Mutual resonance between sources boosts combined power beyond their sum
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 (
#exemplifies, via linked claim)
On the other hand, if the sound waves are uncorrelated, then they do not add algebraically, like correlated waves; instead, we must add the powers of the individual waves together. As stated earlier, the power in a waveform is proportional to the square of the pressure levels, so in order to sum the powers of the waves, we must square the pressure amplitudes before adding them together. If we want the result as a pressure, then we must take the square root of the result. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 244 (
#qualifies, via linked claim)
Categorization
- XREF: connects to: Adjacent in-phase sources boost each piston’s efficiency N-fold through mutual pressure; Reciprocity forces resonance gain to be symmetric between inside and outside.; In-phase coupled resonators radiate four times the power of one resonator. — Eric J. Heller, Why You Hear What You Hear- An…, 1233 (+2 more)
Broader Connections
- In-phase coupled resonators radiate four times the power of one resonator.
#exemplifies(0.90) — Eric J. Heller, Why You Hear What You Hear- An…, 1233 - Uncorrelated sound waves sum by power, not by amplitude.
#qualifies(0.80) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 244 - Reciprocity forces resonance gain to be symmetric between inside and outside.
#qualifies(0.75)