Speaker Enclosure Calc

This program calculates acoustic parameters for a bass-reflex (ported) speaker enclosure, taking ten user-supplied driver and cabinet measurements as inputs. For each frequency from 15 Hz to 250 Hz in 5 Hz steps, it computes and displays the output power and admittance using a 4×4 matrix determinant solved via a brute-force permutation loop. The determinant subroutine at line 1010 iterates over all combinations of four distinct column indices to evaluate the Leibniz expansion of the determinant, toggling the sign variable `E` to handle the alternating sign. Physical constants embedded in the formulas (e.g., 1.43E6, 3.49E-2, 39.4784) encode relationships between SI units and the acoustic impedance model.

---

Program Structure

The program is divided into three logical phases. Lines 7–136 handle initialization and user input, collecting ten parameters: coil resistance (RC), mounting compliance (MC), speaker radius (RS), enclosure volume (V), BL product (BL), free resonance (FO), port radius (RP), port length (LP), speaker damping (SD), and port damping (PD). Lines 140–300 precompute the stiffness matrix B and compliance matrix C from the physical parameters. Lines 310–900 form the main frequency sweep loop (48 iterations, 5 Hz steps starting at 15 Hz), building the system matrix A at each frequency and repeatedly calling the determinant subroutine to solve the acoustic circuit equations.

Matrix Determinant Subroutine (Lines 1010–1240)

The subroutine at line 1010 computes the determinant of the 4×4 matrix A using an explicit Leibniz (permutation) expansion. Four nested loops over indices I, J, K, and X enumerate all combinations of four distinct column indices, accumulating the signed product A(1,I)*A(2,J)*A(3,K)*A(4,X) into D. The sign variable E (initialized to 1 at line 10) is toggled by LET E=-E at lines 1195 and 1215 to implement the alternating sign rule. This approach avoids any pivot-based Gaussian elimination, at the cost of evaluating all 4! = 24 terms explicitly.

Cramer’s Rule Application

The main loop applies Cramer’s rule to solve for the velocity components of the acoustic circuit. The determinant of the unmodified matrix is stored as A0. Each subsequent call to the subroutine substitutes a column of A with the forcing vector (derived from IS = BL/RC) and saves the result as A1, A2, A3, and D (for the fourth column). The column is restored from the temporary array T between calls. Velocity components VA, VB, VC, VD are then ratios of the modified determinants to A0.

Frequency Sweep and Output

The frequency sweep runs from 15 Hz to 250 Hz in steps of 5 Hz (48 iterations of the FOR Z=1 TO 48 loop, with F initialized to 10 and incremented by 5 each iteration). At each frequency, three values are printed: frequency F, acoustic output power PS, and cone admittance magnitude IM. Power is computed as:

• P = 3.49E-2 * F^2 * RS^4 (radiation resistance factor)
• PS = P * ((VA+VC)^2 + (VB+VD)^2) (total radiated power combining real and imaginary velocity components)

Admittance IM is the magnitude of the cone current divided by BL, computed as SQR(IA*IA + IB*IB)/BL.

Bugs and Anomalies

• Lines 760–770: Both VA and VB are assigned A1/A0, making them identical. VB should almost certainly be A2/A0 to represent the imaginary component of the first velocity. This is likely a transcription error from the original magazine listing.
• Line 700: The loop reads FOR I=I TO 4 instead of FOR I=1 TO 4. Since I retains the value 4 from the previous loop exit, this loop executes only once (for I=4), meaning A(1,4), A(2,4), and A(3,4) are not zeroed before the fourth determinant call. This is almost certainly a typo for FOR I=1 TO 4.
• Sign toggling logic: The placement of LET E=-E at line 1215 (inside the J loop but outside the K loop) interacts with the toggling at line 1195 (inside the X loop). The global state of E persists across subroutine calls since E is never reset inside the subroutine. Because there are exactly 24 sign toggles per complete determinant evaluation (an even number), E returns to its entry value after each full call, but this relies on all loops completing without early exits — the GO TO skips do affect the toggle count and the correctness of the sign sequence is non-obvious.
• Line 150: The constant 39.47818 is used here but 39.4784 is used at line 420 — a minor inconsistency likely from manual transcription.

Key BASIC Idioms

• Use of 2* PI*F for angular frequency ω throughout the matrix construction.
• Column save/restore via the temporary array T(4) to implement Cramer’s rule without a separate matrix copy.
• Physical embedded constants (e.g., 1.43E6, 0.219) fold unit conversions and π factors into single numeric literals.