Total marks for this assignment: 30 Once you have completed Unit 6, please submit Assignment 6 using the assignment submission tool in Moodle so that your Open Learning Faculty Member can grade it and provide you with feedback. It covers material from chapters 13 and 14. 1. A particle moves with amplitude A and period T, as shown in the figure. Express the following in terms of A and T and numerical constants (if necessary). (3 marks) A x MA T a. The time at which the phase is TV/2. b. The maximum velocity. c. The maximum acceleration. d. The first time for t> 0 at which the acceleration is a maximum. 2. The motion of a particle is given by: x = (6.0 m) cos (0.586t + 0.72) (4 marks) a. Find the amplitude. b. Find the period. c. Find the first time for t> 0 when v = 0. d. Find the maximum acceleration. e. Find the phase at time t = 1.38 s. Unit 6 Vibrations and W d. Find the maximum acceleration. e. Find the phase at time t = 1.38 s. 3. A freight car of mass 1800 kg is timed at 4.2 m/s just after it runs into a spring-loaded bumper at the end of the track. The bumper consists of an 800 kg mass that the car runs into, and a pair of large springs. The car travels 2.4 m before coming to rest. (3 marks) a. Using an appropriate conservation law, find the speed of the freight car before it struck the bumper. b. Find the time taken for the car to be brought to rest. 4. An 80.0 kg student sits down in his 920 kg car, and his weight causes the car's springs to sink an additional 4.0 10-3 m. The student then gets out of his car and bounces it up and down. Treating the system as a simple single spring and mass, calculate the frequency for the vertical vibration. (3 marks) 5. Ardent Franz is playing his alpenhorn at a distance several kilometres from a vertical rock face in front of which his beloved Grizelda is tending her flock of goats. He is playing Grizelda's favourite note, 24.0 Hz. The speed of the sound is 343 m/s. (2 marks) a. Find the wavelength of the sound. b. Sketch the standing wave for the air displacement in front of the rock face and find the closest distance to the rock face where Grizelda should sit in order to be at a node. 6. Two loudspeakers are placed on a stage 5.4 m apart and are radiating the same frequency, in phase. An observer walks along a line parallel to the loudspeakers and 12.7 m from them. Starting from the central point of the line (equidistant from the two loudspeakers) she observes that, as she walks, the sound intensity first decreases and then increases to a maximum again when she has travelled 1.4 m. (3 marks) a. Explain this observation. b. Calculate the frequency of the sound, given that the speed of sound is 343 m/s. 7. A student uses an audio oscillator of adjustable frequency to measure the depth of a water well. He reports two successive Ind How doon in the wal10 10 maulal vibrations and w marks) a. Find the wavelength of the sound. b. Sketch the standing wave for the air displacement in front of the rock face and find the closest distance to the rock face where Grizelda should sit in order to be at a node. 6. Two loudspeakers are placed on a stage 5.4 m apart and are radiating the same frequency, in phase. An observer walks along a line parallel to the loudspeakers and 12.7 m from them. Starting from the central point of the line (equidistant from the two loudspeakers) she observes that, as she walks, the sound intensity first decreases and then increases to a maximum again when she has travelled 1.4 m. (3 marks) a. Explain this observation. b. Calculate the frequency of the sound, given that the speed of sound is 343 m/s. 7. A student uses an audio oscillator of adjustable frequency to measure the depth of a water well. He reports two successive resonances at 52.0 Hz and 60.0 Hz. How deep is the well? (3 marks) 8. At a cocktail party each person is speaking equally loudly. If only one person was speaking, the sound level would be 72 dB. What is the actual sound level if 38 people are present (and all are speaking at the same time without listening)? (2 marks) 9. A bat flying at 5.25 m/s is chasing an insect flying at 3.49 m/s in the same direction. The bat emits a steady chirp of frequency 2000 Hz. (4 marks) a. What frequency, fo, does the insect hear? b. The insect becomes a moving source at frequency fo. What frequency does the bat hear reflected from the insect? c. The bat hears its own sound, plus the sound reflected by the insect. What beat frequency does the bat hear? 10. A tuning fork is held over the top of a graduated cylinder that is slowly filled with water. Two resonances are noted as the cylinder is filled. They occur when the water level is 56.5 cm and 17.5 cm below the rim. Note that there is an end correction, meaning that the effective length of the air column is longer than the observed length by a fixed constant amount. If the speed of sound is 343 m/s, find the frequency of the tuning fork. (3 marks)