Estimate cavity resonance frequencies and nodal structures for Experiment 15

Frequencies of the first two resonances

(RowDefault)

Edit the assignments for the frequencies of these the two lowest modes
and evaluate the following cell:

Clear[f];
f[1,0]=1131.0 (* Hz *)
f[0,1]=1504.0(* Hz *)

Frequency estimates  of the other modes

Assume that air is non-dispersive, so that frequency and wave number are proportional.
If the box is rectangular, then the number of nodal lines along x and along y gives the x and y components of the mode’s wave vector. Thus, if n and m are the nodal line counts in x and y, respectively, then:

((((Subscript[k, n,m])))^2) =  (Subscript[k, x]^2) + (Subscript[k, y]^2) =  (((n (Subscript[k, 1,0])))^2) + (((m (Subscript[k, 0,1])))^2)

If frequency is proportional to wave number, then we can substitute frequency for wave number in the above expression:

((((Subscript[f, n,m])))^2) =  (((n (Subscript[f, 1,0])))^2) + (((m (Subscript[f, 0,1])))^2)

Evaluate the following to generate a function for  (Subscript[f, n,m]):

f[n_Integer,m_Integer]:=(Sqrt[1.0(((n f[1,0]))^2)+1.0(((m f[0,1]))^2)])

Examples:

f[1,1]
f[2,1]

Table of frequency estimates  and corresponding n, m values

Generate a table of the frequencies and the associated n, m nodal line counts:

freqs=Table[{f[n,m],{n,m}},{n,0,5},{m,0,5}];

Use Flatten[ ] to turn the matrix returned by Table[] into a list, then Sort by frequency, then remove the first entry (n = m = 0) using Rest:

freqs=(Flatten[freqs,1]//Sort//Rest)

Keep frequencies below, say, 5.5 kHz using Select[]:

(freqs=Select[freqs,(First[#]<=5500.) &])//Column