Tutorial 17 Vibrating Beams (2)

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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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Name:____________________________________________ Group Members:_____________________________________________ _______________ Physics 1240 Tutorial 17: Vibrating Beams 1) Consider a tuning fork which is tuned to the musical note A 5 (880 Hz). We can model this system as two beams each clamped at one end and free at the other, each one of which is shown in the diagram below. a. What are the frequencies of the second, third, and fourth modes (in kHz)? 2nd mode: 1.102 kHz 3rd mode: 3.088 kHz 4th mode: 6.052 kHz b. If you hang the tuning fork from a string attached to the center of both beams (at 0.5 on the x-axis of the diagram below) and strike it, what frequency will you hear? Why? The 2nd mode because it involves the most motion at that point c. Where should you strike the tuning fork to sound the 4th mode most effectively? (Express your answer as a percentage, e.g. 25% of the way from the base.) If you do this, how likely is it that you will hear this mode? 20% away from the base. It is fairly likely that you will hear this mode.
1 2) The plot above shows the plot of pressure versus time for a sound produced by an instrument hit by a mallet. a. Measure the fundamental frequency of this sound. (Hint: You will first need to measure the period—which periodic part of the wave is longest?) The fundamental frequency is 400 Hz b. You should also notice a second, smaller period corresponding to the next-highest mode. Find the frequency of this mode. The next highest mode frequency is 2.506 kHz c. In the space below, draw two frequency spectra (plots of amplitude versus frequency) corresponding to this sound wave. The first spectrum should be for the beginning of the sound (at around 0–20 ms), and the second should be for the latter half (around 30–50 ms). Be sure to label the x-axis with the frequencies you found in parts (a) and (b).
d. Why does the sound's spectrum change over time? Is there a term we use for this physical phenomenon? The sound’s spectrum changes over time because of damping. e. Based on the spectra you drew, what instrument is likely being played in this plot? Why? Some kind of idiophone. 2
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