Questions: Acoustic Impedance and Mechanical Impedance

Question 1

A diver shouts underwater near the surface. A person above the water can barely hear the shout. Which explanation is correct?

• A. Sound cannot travel upward because it is denser than the surrounding water
• B. The large impedance mismatch between water and air causes most acoustic energy to reflect at the boundary — very little transmits into the air above
• C. Sound travels faster in water, so it slows down too abruptly at the water-air interface and loses energy
• D. The frequency of the sound changes as it crosses the boundary, shifting it out of the audible range

Answer: (B)

Water has roughly 3,500 times greater acoustic impedance than air. When a wave hits a boundary with such a large mismatch, nearly all energy reflects back into the water and almost none transmits into the air. The same physics explains why you hear very little from an underwater speaker when you're standing above it. This is the direct consequence of the impedance ratio — not wave speed or density alone, but the product Z = ρv compared between the two media.

Question 2

Two materials have the same wave speed but different densities. When a sound wave crosses the boundary from one to the other:

• A. No reflection occurs, because equal wave speeds mean equal impedances
• B. Reflection still occurs, because Z = ρv depends on density — different densities mean different impedances even when speed is equal
• C. Transmission is complete because only the speed ratio, not the density, determines reflection
• D. The wave slows down at the boundary and all energy reflects

Answer: (B)

Acoustic impedance Z = ρv depends on both density and wave speed. Equal speeds do not imply equal impedances if the densities differ. For example, two materials could have the same sound speed but one could be twice as dense — giving twice the impedance. Any mismatch in Z, regardless of which factor causes it, produces partial reflection at the boundary. This is why Z = ρv bundles both properties into a single number: it is the *combination* that determines boundary behavior.

Question 3

Acoustic impedance Z = ρv captures both the density and the stiffness of a medium (through wave speed), so a material can have high impedance due to high density, high wave speed, or both.

• T. True
• F. False

Answer: True

Wave speed v = √(B/ρ) in a fluid, where B is the bulk modulus (a measure of stiffness). So Z = ρv = ρ√(B/ρ) = √(Bρ) — it combines both density and stiffness. Steel, for instance, has very high impedance because it is both dense and extremely stiff (fast wave speed). Air has very low impedance because it is neither dense nor stiff. The formula Z = ρv makes both contributions explicit: a material can achieve high impedance through high density, high stiffness (fast speed), or both.

Question 4

A wave traveling from a low-impedance medium into a high-impedance medium will pass through with no reflection, since it is entering a 'stronger' medium that can carry the wave more effectively.

• T. True
• F. False

Answer: False

Any impedance mismatch — in either direction — causes partial reflection. A wave going from low-Z to high-Z reflects just as a wave going from high-Z to low-Z does; the fraction reflected depends on the ratio Z₁/Z₂, not on which direction the wave travels. Complete transmission only occurs when Z₁ = Z₂ exactly. The 'stronger medium carries better' intuition is wrong — what matters is matching, not magnitude. This is why impedance *matching* — bringing the two impedances as close as possible — is the engineering goal.

Question 5

Why does an ultrasound technician apply coupling gel between the transducer and the patient's skin, and how does the gel reduce reflection losses?

Model answer: The transducer and skin have significantly different acoustic impedances. Without gel, the air gap between them creates a near-total mismatch (the transducer-air and air-skin interfaces each cause nearly complete reflection), so almost no ultrasound energy enters the body. The coupling gel has an impedance intermediate between the transducer and skin, replacing two large mismatches with two smaller ones. Each smaller mismatch allows more energy to transmit, dramatically increasing the fraction of energy that reaches and returns from the tissue being imaged.

This is impedance matching in practice. The ideal intermediary has Z_gel = √(Z_transducer · Z_skin), which minimizes total reflection across the two boundaries. Even an imperfect match is far better than an air gap. The same principle is used in audio engineering (transformers match speaker to amplifier impedance), optical coatings (antireflection films), and seismic sensing (coupling material between geophone and ground). In all cases, the goal is to make adjacent media 'look similar' to an incoming wave.