# Run this Python cell by selecting it and then pressing shift-enter # Do not change anything in this cell # These commands load the libraries for Python to use !pip install pandas import pandas as pd import numpy as np !pip install openpyxl

#Code cell provided for calculations of the theoretical resonant wavelenths and frequencies. #Show your work to receive credit. L = 1.2 mu = 0.0012 g = 9.8 F1 = 0.1 * g F2 = 0.2 * g waveL_1 = 2*L/1 waveL_2 = 2*L/2 waveL_3 = 2*L/3 waveL_4 = 2*L/4 waveL_5 = 2*L/5 print("Wavelengths") print(waveL_1) print(waveL_2) print(waveL_3) print(waveL_4) print(waveL_5) v1 = np.sqrt(F1/mu) f1_1 = v1/waveL_1 f1_2 = v1/waveL_2 f1_3 = v1/waveL_3 f1_4 = v1/waveL_4 f1_5 = v1/waveL_5 print("\nFrequency 100g") print(f1_1) print(f1_2) print(f1_3) print(f1_4) print(f1_5) v2 = np.sqrt(F2/mu) f2_1 = v2/waveL_1 f2_2 = v2/waveL_2 f2_3 = v2/waveL_3 f2_4 = v2/waveL_4 f2_5 = v2/waveL_5 print("\nFrequency 200g") print(f2_1) print(f2_2) print(f2_3) print(f2_4) print(f2_5)

#Code cell provided for calculations of the corresponding wavelengths. Show your work to receive credit. #It may be helpful to first calculate the wavespeed using Eq. 44 for both scenarios and then use Eq. 43 to use #the wave speed to convert the frequencies from Table 2 into a wavelength. #To calculate % Error, use (Corresponding - Theoretical)/ Theoretical x 100 def percentError(corr_wavelength, theo_wavelength): return ((corr_wavelength - theo_wavelength) / theo_wavelength * 100) wL1_100 = v1 / 11.2 wL2_100 = v1 / 22.3 wL3_100 = v1 / 35.5 wL4_100 = v1 / 48.7 wL5_100 = v1 / 61.2 print("Wavelength Corresponding 100g") print(wL1_100) print(wL2_100) print(wL3_100) print(wL4_100) print(wL5_100) print("\nPercent Error 100g") print(percentError(wL1_100, waveL_1)) print(percentError(wL2_100, waveL_2)) print(percentError(wL3_100, waveL_3)) print(percentError(wL4_100, waveL_4)) print(percentError(wL5_100, waveL_5)) wL1_200 = v2 / 16.3 wL2_200 = v2 / 33.0 wL3_200 = v2 / 52.5 wL4_200 = v2 / 70.0 wL5_200 = v2 / 87.3 print("\nWavelength Corresponding 200g") print(wL1_200) print(wL2_200) print(wL3_200) print(wL4_200) print(wL5_200) print("\nPercent Error 200g") print(percentError(wL1_200, waveL_1)) print(percentError(wL2_200, waveL_2)) print(percentError(wL3_200, waveL_3)) print(percentError(wL4_200, waveL_4)) print(percentError(wL5_200, waveL_5))

#Code cell provided for calculations of the corresponding wavelengths #and the theoretical resonant wavelengths and frequencies. Show your work to receive credit. #Eq. 43 and 49 from the Lab Manual will be helpful. #The first corresponding wavelength column is for your measured frequencies #The second theo. wavelength column is using Eq. 49, then convert this to frequency with Eq. 43 v_air = 340.3 #m/s (speed of sound in air) sWaveL1_corr = v_air/132 sWaveL2_corr = v_air/269 sWaveL3_corr = v_air/405 sWaveL4_corr = v_air/529 sWaveL5_corr = v_air/656 print("Corresonding Wavelengths") print(sWaveL1_corr) print(sWaveL2_corr) print(sWaveL3_corr) print(sWaveL4_corr) print(sWaveL5_corr) sWaveL1_theo = 2*L/1 sWaveL2_theo = 2*L/2 sWaveL3_theo = 2*L/3 sWaveL4_theo = 2*L/4 sWaveL5_theo = 2*L/5 print("\nTheoretical Wavelengths") print(sWaveL1_theo) print(sWaveL2_theo) print(sWaveL3_theo) print(sWaveL4_theo) print(sWaveL5_theo) sTheoF1 = v_air/sWaveL1_theo sTheoF2 = v_air/sWaveL2_theo sTheoF3 = v_air/sWaveL3_theo sTheoF4 = v_air/sWaveL4_theo sTheoF5 = v_air/sWaveL5_theo print("\nTheoretical Frequencies") print(sTheoF1) print(sTheoF2) print(sTheoF3) print(sTheoF4) print(sTheoF5)

df1 = pd.read_excel("Lab11_classdata.xlsx") #Here we take the columns of the xlsx files and separate them so that each of the resonant frequencies #for each normal mode can be analyzed separately; we also remove any empty rows with .dropna() mode1 = df1['number1'].dropna() mode2 = df1['number2'].dropna() mode3 = df1['number3'].dropna() mode4 = df1['number4'].dropna() mode5 = df1['number5'].dropna() stringmodes = [mode1,mode2,mode3,mode4,mode5]

def get95PercentConfidenceInterval(mean,sigma,N): sigma_x = sigma/np.sqrt(N) print('The Error of the mean is '+str(sigma_x)+'.') lbof95CI = mean - 1.96*sigma_x print('The Lower Bound of the 95% confidence interval is '+str(lbof95CI)+'.') ubof95CI = mean + 1.96*sigma_x print('The Upper Bound of the 95% confidence interval is '+str(ubof95CI)+'.') widthof95CI = ubof95CI - lbof95CI print('The Width of the 95% confidence interval is '+str(widthof95CI)+'.')

for index,mode in enumerate(stringmodes): mean_mode = np.mean(mode) std_dev_mode = np.std(mode) print('Statistics for the resonant frequency of normal mode '+str(index+1)) print('Mean: '+str(mean_mode)) print('Std. Dev.: '+str(std_dev_mode)) print('samples: ' + str(len(mode))) get95PercentConfidenceInterval(mean_mode,std_dev_mode,len(mode)) print()