Resonance peaks are always balanced by anti-resonant valleys nearby

Evidence

Suppose we have a body that extends to infinity and returns no echoes. The power as a function of frequency will be smooth, and forms a reference level. If echoes and resonances are induced by adding structures and boundaries some distance away, resonances will develop, enhancing the power at certain frequencies. The average power theorem dictates that resonance peaks must rob Peter to pay Paul; resonance peaks must be compensated by nearby dips where the power is lower—that is, anti-resonant valleys. The power averaged over large enough frequency intervals must equal the power that would be delivered if the echoes and their resonances didn’t exist. — Eric J. Heller, Why You Hear What You Hear- An…, 1092

Categorization

Category: Causal Relationships

• SEED: The ‘rob Peter to pay Paul’ conservation picture — resonance enhancement inevitably costs sensitivity elsewhere — is a ready-made article angle on what resonances really do.
• CANDY: Resonance peaks are fiscally conservative: they rob Peter to pay Paul, balanced by compensating dips.

Related

• Resonance peaks always require compensating anti-resonant valleys in the spectrum (similarity 0.96)
• Resonance peak height scales with the strength of the returning echo amplitude (similarity 0.83)
• Very early reflections can resonantly boost power across the whole audible range (similarity 0.82)
• Resonances compete for power as a zero-sum game when crowded together. (similarity 0.82)
• Resonance occurs where impedance vanishes, yielding huge response (similarity 0.80)
• Resonance requires round-trip reflections arriving in phase with the source (similarity 0.80)
• Power fluctuations persist even where resonances overlap completely (similarity 0.79)
• Audible resonance requires balancing energy confinement against energy leakage (similarity 0.78)
• Confinement reflections amplify sources only when wave sign is preserved (similarity 0.78)
• Resonance requires old amplitude to add constructively with new drive (similarity 0.78)
• Resonance lowers impedance dramatically at an oscillator’s natural frequency (similarity 0.78)
• Resonant peaks bother more listeners than nulls because they occupy most of the room (similarity 0.78)
• Strong resonances cannot be packed tightly because they drain surrounding power (similarity 0.78)
• Resonant reflections raise impedance in throats and reproducers (similarity 0.78)