PH 202 вЂ“ Exam2 Practice Problems Following is some sample problems to gauge your preparation for exam1. They are to show you what area you may need to reinforce and study more. (Note: your test may include problems that no sample is shown in this practice exam) 1. The figure shows two examples of SHM, labeled A and B. (a) What the amplitude for A? (b) What is the amplitude for B? (c) What is the frequency for A? (d) What is the frequency for B? (e) What is the period for A? (f) What is the period for B? (g) Write the equations for A in the form of a sine or cosine. (h) Write the equations for B in the form of a sine or cosine. Ans: (g) 2.5 sin(0.5пЃ°t) (h) 3.5cos(пЃ°t) is 2. Draw a graph U vs. x for a horizontal spring whose spring constant is 95 N/m and which has a mass of 55g on the end of it. Assume the spring was started with an initial amplitude of 2.0 cm. Neglect the mass of the spring and any friction with the horizontal surface. (b) Use your graph to estimate the potential energy x = 1.5 cm. (c) Use your graph to estimate the kinetic energy x = 1.5 cm. (d) Use your graph to estimate the speed of the mass, for x = 1.5 cm. Ans: (b) 0.011 J (b) 0.008 J (d) 0.5 m/s 3. At t = 0, a 785-g mass at rest on the end of a horizontal spring (k=184 (N/m)) is struck by a hammer which gives it an initial speed of 2.26 m/s. (a) Determine the period , frequency ,amplitude and maximum acceleration of the motion. (b) Determine the position as a function of time. (c) Determine the total energy. (d) Determine the kinetic energy when x = 0.40A where A is the amplitude. Ans: (a) 0.410 s, 2.44 Hz, 0.148 m, 34.6 m/s2 (b) 0.148sin (15.3t) m, (c) E = 2 J, (d) K = 1.68 J 4. Two equal masses are attached to separate identical springs next to one another. One mass is pulled so its spring stretches 20 cm and the other is pulled so its spring stretches only 10 cm. The masses are released simultaneously. Which mass reaches the equilibrium point first? 5. At what displacement from equilibrium is the speed of a SHO half the maximum value? Ans: 6. A mass attached to the end of a spring is stretched a distance x0 from equilibrium and released. (a) At what distance from equilibrium will it have velocity equal to half its maximum velocity? (b) At what distance from equilibrium will it have acceleration equal to half its maximum acceleration? Ans (a): xv = 7. A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Ans: 346 Hz 8. Your auditory system can accommodate a huge range of sound levels. (a) What is the ratio of highest to lowest intensity at 100 Hz? (b) What is the ratio of highest to lowest intensity at 5000 Hz? Ans: (a) 109 (b) 1012 or 1011 9. If you were to build a pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? Ans: 8.6m , (b) 0.008.6 m 10. When a player's finger presses a guitar string down onto a fret, the length of the vibrating portion of the string is shortened, thereby increasing the string's fundamental frequency. The string's tension and mass per unit length remain unchanged. If the unfingered length of the string is L = 65.0 cm, determine the positions x of the first six frets, if each fret raises the pitch of the fundamental by one musical note in comparison to the neighboring fret. Note: On the equally tempered chromatic scale, the ratio of frequencies of neighboring notes is 21/12. 11. At a race track, you can estimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going? (speed of sound is 342 m/s). Ans: 114 m/s 12. When a sound wave passes from air into water, do you expect the frequency or wavelength to change? 13. A bat flies toward a moth at speed 7.5 m/s while the moth is flying toward the bat at speed 5.0 m/s. The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth? Ans: 55 kHz 14. (a) What is the intensity of a sound at the pain level of 120 dB? (b) Compare it to that of a whisper at 20 dB. Ans: (a) 1 w/m2 (b) 1010 15. A fireworks shell explodes 100 m above the ground, creating a colorful display of sparks. How much greater is the sound level of the explosion for a person standing at a point directly below the explosion than for a person a horizontal distance of 200m away? Ans: 7 dB 16. The spectra change when the instruments play different notes. (a) Approximately what are the intensities of the first overtone of a violin compared to the fundamental? (b) Approximately what are the intensities of the second overtone of a violin compared to the fundamental? (c) How many decibels softer than the fundamental is the first overtone? (d) How many decibels softer than the fundamental is the second overtone? Ans: (a) 0.64 (b) 0.2 (c) 2 (d) 7 17. An unfingered guitar string is 0.73 m long and is tuned to play E above middle C (330 Hz). (a) How far from the nut must a fret (and your finger) be placed to play A above middle C (440 Hz)? (b) What is the wavelength on the string of this 440-Hz wave? (c) What is the frequency of the sound wave produced in air at 25 oC by this fingered string? (d) What is wavelength of the sound wave produced in air at 25oC by this fingered string? Ans: (a) 0.18m (b) 1.1 m (c) 440 Hz (d) 0.78 m 18. The third-order bright fringe of 630 nm light is observed at an angle of 24o when the light falls on two narrow slits. How far apart are the slits? Ans: 4.65 x 10-6 m 19. Light of wavelength 690 nm falls on two slits and produces an interference pattern in which the thirdorder bright fringe is 44 mm from the central fringe on a screen 2.9 m away. What is the separation of the two slits? Ans: 1.36 x 10-4 m 20. Two narrow slits separated by 1.7 mm are illuminated by 594 nm light. Find the distance between adjacent bright fringes on a screen 5.2 m from the slits. Ans: 5.94 x 10-4 m 21. (a) When a sinusoidal wave crosses the boundary between two sections of cord as in the figure, does the frequency change? (b) Is energy always conserved when two waves interfere? 22. Consider a sine wave traveling down the stretched two-part cord of the figure. The mass density of light cord is 1.25 g/m and heavy cord is 2.00 g/m. (a) Determine the ratio of the speeds of the wave in the two sections, vH /vL. (b) Determine the ratio of wavelengths in the two section, пЃ¬H/ пЃ¬L (Hint: frequency stays the same in both sections). (c) Is the wavelength larger in the heavier cord or the lighter? 23. When a standing wave exists on a string, the vibrations of incident and reflected waves cancel at the nodes. (a) Does this mean that energy was destroyed? 24. What kind of waves do you think will travel down a horizontal metal rod if you strike its end vertically from above? What kind of waves do you think will travel down the metal rod if you strike its end horizontally parallel to its length? 25. Two linear waves have the same amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. (a) Which transmits more energy? (b) By what factor? Ans: (b) 4 26. Two loud speakers are 1.8m apart. Amber is adjusting the frequency of a sound broadcasted from the speakers. Madison stands 3.0m from one speaker and 3.5m from the other. (a) What is the lowest frequency at which destructive interference will occur at her location? (b) As Amber changes frequency, what are next two highest frequencies that Madison reports as destructive interference? Ans: (a) 343 Hz, (b) 1030 Hz, 1715 Hz