Two opposing coupled resonances can cancel response at intermediate frequencies

Evidence

Both modes, the in-phase mode of lower frequency f = 10.2, and the out-of-phase higher frequency mode f = 15.8, stand out as resonances. The force is in phase with the velocity when the phase shift is π/2, shown by the green dashed line. Although the force is also in phase with the velocity around the test frequency f = 13 (dashed vertical line), there is little power delivered at that frequency because the velocity attained by the pendulum is very small. This is owing to the out-of-phase competition of both resonances, one above and one below f = 13. One of the resonances “wants” the velocity to lead the drive, and the other, to lag it, so as a result there is very little velocity at all. — Eric J. Heller, Why You Hear What You Hear- An…, 1029

Categorization

• QUESTION: This competition between adjacent resonances suppressing velocity at an intermediate frequency suggests a mechanism worth exploring for how coupled air-column modes shape wind-instrument timbre.
• XREF: Relates to why certain driving frequencies in coupled systems (like reeds on air columns, section 16.7) produce weak output despite nominal resonance conditions.