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by: Carlotta Dare DVM


Carlotta Dare DVM
GPA 3.68


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Class Notes
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This 3 page Class Notes was uploaded by Carlotta Dare DVM on Saturday September 12, 2015. The Class Notes belongs to Physics 15 at University of California - Irvine taught by Staff in Fall. Since its upload, it has received 38 views. For similar materials see /class/201925/physics-15-university-of-california-irvine in Physics 2 at University of California - Irvine.




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Date Created: 09/12/15
Physics of Music Final Exam Review The nal exam will take place in PSCB 120 on Friday Dec 13 1030 1230 The nal exam format will be similar to that of the midterm with a multiple choice section followed by free form questions The duration of the exam will be 90 minutes The exam will test materials from the whole course Lecture 1718 and Problem Sets 177 Lecture notes and problem sets are linked to the course web site Examples of possible free form questions are given below The key formulas and facts given below will be provided with the exam No other aids are permitted in the exam In particular calculators are not required and not permitted lBring a Scantron 8000 form a 2 pencil and your student ID Formulas and Facts 0 Frequency and period f 1T 0 Wave velocity frequency and wavelength 1 f A o Harmonic series 72 1 is rst harmonic n 2 is rst overtone fn nfl 0 Boundary conditions node at xed end of a rope or closed end of an air column anti node at free end of a rope or open end of an air column 0 Musical intervals octave 21 perfect fth 32 perfect fourth 43 major third 54 0 Sampling limit is f lt 12T Circle of Fifths Db Eb Gb Ab Bb Db Eb Gb Ab Bb C D F G A C D F G A Sample FreeForm Questions 1 Suppose that a plane wave of sound is travelling towards a ballooon as shown in the diagram below Paths A7B7C on the diagram show the directions of the sound wave front7 before reaching the balloon7 at three di erent locations a Sketch the paths for the wave fronts A7 B7 C as they pass through the balloon Assume that the ballon is lled with Helium gas in which the speed of sound is about three times faster than in air I do not expect you to get the angles exactly right7 but the general features should be correct b Repeat the previous question but now assume that the balloon is lled with exhaled air in which some of the Oxygen has been replaced with Carbon Dioxide7 giving a speed of sound that is slightly slower than in atmospheric air A 0 V Will a person listening on the other side of the balloon hear a louder sound when it is lled with Helium or exhaled air A6 B Ce 2 Imagine a string of length L that is xed at both ends7 for example7 on a violin or a guitar a Sketch the ve lowest frequency standing waves of the string b Give the wavelengths of each standing wave Express your answer in terms of the unknown string length L 03 P 5quot G 1 c Give the frequencies of each standing wave Express your answer in terms of the unknown speed 1 of transverse waves along the string Adjaceant pairs of strings on a guitar are usually tuned so that their fundamental frequencies are in the ratio 43 a perfect fourth interval Pressing down on a string with your nger creates a new node and changes the e ective length of the string for vibrations a Where should you position your nger along a string7s length to raise its funda mental resonant frequency by a factor of two one octave b Where should you position your nger along a string7s length to raise its funda mental resonant frequency by a major third Assume that the distance between your ears is D and that the speed of sound is v a Calculate the frequency f at which the wavelength equals the distance between your ears Express your answer in terms of the unknowns D and 1 b Calculate the time delay T between the left and right ears for sound that ap proaches directly from your left side Express your answer in terms of the un known D and 1 In this problem7 you will calculate the frequencies of the note that is a major third above C in the Pythagorean and Equal Temperament scales a Using the circle of fths7 count how many steps up by a fth are required to take you from C to E What is the corresponding frequency ratio for these steps b How many whole octaves can you shift this E down by and still be above the original C What is the ratio between the frequency of this shifted down E and the original C This ratio measures the size of a major third in the Pythagorean scale c How many semitones above C is E What is the corresponding frequency ratio EC 7 a major third in the equal temperament scale How does the reverberation time of a rectangular room change if all its dimensions height7length7width are doubled The reverberation time RT is related to the rooms volume V and e ective area A by the formula RT 0161 V in mg A in m2 Suppose the air column in a trombone has an e ective length of L when its slide is fully retracted at its shortest Assume that the speed of sound is v


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