin film? Again, be sure to explain the phase change of light as it is reflected from the relevant boundaries. (5 pts)

7 Physics 7E Final Exam 7 2. In class, we saw and heard a demonstration in which two plastic hoot tubes, open at both ends, were forced to resonate at their fundamental frequencies by heating them over gas flames. Assume that the air temperature in the tubes is 20 o C. (A) Suppose one hoot tube is cm long. What is its fundamental frequency? (2 pts) (B) Now suppose a 2nd hoot tube is played at the same time as the first. If they produce a beat frequency of 4 Hz, what are the possible lengths of the 2nd tube? Note: there are two possible lengths. (4 pts) (C) Now suppose that one end of each of the tubes is closed, so that each tube has one end closed and one end open. If they are again played together, what beat frequency would be heard? (4 pts)

8 Physics 7E Final Exam 8 3. A light ray with wavelength λ = 500 nm travels through air and is incident at an angle θ on the vertical left surface of a block of glass, as shown in the figure. The glass has index of refraction n = (A) What are the lights frequency and wavelength in the glass? (4 pts) (B) What is the maximal possible angle θ for which the refracted light ray undergoes total internal reflection at the horizontal top face of the block? (6 pts)

9 Physics 7E Final Exam 9 4. A cube of ice with sides of length L = 4.00 cm floats in a large tank of water, as shown in the figure. It is then pushed down a very small distance and then released, after which it moves up and down. Determine its period of oscillation. To account for surface tension and other damping effects, assume that these effects change the period by a factor of 2 relative to what it would have been had there been no damping. Free-fall acceleration at the Earths surface is g = 9.80m/s 2. (10 pts)

10 Physics 7E Final Exam A screen is placed 50.0 cm from a slit, which is illuminated with 600 nm light. (A) If the distance between the first and the third minima in the diffraction pattern is 3.00 mm, what is the width is the slit? (2 pts) (B) Plot I/I max (intensity relative to the maximum intensity I max ) as a function of sin θ, where θ is the angle of deviation. Carefully mark the positions of the first and second minimum away from the central point. (4 pts) (C) Now replace the slit by a diffraction grating, which has 4000 grooves per centimeter. Find the angle at which the first-order maxima can be observed. What s the highest order maxima can you observe? (4 pts)

11 Physics 7E Final Exam (A) State Snells Law of Refraction, defining all relevant symbols. (2 pts) (B) State Huygens s Principle. (2 pts) (C) Derive Snells Law of Refraction using Huygens s Principle. (6 pts)