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Unformatted text preview: hysics 13224 §@i art 1: Short Answer (Answer and explain in one or two sentences or equations.) Each question is worth 5 Exam 1, Winter 2005 NAME: points. 1. Write the equations which relate position x, velocity v, and acceleration a to time t for a simple harmonic
oscillator of amplitude A, frequency a), and phase constant 0. 2. Write the general expression representing a onedimensional wave traveling in the +x direction. Identify all
symbols used in your expression, and designate which part of your expression represents the phase of the
wave. 3. What two factors in general determine the speed of a mechanical wave? State the speciﬁc result for a wave in
a stretched string. 4. An observer hears an increase in frequency of sound emitted by a source if the distance between source and observer is decreasing, yet the cause of the effect is ﬁindamentally different depending on whether it is the
source or the observer that is moving. Explain the difference. Part II: Multiple Choice. Circle the one best answer to each of the following questions. Each question is worth
5 points. 1. 2. 3. A mass m oscillates with equency to at the end of a spring of stiffness k. If the spring is then cut in half and same mass attached one of the halves, the mass will oscillate with frequency (a) 0); (b) 20); (c) (9/2;
2 a); (e) (DH 2 If the amplitude of a simple h onic oscillator is increased by a factor of 2, then (a) the maximum velocity
and maximum acceleration ch increase by a factor of 4; (b) the total energy increases by a factor of 2;
creases by a factor of 2, but the maximum acceleration increases by a factor of 4; c the maximum veloc
(@i e total energy increases by a factor of 4; (e) none of the above. third harmonic. The wave speed is (a) 570 m/s 80 s; (c) 855 m/s; (d) impossible to know without
knowing the linear density of the string; (e) none 0 t above. A stretched string of length 60 cm fixed at both ends and girder tension T = 20 N35 vibrating at 950 Hz in its Two strings have equal lengths and equal diameters and are made of the same /xf1aterial. String 2 is under
greater tension than string 1. When the strings vibrate simultaneously in the' fundamental modes, six beats
per second are heard. When the tension in one of the strings is change the umber of beats per second
changes from six to four. (a) The tension in string 1 was decreased; a) tension in string 2 was decreased; (0) the tension in string 1 was increased; (d) the tension in string 2 was creasepossible to tell. Part III: Problem Solving. Work each of the following problems. Show your work. Credit for your answers
b0 depends on the quality of your explanations. Each problem is worth 20 points. 1. 2. 3. A weight is suspended from a light spring. When pulled down 4.0 cm and released, it starts upward with an
acceleration of36 cm/s‘. (a) What is the period of vibration? (b) With what speed does it pass through its . . . . . 9
ethbrlmnposmon' a) 9. 0‘1 Sac. b) 0.02m/5 or” ll, Cm /5
Spherical waves are emitted from a 1.0 watt source. Find the intensity 1.0 meter ﬁom the source.
0 O ‘7 g 5 (4.3/59, 7..
A 50 cm long wire ﬁxed at both ends, with mass 1.0 g and under tension 440 N, vibrates in its fundamental mode near an open pipe of variable length. The length of the pipe is adjusted until it resonates in its
fundamental mode. What is the length of the pipe? Assume vsound = 340 m/s. O~36m 0/ 35¢,“ Mew/X aantWA ‘
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