Lab 9 Wave

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Houston Community College *

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2125

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Electrical Engineering

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May 1, 2024

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Objective: To determine the speed of a wave. Equipment: Simulation Theory: For any wave (electromagnetic or physical wave: For wave on string: v = fλ v = speed of wave (m/s) f = frequency of oscillation (hz) ʎ = wave length (m) v = √ f μ f = tension of the string (N) µ = linear mass density (mass/length) ʎ π 2π v = fλ f = v∙ 1 λ y-axis x-axis slope = v

Procedure: The simulation was set to a specified frequency and the wavelength was measured. This was repeated for each frequency. The velocity was then calculated from the measured wavelengths. Graph: Data: f (Hz) λ 1 (m) λ 2 (m) λ (m) 1/ λ m -1 v = f λ (m.s) 1.50 0.043 0.044 0.043 5 22.99 0.065 2 1.75 0.036 0.035 0.035 5 28.16 7 0.062 1 2.00 0.031 0.032 0.031 5 31.75 0.063 0 2.25 0.028 0.029 0.028 5 35.09 0.064 1 2.50 0.023 0.025 0.024 41.67 0.060 0 2.75 0.023 0.023 0.023 43.48 0.063 4 3.00 0.022 0.021 0.021 5 46.51 0.064 5 Average v 0.063 2 Calculations: From graph: 20 25 30 35 40 45 50 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 1.50 1.75 2.00 2.25 2.50 2.75 3.00 f(x) = 0.06 x + 0.04 Lab 9: Waves 1/λ (m) f (hz)

f = v∙ 1 λ y = 0.0621 x + 0.0352 Calculated average v: Standard Deviation of calculated v’s = 0.0016 Percent difference between average v and v from graph: 0.0621 − 0.0632 0.0621 + 0.0632 2 × 100 = 1.755% Results: Calculated v: v = 0.0632 ± 0.0016 m/s v from graph: v = 0.0621 m/s Discussion: The velocity was determined to be 0.0632±0.0016 m/s based on the data calculations and 0.0621 m/s based on the slope of the graph. The percent difference was found to be 1.755% indicating that the measurements were very accurate. Any difference may have been due to the variation in when the simulation was paused to measure the wavelength. Questions: Why do you take two values of wavelength? Taking two measurements helps to reduce the errors and ensures the accuracy of the results. Why do you need to keep the amplitude of each wave segment more over the same? If the amplitude varies for each segment, then we cannot measure the wavelength accurately since it will differ for each section. The will result in inconsistency in our calculated wave speed. v = 0.0632 m/s

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What will happen if you increase the tension of the string? Explain it clearly. If the tension is increased and linear density remains the same then the result will be a higher wave speed. The theory explains that wave speed is related to tension (f) and the linear density(µ) v = √ f μ . When the tension (f) is increased then the resulting v will increase.

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