Lab 13 - standing waves on a string

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Arizona State University *

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Electrical Engineering

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Dec 6, 2023

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docx

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Lab 13: Standing Waves on a String 1. Testable Questions: A. How does the wave frequency relate to the wavelength? B. How does the wave frequency relate to the tension force on the string? 2. Hypothesis: A. If the wavelength increases, the wave frequency will decrease, because a longer wavelength is going to result in less frequent waves. B. If the tension force increases, then the wave frequency will also increase, because a tighter string will require more work on the wave to maintain a constant wavelength. 3. Variables: A. Controls: Tension force (F T ), Linear density of the string ( ), string length (L) Independent: wavelength ( ) Dependent: wave Frequency ( f ) B. Controls: Wavelength ( ), Linear density of the string ( ), string length (L) Independent: Tension Force (F T ) Dependent: wave Frequency ( f ) 4. Experimental Design: A. F T , , L i (m) f (Hz) 1 – 8 1-8 f 1-8 B. , , L i F T (N) f (Hz) 1 – 8 F T 1-8 f 1-8 5. Materials: String vibrator C clamp
String Pulley Various masses Sine wave generator Meter stick Cent-o-gram balance 6. Procedures: Set up: A. 1. Set up as shown above 2. measure and calculate the linear density of the string (control ), record in grams/meters (kg/m) 3. Record the tension force (control F T ), record in N 4. Turn on the Sine Wave Generator and decrease the frequency until you can clearly measure the wavelength 5. record the frequency from the Sine wavelength generator in Hz. 6. calculate the wavelength (distance (m) of the string from the pulley to Sine wave generator / number of standing waves observed). 7. complete measurements for 1, 1.5, 2, 2.5… standing waves, 8 total measurements. 8. equation investigated: f * = v = FT B. 1. Keep the setup the same as part A 2. Record the length of the string (control = L). 3. Place a small mass (100g) on the string that is hanging from the pulley and calculate the new tension force (F = ma) and record as the independent variable 4. Turn on the sine wave generator and decrease the frequency until you can clearly measure 1 standing wave. 5. Record the frequency from the Sine wave generator in Hz when 1 standing wave is visible
6. Complete 8 measurements for a T F and 8 corresponding frequencies 7. Equation investigated: f * = v = FT 8. Data: A. = 0.0016 kg L = 1.320 m Ft = 1962 N i (m) (m) ^-1 f (Hz) 1 1.32 0.76 26.7 2 0.88 1.14 28.3 3 0.66 1.52 38.2 4 0.53 1.89 48.0 5 0.44 2.27 57.3 6 0.38 2.63 67.7 7 0.33 3.03 78.2 8 0.29 3.45 89.0 B. = 0.0016 kg L = 1.320 m i F T (N) F T (N) (^1/2) f (Hz) 1 0.98 1.0 18.5 2 1.96 1.4 26.0 3 2.94 1.7 36.0 4 3.92 2.0 41.0 5 4.90 2.2 46.0 6 5.88 2.4 47.0 7 6.66 2.6 50.0 8 7.84 2.8 51.8 9. Analysis: A.
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