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If we take some material and (somehow) increase its mass density or bulk modulus then its acoustic impedance will increase as $z = \sqrt{\rho \kappa}$. That is, it What is the physical reasoning behind this for (i) mass density and (ii) bulk modulus?

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imagine you wish to impedance test a block of some substance by hitting it with a mechanical impulse and observing its response. Let's do a crude version of this test by using a hammer in your hand as the impulse driver.

First we hit a soft rubber sponge. Its density is low and its stiffness is low. the hammer drives deeply into it and bounces back. the sponge suffered a lot of displacement and it took not much force to displace it; it exhibits low acoustic impedance.

Next we hit a chunk of tungsten. its density is high and its stiffness is high. the hammer bounces back violently. The tungsten deflection is almost zero but it took a severe force to displace it; its acoustic impedance is high.

A massive object is inertially clamped; an impulse bounces off = impedance is high.

A hard and unyielding object is stiffness-clamped; an impulse bounces off = impedance is high.

A dense, unyielding object therefore has very high acoustic impedance.

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