from math import *

## Exp W. Modes of short cylinder ##
u = 343 #speed of sound
l = 0.05
rho = 0.1
alpha = [[0, 1.84, 3.05, 4.20],
         [3.83, 5.33, 6.71, 8.02],
         [7.01, 8.54, 9.97, 11.35]]
fqn = [] #frequencies and respective quantum numbers
f = [] # frequencies

for n in range (0,4):
    for m in range (0,4):
        for j in range (1,4):
            qn = [n,m,j]
            frequency = u*sqrt((n**2/(4*l**2))+(((alpha[j-1][m])**2)/4*pi**2*rho**2))
            if frequency in f: # check for duplicatesq
                continue
            else:
                f.append(frequency)
                fqn.append([frequency,f'n={n}, m={m}, j={j}'])

for i in range(len(fqn)):
    print(sorted(fqn)[i])