Continuing a discussion we opened in the last Quick Concepts installment, today we explore the relationship between density and wave propagation.
Students often struggle initially with the principle that the speed of sound varies as it propagates through the body. Quite possibly, this is due to our general experience with the behavior of sound in air.
The earliest concepts taught in physics involve simplified models like ‘the speed of sound’ and ‘the speed of light’. Indeed, the shorthand method for estimating the distance of an approaching (or receding) thunderstorm involves counting the time between your observation of a flash of lightning and the arrival of the sound of thunder. This strategy treats the speed of light and the speed of sound each as “constants.” This assumption “works” because we are only approximating the distance, and because the thunder (sound) and lightening (light) are always traveling through air and not different mediums. Therefore, our real-world observations do not give us intuition as to what happens as sound travels through varying mediums, as it does when propagating through the body.
So how does sound behave in relation to the density of the medium through which is passes?
Again, our tendency to equate physical principles to real-world experiences might tempt us to compare sound propagation to running through air versus running through water, or the shooting of a bullet through air versus into water. Here too, this analogy would mislead us because both a person and a bullet are slowed down by the higher density medium. So our assumption would be that dense tissues slow the transmission of sound.
Even the equation relating sound propagation to density seemingly implies that these are inversely related parameters. Therefore, it is unsurprising that students are often completely turned around in their ‘gut’ instincts on this relationship.
The missing factor in our assessment of the behavior of sound goes by the imposing name “bulk modulus”. This weighty (pun intended) term equates to the compressibility of a substance. Stated another way, the bulk modulus predicts how a medium responds to pressure…and recall that sound itself is a “pressure wave.”
The properties of density and bulk modulus do have some commonality. More dense objects are generally harder to compress (stiffer). But, the key concept to appreciate is that resistance to compression (stiffness) rises much more rapidly than any proportional increase in density.
Speed error associated with a needle
We are getting into some deep waters here, but to condense (ha) the principle down to how it affects your clinical experience, within the body sound moves faster through dense tissue (muscle, tendons, bones, surgical steel) and slower through less dense mediums (fat, fluids, air pockets).
Understanding this is critical to your clinical anticipation of possible ‘speed error’, and as importantly, it is regularly tested in credentialing examinations.
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This subject matter is discussed more thoroughly in Frank Miele’s Ultrasound Physics and Instrumentation . Introduced in Chapter 2: Waves on pages 27-31, its clinical application is outlined in Chapter 8: Artifacts during discussions on speed error artifact (pages 282-283).
