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The science
Superposition of two sources
Sound in air obeys the linear wave equation, so pressures from two loudspeakers simply add. For a single frequency each speaker gives pi = (ai/ri) cos(k ri + φi - ωt) with k = 2π/λ, λ = c/f and the speed of sound c = 331.3 + 0.606 T m/s (T in °C). Writing each term as a complex amplitude P = ∑ ai ej(k ri + φi)/ri, the time-averaged intensity is I ∝ |P|2/2 and the level is L = 10 log10(|P|2/2 / pref2) with pref = 20 μPa.
Nodes, antinodes and lobes
Where the path difference Δ = rB - rA satisfies kΔ + φ = 2πm the waves arrive in step and the level peaks (constructive); at kΔ + φ = (2m+1)π they cancel for equal amplitudes (destructive). Curves of constant Δ are hyperbolas with the speakers as foci, drawn on the map. Far away (distance much larger than d) the hyperbolas become straight lobes at sin θm = (m - φ/2π) λ/d, so the number of lobes grows with d/λ. Between the speakers the two waves travel in opposite directions and make a standing-wave pattern with nodes every λ/2.
Unequal sources and why real rooms differ
If the two levels differ the nulls fill in because |aA - aB| > 0 remains at the best cancellation, with depth 20 log10((aA + aB)/(aA - aB)) relative to the peaks. Lowering the temperature lowers c, so λ shrinks and more lobes appear at the same frequency.
Honest simplifications
The speakers are ideal point (or line) sources radiating equally in all directions; there are no reflections from walls or the floor, no air absorption, no directivity of real cones and no near-field effects. A real room adds reflected images that behave like more coherent sources, which is why measured nodes are never as deep as in this model. The 3D companion places the same two sources in an anechoic chamber, where reflections are absorbed.
Model checks: the lobe angles from the formula are compared with a brute-force scan of the summed far field; the number of nodes between the speakers is compared with a fine scan of |P|; and the mean of p(t)2 integrated over a period is compared with |P|2/2.