A free mass has impedance proportional to its mass and forcing frequency

Evidence

In section 1.1, we mentioned that a free solid mass such as a coin has an impedance proportional to its mass m—specifically, it is Z(f) = 2π fm, where f is the frequency of the sinusoidal force. Indeed, a free, perfectly rigid object (not attached to anything) has no resistance to acceleration other than its own mass. A sinusoidal force acts for a shorter time in each direction at higher frequency f, so the velocity the forced object attains decreases as 1/f, making the impedance (applied force/velocity attained) proportional to the forcing frequency f. — Eric J. Heller, Why You Hear What You Hear- An…, 996

Categorization

• DEFINE: Grounds the abstract concept of impedance in the concrete case of a free rigid mass, connecting mechanics to acoustics — core to the reader’s why-we-hear question since impedance governs how the eardrum responds to sound.
• XREF: Provides the mechanical impedance foundation that carries over to acoustic impedance, the eardrum, and the cochlea — all central in hearing.