Tutorial 9 Spectra

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University of Colorado, Boulder *

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1240

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Physics

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Apr 3, 2024

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pdf

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Physics 1240 Tutorial 9: Spectra 1 a) Shown above is part of the spectrogram for a plucked string from a monochord. The y-axis is frequency in kHz, and the x-axis is time in seconds. Approximately what are the frequencies of the first and second harmonics? The first harmonic frequency is around 200Hz. The second harmonic is around 400Hz. b) Which harmonic shown in the spectrogram above is strongest (i.e., has the largest amplitude in a Fourier decomposition), and which is weakest? How can you tell? The first harmonic is the strongest because it’s the brightest on the spectrum. The lighter colors represent higher amplitude. c) Though it is not shown in the plot above, what should the frequency of this string’s tenth harmonic be? 2kHz d) Use the space below to draw two plots: the sound envelope (amplitude vs time)
and the spectrum (amplitude vs frequency) of the sound produced when the string from the plot above is plucked. Don’t worry about the units for amplitude, but all other units and numbers should be included in your labels. 2) You are trying to tune two monochords so that they produce the same pitch. At first, when the strings are plucked together, you notice beats occurring once every two seconds. Then, you tighten the 1 st string, and the beats change to twice a second. Should you keep tightening the 1 st string, or tighten the 2 nd string? Use physics to justify your answer! You should tighten the second string because an increase in beats means that interference between the two strings is increasing and becoming more regular. If tightening the 1st string increases interference, it means it’s being tuned further away from the other string.
3) Two flutes that are slightly out of tune from each other play notes with frequencies 760 Hz and 763.5 Hz, respectively. What is the beat frequency? 3.5 Hz 4) You are going on a hike and come across a large cliff face about a mile ahead of you. Being the curious PHYS 1240 student you are, you decide to shout, “Physics rocks!” straight in the direction of the wall. After counting seven and a half seconds, you hear an echo return to you. How far away is the cliff wall, in kilometers? 1.29 Km
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