# 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 import pandas as pd import numpy as np

#Code cell provided for calculations of the theoretical resonant wavelenths and frequencies. #Show your work to receive credit. L = 1.22 mu = .0012 m100 = .1 m200 = .2 F100 = mu * m100 F200 = mu * m200 #48 lam = 2*L/n -> n = # of wavelenghts (1-5) lam101 = (2*L) lam102 = (2*L)/2 lam103 = (2*L)/3 lam104 = (2*L)/4 lam105 = (2*L)/5 #44 vel = sqrt(F/mu) v100 = np.sqrt(F100/mu)*100 #without the 100 multiplier my Hz are off by a factor of 100 v200 = np.sqrt(F200/mu)*100 #43 vel = w/k = f*lam => frec = vel/lam f101 = v100/lam101 f102 = v100/lam102 f103 = v100/lam103 f104 = v100/lam104 f105 = v100/lam105 f201 = v200/lam101 f202 = v200/lam102 f203 = v200/lam103 f204 = v200/lam104 f205 = v200/lam105 print (lam101,lam102,lam103,lam104,lam105) print (f101,f102,f103,f104,f105) print (f201,f202,f203,f204,f205)

#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 #43 vel = w/k = f*lam => frec = vel/lam #44 vel = sqrt(F/mu) #frec is known, vel is known. #lam = vel/frec f1 = 11.2 f2 = 22.3 f3 = 35.5 f4 = 48.7 f5 = 61.2 f21 = 16.3 f22 = 33 f23 = 52.5 f24 = 70 f25 = 87.3 lam1 = v100/f1 lam2 = v100/f2 lam3 = v100/f3 lam4 = v100/f4 lam5 = v100/f5 lam21 = v200/f21 lam22 = v200/f22 lam23 = v200/f23 lam24 = v200/f24 lam25 = v200/f25 print (lam1,lam2,lam3,lam4,lam5) print (lam21,lam22,lam23,lam24,lam25) error1 = (lam1-lam101)/(lam101*100) error2 = (lam2-lam102)/(lam102*100) error3 = (lam3-lam103)/(lam103*100) error4 = (lam4-lam104)/(lam104*100) error5 = (lam5-lam105)/(lam105*100) error21 = (lam21-lam101)/(lam101*100) error22 = (lam22-lam102)/(lam102*100) error23 = (lam23-lam103)/(lam103*100) error24 = (lam24-lam104)/(lam104*100) error25 = (lam25-lam105)/(lam105*100) print(error1,error2,error3,error4,error5) print(error21,error22,error23,error24,error25)

#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) #43 vel = w/k = f*lam => frec = vel/lam # lam = vel/f #49 lam = (2L)/n => same as Experiment 1 #2.44 1.22 0.8133333333333334 0.61 0.488 f1 = 132 f2 = 269 f3 = 405 f4 = 529 f5 = 656 lam1 = v_air/f1 lam2 = v_air/f2 lam3 = v_air/f3 lam4 = v_air/f4 lam5 = v_air/f5 theof1 = v_air/lam101 theof2 = v_air/lam102 theof3 = v_air/lam103 theof4 = v_air/lam104 theof5 = v_air/lam105 print(lam1,lam2,lam3,lam4,lam5) print(theof1,theof2,theof3,theof4,theof5)

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(modes): 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()