Lab 11 - Waves and Sound - Duplicate

# 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 F_1 = 0.1 * 9.81 F_2 = 0.2 * 9.81 lambda_1 = (2*L)/1 lambda_2 = (2*L)/2 lambda_3 = (2*L)/3 lambda_4 = (2*L)/4 lambda_5 = (2*L)/5 print(lambda_1,lambda_2,lambda_3,lambda_4,lambda_5) f_1 = (np.sqrt(F_1/mu))/lambda_1 f_2 = (np.sqrt(F_1/mu))/lambda_2 f_3 = (np.sqrt(F_1/mu))/lambda_3 f_4 = (np.sqrt(F_1/mu))/lambda_4 f_5 = (np.sqrt(F_1/mu))/lambda_5 print(f_1,f_2,f_3,f_4,f_5) f_6 = (np.sqrt(F_2/mu))/lambda_1 f_7 = (np.sqrt(F_2/mu))/lambda_2 f_8 = (np.sqrt(F_2/mu))/lambda_3 f_9 = (np.sqrt(F_2/mu))/lambda_4 f_10 = (np.sqrt(F_2/mu))/lambda_5 print(f_6,f_7,f_8,f_9,f_10)

#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 R = np.sqrt(F_1/mu) actualL_1 = R/11.2 actualL_2 = R/22.3 actualL_3 = R/35.5 actualL_4 = R/48.7 actualL_5 = R/61.2 print(actualL_1,actualL_2,actualL_3,actualL_4,actualL_5) K = np.sqrt(F_2/mu) actualL_6 = K/16.3 actualL_7 = K/33 actualL_8 = K/52.5 actualL_9 = K/70 actualL_10 = K/87.3 print(actualL_6,actualL_7,actualL_8,actualL_9,actualL_10) pe_1 = ((actualL_1 - lambda_1)/actualL_1)*100 pe_2 = ((actualL_2 - lambda_2)/actualL_2)*100 pe_3 = ((actualL_3 - lambda_3)/actualL_3)*100 pe_4 = ((actualL_4 - lambda_4)/actualL_4)*100 pe_5 = ((actualL_5 - lambda_5)/actualL_5)*100 print(pe_1,pe_2,pe_3,pe_4,pe_5) pe_6 = ((actualL_6 - lambda_1)/actualL_6)*100 pe_7 = ((actualL_7 - lambda_2)/actualL_7)*100 pe_8 = ((actualL_8 - lambda_3)/actualL_8)*100 pe_9 = ((actualL_9 - lambda_4)/actualL_9)*100 pe_10 = ((actualL_10 - lambda_5)/actualL_10)*100 print(pe_6,pe_7,pe_8,pe_9,pe_10)

#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) nmclamda_1 = v_air/132 nmclamda_2 = v_air/269 nmclamda_3 = v_air/405 nmclamda_4 = v_air/529 nmclamda_5 = v_air/656 print(nmclamda_1,nmclamda_2,nmclamda_3,nmclamda_4,nmclamda_5) print(lambda_1,lambda_2,lambda_3,lambda_4,lambda_5) Tf_1 = (v_air/((2*L)/1)) Tf_2 = (v_air/((2*L)/2)) Tf_3 = (v_air/((2*L)/3)) Tf_4 = (v_air/((2*L)/4)) Tf_5 = (v_air/((2*L)/5)) print(Tf_1,Tf_2,Tf_3,Tf_4,Tf_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()