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Unformatted text preview: Physics 63L Exam 1 Spring 2009 Name: _________________________ Recitation Section:______ Closed book; no notes; calculators may be used. Exam 1 A. MULTIPLE CHOICE
Circle the best answer (5 points each): 1. Consider a vibrating string of length L = 2 m. It is found that there are successive standing wave resonances at 70 Hz and 90 Hz. Then the fundamental frequency is: a. b. c. d. e. 10 Hz 20 Hz 30 Hz 70 Hz 90 Hz 2. A bat is flying directly towards a wall at unknown speed. If the bat emits a 40 kHz chirp and receives back an echo at 41.0 kHz, at what speed is the bat moving toward the wall? (assume for the speed of sound v = 340 m/s). Then: a. b. c. d. e. 1.00 m/s 3.30 m/s 4.20 m/s 8.29 m/s 8.50 m/s 1 Physics 63L Exam 1 Spring 2009 3. An interference pattern in produced at point P on a screen as a result of direct rays from a monochromatic source (wavelength λ) and the rays reflected from a mirror as shown in the sketch below (not drawn to scale). Then, the condition for maximum intensity (constructive interference) at P is: a. a sin θ = mλ b. ⎛ 1⎞ a sin θ = ⎜m + ⎟λ ⎟ ⎜ ⎟ ⎜ ⎝ 2⎠ c. 2a sin θ = mλ ⎛ 1⎞ d. 2a sin θ = ⎜m + ⎟λ ⎟ ⎜ ⎟ ⎜ ⎝ 2⎠
e. There is no interference pattern.
source P y θ θ
mirror a screen 4. A light source emits light with a wavelength 600 nm in its own reference frame. With what velocity should the source move toward a detector, in order for the detector to measure the wavelength as 400 nm? a. b. c. d. e.
2.33 × 10 8 m/s 3.00 × 10 7 m/s 6.45 × 10 7 m/s 1 .00 × 10 8 m/s 1.15 × 10 8 m/s 2 Physics 63L Exam 1 Spring 2009 B. TRUE/FALSE
Circle the best answer (3 points each): 1. The phenomena of wave interference require that the waves are sinusoidal. TRUE FALSE 2. Consider three different sound sources that each produce a sound wave at point P with an intensity of 20 dB. If the three sound sources act at the same time (and are also mutually incoherent), then the combined intensity at P is given by 60 dB. TRUE FALSE 3. Two events are observed in the S frame and found to have spatial separation Δr = L and temporal separation Δt = 0 (they are simultaneous). Now consider the same two events as viewed in the S’ frame, where the S’ frame moves at a non-zero velocity in the Δr direction with respect to the S frame. Then, the spatial separation of the two events is greater in the S’ frame than in the S frame, i.e., Δr ′ > Δr . TRUE FALSE 4. A diffraction pattern is observed to have a total of Nred principal maxima when red light shines through a transmission diffraction grating. If blue light is used instead, then the number of principal maxima Nblue satisfies the inequality Nblue ≥ Nred. 3 Physics 63L Exam 1 Spring 2009 TRUE FALSE 4 Physics 63L Exam 1 Spring 2009 24 points PROBLEM C-1. Consider a horizontal string of length L = 10 m under a tension of 1000 N and which is clamped at both ends. It is found that the frequency difference between successive characteristic frequencies of vibration for this string is equal to 100 Hz. (a) Find the speed v for waves on this string. (b) Determine the lowest two characteristic frequencies of vibration for standing waves on this string. (c) Assume that the string is oscillating at the lowest characteristic frequency and has a total vibrational energy of 1 J. What is the maximum transverse displacement of the string? 5 Physics 63L Exam 1 Spring 2009 22 points PROBLEM C-2 The objective of this problem is to estimate the capability of a given satellite to resolve two nearby objects on the earth (when the satellite is positioned directly over those two objects). Let D denote the diameter of the circular aperture in the satellite imaging system, let d denote the distance between the two objects on the ground, and let H denote the height of the satellite above the earth. (a) Show that the angle subtended by the distance d at the satellite position is given (in radians) by: θ = d H . Briefly state why this expression is not truly exact, but is nonetheless an excellent approximation. (b) Letting λ denote the wavelength of light that is used, find an expression for dmin in terms of λ, H, and D, where dmin denotes the minimum distance between the two objects that can be resolved by the satellite. (c) If λ = 500 nm, H = 300 km, and D = 1m, what is dmin? 6 Physics 63L Exam 1 Spring 2009 22 points PROBLEM C-3 Light from a He-Ne laser – emitting at wavelength of 632 nm - is normally incident on a transmission diffraction grating with N = 100 grooves. The diffracted light has central and first order principal intensity maxima separated by 0.40 m as observed on a large viewing screen that is 2.20 m from the grating (and oriented so that the plane of the grating and the plane of the screen are parallel). (a) Calculate the spacing between adjacent grooves in the diffraction grating. Express your answer in nm units. (b) What is the total number of principal intensity maxima that are visible on the viewing screen? (c) What is the width (in millimeters) of the first order principal intensity maximum on the screen? 7 Physics 63L Exam 1 Spring 2009 A. B. C-1 C-2 C-3 total 8 ...
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This note was uploaded on 05/21/2010 for the course PHYS 63 taught by Professor Chang during the Spring '10 term at Duke.
- Spring '10