Impedance can peak or dip at resonance depending on measurement point

Evidence

In other situations, the impedance does have a maximum on resonance. If we are pushing sinusoidally on the mass, and the far end of the spring is connected to a wall, the mass oscillates with large amplitude on resonance, reaching high velocity and lowering the impedance. But suppose we push on the end of the spring opposite to the mass (see figure 10.3). This requires some thought—it can’t be attached to a rigid wall anymore, because that wouldn’t move at all. Instead, we decide to specify the movement of the free end of the spring, say, the velocity is νend = ν0 sin(2πf0t). Now, the velocity is specified, and the force on the end required to keep up that velocity is to be measured and put into the definition of impedance at the free end, Z = force/velocity. It is the impedance of the spring end, not the mass, that is being measured. It doesn’t have to be the same! Velocity of the wall is specified and is steadily oscillating, but on resonance, the mass again moves violently. We aren’t measuring that velocity, but the end of the spring feels large forces. Therefore, the impedance as measured from the free end of the spring is a maximum on resonance. — Eric J. Heller, Why You Hear What You Hear- An…, 1009

Categorization

• DEFINE: Clarifies that impedance is not an intrinsic property — it depends entirely on where and how it is measured.
• QUESTION: This point — that impedance is measurement-location dependent — seems like it would matter for how the cochlea ‘loads’ the ossicles; worth checking whether Heller applies this later.