# 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 u = 0.0012 v = np.sqrt((9.8*.1)/u) waveL1 = (2*L)/1 f1 = v/waveL1 waveL2 = (2*L)/2 f2 = v/waveL2 waveL3 = (2*L)/3 f3 = v/waveL3 waveL4 = (2*L)/4 f4 = v/waveL4 waveL5 = (2*L)/5 f5 = v/waveL5 v2 = np.sqrt((9.8*.2)/u) newf1 = v2/waveL1 newf2 = v2/waveL2 newf3 = v2/waveL3 newf4 = v2/waveL4 newf5 = v2/waveL5 print(waveL1, waveL2, waveL3, waveL4, waveL5) print(f1, f2, f3, f4, f5) print(newf1, newf2, newf3, newf4, newf5)

#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. v = np.sqrt((9.8*.1)/u) waveL100_1 = v/11.2 waveL100_2 = v/22.3 waveL100_3 = v/35.5 waveL100_4 = v/48.7 waveL100_5 = v/61.2 v2 = np.sqrt((9.8*.2)/u) waveL200_1 = v2/16.3 waveL200_2 = v2/33 waveL200_3 = v2/52.5 waveL200_4 = v2/70 waveL200_5 = v2/87.3 #To calculate % Error, use (Corresponding - Theoretical)/ Theoretical x 100 error1 = (waveL100_1 - waveL1)/(waveL1 * 100) error2 = (waveL100_2 - waveL2)/(waveL2 * 100) error3 = (waveL100_3 - waveL3)/(waveL3 * 100) error4 = (waveL100_4 - waveL4)/(waveL4 * 100) error5 = (waveL100_5 - waveL5)/(waveL5 * 100) errornew1 = (waveL200_1 - waveL1)/(waveL1 * 100) errornew2 = (waveL200_2 - waveL2)/(waveL2 * 100) errornew3 = (waveL200_3 - waveL3)/(waveL3 * 100) errornew4 = (waveL200_4 - waveL4)/(waveL4 * 100) errornew5 = (waveL200_5 - waveL5)/(waveL5 * 100) print(waveL100_1, waveL100_2, waveL100_3, waveL100_4, waveL100_5) print(waveL200_1, waveL200_2, waveL200_3, waveL200_4, waveL200_5) print(error1, error2, error3, error4, error5) print(errornew1, errornew2, errornew3, errornew4, errornew5)

#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) cWaveL1 = v_air/132 cWaveL2 = v_air/269 cWaveL3 = v_air/405 cWaveL4 = v_air/529 cWaveL5 = v_air/656 print(cWaveL1, cWaveL2, cWaveL3, cWaveL4, cWaveL5) L = 1.22 waveL1 = (2*L)/1 f1 = v_air/waveL1 waveL2 = (2*L)/2 f2 = v_air/waveL2 waveL3 = (2*L)/3 f3 = v_air/waveL3 waveL4 = (2*L)/4 f4 = v_air/waveL4 waveL5 = (2*L)/5 f5 = v_air/waveL5 print(waveL1, waveL2, waveL3, waveL4, waveL5) print(f1, f2, f3, f4, f5)

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()