PHY105M-Lab4

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University of Texas *

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105M

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Computer Science

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Dec 6, 2023

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pdf

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4

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Part 1: Speed of Sound Method : Hypothesis : Plucking two strings at different frequencies will have the same speed of sound. Designing experiment: 1. Measure the length of two strings on a ukulele. 2. Using the Audacity program, set up the UMIK audio input to record the sound for both strings. 3. Pluck one of the strings and plot a spectrum of the sound and determine the highest frequency of the sound. 4. Repeat step 3 with the 2nd chosen string. 5. Calculate the C s for each string using the equation 2fL = C s Data and Analysis : String 1 and 2 Length: 35.5 ± 0.05 cm = 0.355 ± 0.0005 m Frequency (Hz) Calculated c s ( m/s) String 1 260 ± 40 184.6 ± 28.40 String 2 309 ± 53 219.4 ± 37.63 T-score comparing string 1 and 2 c s : 𝑡 𝑐 = |184.6−219.4| √28.4 2 +37.63 2 = 0.74 Conclusion : After conducting a t test between the two C s values of both strings, we were able to determine that the velocities of the two strings had similar speed of sound. This is shown with a t c score of 0.74, where anything below 1 is considered indistinguishable between values. This similarity can be explained by the difference in string thickness and tension found between the strings although the two are the same length, meaning that both contribute to produce different sounds, but they all resonate at the same speed of sound.
Part 2: Physiology of Sound Perception Method : When you speak, sound resonates throughout your skull which produces different sounds due to bone conduction. This means there would be less attenuation in comparison to when your voice travels through the air and you hear it from a recording. This helps explain why the your own voice you hear is perceived to be lower than the voice on a recording. Designing experiment: 1. Tune the ukulele to the proper notes. 2. Pluck the same string on the ukulele recording the frequency and pitch at each chosen note. 3. Determine the K constant for each of the notes at the given frequencies and pitches, using the two following models. a. 𝐾 𝐿1 = 𝑃 (? −? 𝑜 ) b. 𝐾 𝑊𝐹 = 𝑃 𝑙𝑜?(? / ? 𝑜 ) Hypothesis : Both models present accurate representations when determining the relationship between frequency and pitch. Data and Analysis : 𝑓 𝑐 4 = 282 ± 39 Hz Tension = 305 g Model 1 Pitch Frequency (Hz) 2 292 ± 48 𝐾 𝐿1 = 𝑃 1 (? 1 −? 𝑐4 ) = 0.20 ± 9.6 12 537 ± 44 𝐾 𝐿2 = 𝑃 2 (? 2 −? 𝑐4 ) = 0.47 ± 2.1 9 446 ± 59 𝐾 𝐿3 = 𝑃 3 (? 3 −? 𝑐4 ) = 0.55 ± 3.2 Model 2 Pitch Frequency (Hz)
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