In-phase coupled resonators radiate four times the power of one resonator.

Evidence

Three of the four cases mentioned here are illustrated in figure 13.7. Starting with the same pressure in both resonators, there is a resonant addition of amplitudes resulting in louder sound. Since the sound is louder, the energy is drained faster from the resonators (figure 13.7, left). For in-phase oscillation of the resonators, their amplitudes add, giving approximately twice the amplitude far away, and thus instead of twice the power, we get four times the power of a single resonator. This means a doubling of the rate of energy dumping per resonator—that is, exponential decay with an exponent that is twice as large, and a Q half as large (see section 10.3). Indeed, from the figure we see this faster decay and an estimate gives a Q of 9 for the in-phase case as compared to 18 for the single oscillator. — Eric J. Heller, Why You Hear What You Hear- An…, 1233

Categorization

• DEFINE: Concrete mechanism showing how amplitude addition quadruples radiated power and accelerates energy drain.
• corroborated: 2 independent passages support this claim — Eric J. Heller, Why You Hear What You Hear- An…, 1233
• XREF: connects to: Mutual resonance between sources boosts combined power beyond their sum; Oppositely phased resonators short-circuit each other and prolong sound decay.; Doubling sound wave amplitude quadruples the power delivered

Broader Connections

• Doubling sound wave amplitude quadruples the power delivered #corroborates (0.82)