High-frequency forcing is resisted by mass while low-frequency forcing is resisted by spring stiffness

Evidence

The physical situation is a mass connected to a rigid wall by a spring, and the applied force pushes on the mass (figure 10.5). For high-frequency forcing (large f), the spring is almost unnoticeable—the force is reversing to and fro so quickly that the mass hardly has a chance to move and compress the spring; only the mass is resisting the force. The first term in equation 10.8 dominates—the mass term. This is mass-dominated impedance. Notice that the first term increases with increasing f, while the second term decreases. For low-frequency forcing, the mass barely accelerates; but there is plenty of time to displace it, compressing the spring; thus it is the spring that pushes back. The second term in equation 10.8 dominates—the stiffness term. The denominator gets small, and the result gets large. This regime is stiffness-dominated impedance. — Eric J. Heller, Why You Hear What You Hear- An…, 1001

Categorization

• DEFINE: Explains mass-dominated vs stiffness-dominated impedance regimes — the frequency-dependent response that underlies how physical systems (including hearing structures) filter frequencies.
• XREF: Mass versus stiffness domination maps directly onto the basilar membrane and cochlear mechanics in hearing — different frequencies excite different regions — and onto the middle-ear’s design tradeoffs in acoustics.