Problem+Solving+for+Complex+Sounds+Unit+%282%29

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University of Colorado, Boulder *

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3016

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Electrical Engineering

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Dec 6, 2023

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docx

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Learning Goals: Complex Vibration and Modulation 1 Relevant readings: Chapter 4 of Emanuel & Letowski (pgs 67-75). Plack 3 rd edition pages 15-30 (second edition pages 12-26) Set A. Given a time waveform of a complex periodic sound, identify/calculate the fundamental period and the fundamental frequency of the sound. A.1. Consider the time waveform below. What is the period of this sound? What is the fundamental frequency of this sound? 0 0 0.01 0.01 0.01 -50 0 50 Time Waveform Time (seconds) Relatve Amplitude A.2. Consider the time waveform below. What is the period of this sound? What is the fundamental frequency of this sound? Would this sound be more likely to emerge from a piano or from a snare drum? Why? -4 -2 0 2 4 Time Waveform Time (milliseconds) Relatve Amplitude Set B. A complex periodic tone has a fundamental frequency and harmonics that are integer multiples of that fundamental frequency. A complex periodic sound will maintain a period corresponding to the fundamental frequency if it contains several harmonics, even if the fundamental frequency is missing. B.1. Suppose the fundamental frequency is 300 Hz. What are the first five harmonics? (Note: the first harmonic is the fundamental frequency). B.2. Suppose the fundamental frequency is 200 Hz. What are the 11 th , 12 th , 13 th harmonics?
Learning Goals: Complex Vibration and Modulation 2 B.3. What is the fundamental frequency of a sound with the following harmonics: 400 Hz, 800 Hz, 1000 Hz, 1200 Hz, 1400 Hz. B.4. What is the period of a complex periodic sound with the following harmonics: 300 Hz, 400 Hz, 500 Hz, 600 Hz, 700 Hz. Set C. State three aspects of sine wave components that must be known in order for a complete description of a complex waveform. Set D. Explain how the time waveform of a complex tone is constructed based on the time waveforms of its constituent sine waves. In particular, consider the time waveforms of the following three sine waves. Assume the x-axis units are time (in seconds.). These three sine waves are constituents of a complex tone. Explain how you will use these three waveforms to determine the shape of the complex waveform? Use the sine wave formula as part of your explanation. Set E. Describe and sketch graphical illustrations of simple and complex vibrations in the time domain (time waveform) and in the frequency domain (amplitude spectrum). E.1. Consider a pure tone of 2000 Hz with a (relative) peak amplitude of 5 and a starting phase of 90. Sketch graphs of this sound in both the time domain and in the frequency domain. Would this sound be more likely to emerge from a piccolo or from a tuning fork? Why? E.2. Consider a white noise in which each frequency has a relative amplitude of 1 and which has a bandwidth of 10,000 Hz. Sketch its amplitude spectrum. Would this sound be more likely to emerge from a piano, a tuning fork, or a trumpet? Explain. Set F. For each of the sounds below, indicate the following: Is the graph showing the sound in the time domain or in the frequency domain? Is the sound periodic or aperiodic? What is the fundamental frequency and the period of the sound? Identify all the sounds that show a continuous spectrum. Identify all of the sounds that show a line spectrum. For each sound, provide an example of what the source of the sound might be.
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