# 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. W = 2 * 1.22 W2 = 2 * 1.22/2 W3 = 2 * 1.22/3 W4 = 2 * 1.22/4 W5 = 2 * 1.22/5 print(W) print(W2) print(W3) print(W4) print(W5) #We note that the wavelengths are independent of mass v = np.sqrt((100 * 9.8/1000)/0.0012) F1 = v/W F2 = v/W2 F3 = v/W3 F4 = v/W4 F5 = v/W5 print(F1) print(F2) print(F3) print(F4) print(F5) #Since the mass is doubled, we now create f1, f2, f3... which are F1, F2, F3 * sqrt(2) f1 = F1 * np.sqrt(2) f2 = F2 * np.sqrt(2) f3 = F3 * np.sqrt(2) f4 = F4 * np.sqrt(2) f5 = F5 * np.sqrt(2) print(f1) print(f2) print(f3) print(f4) print(f5)

#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 wavelength_computation_and_error(mass, frequency, original_wavelength): wavelength = np.sqrt(9.8 * mass/0.0012)/frequency error = (wavelength - original_wavelength)/original_wavelength * 100 print(wavelength) print(error) wavelength_computation_and_error(0.1, 11.2, 2.44) wavelength_computation_and_error(0.1, 22.3, 1.22) wavelength_computation_and_error(0.1, 35.5, 0.8133333333333334) wavelength_computation_and_error(0.1, 48.7, 0.61) wavelength_computation_and_error(0.1, 61.2, 0.488) wavelength_computation_and_error(0.2, 16.3, 2.44) wavelength_computation_and_error(0.2, 33, 1.22) wavelength_computation_and_error(0.2, 52.5, 0.8133333333333334) wavelength_computation_and_error(0.2, 70, 0.61) wavelength_computation_and_error(0.2, 87.3, 0.488)

#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) L = 1.22 #m w_1 = v_air/132 w_2 = v_air/269 w_3 = v_air/405 w_4 = v_air/529 w_5 = v_air/656 wavelength_1 = 2 * L wavelength_2 = 2 * L/2 wavelength_3 = 2 * L/3 wavelength_4 = 2 * L/4 wavelength_5 = 2 * L/5 f1 = v_air/wavelength_1 f2 = v_air/wavelength_2 f3 = v_air/wavelength_3 f4 = v_air/wavelength_4 f5 = v_air/wavelength_5 print(f1) print(f2) print(f3) print(f4) print(f5) print(w_1) print(w_2) print(w_3) print(w_4) print(w_5) print(wavelength_1) print(wavelength_2) print(wavelength_3) print(wavelength_4) print(wavelength_5)

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()