Supplements for Chapter 2:
Introduction to decibels: hyperphysics
Many good animations illustrating diverse wave phenomenology are found on Prof. Dan Russell's website, conveniently organized on this page.
This is the chapter that you should start to become familiar with Ripple, by Paul Falstad and Harvard University Instructional Computing Group. A description of it is found under "Using Falstad Applets" at the top of this and every page.
This waveguide of the deep (about 1 kilometer down from the surface of the ocean), allowing long range (perhaps thousands of kilometers) communication between whales, and between ships lowering microphones and loudspeakers, is discussed here.
Noise canceling headsets
Jet cabin noise seat 12a was recorded at 30,000 feet on a Boeing 757 at 30,000 feet. In addition, Rhapsody in Blue is played overlaying the noise and also the noise reduced by 18 dB, typical of the reductions in noise canceling headsets.
Launching a pulse in two different length pipes
This movie shows the longer period of the longer pipe. Both pipes emit the higher frequency components that make up the initial short pulse more readily than the longer wavelength, lower frequency components; thus, over time, only the lowest frequencies remain inside the pipe. At the end of the movie, especially at the bottom where more "emissions" have occured, only the lowest mode remains.
Note too the sign reversal of the pressure each time the pulse collides with the open end, and how much is released each time.
The importance of impedance.
Chapter 2 is fairly dense with Ripple studies of wave properties. Ripple gets a workout, and this is an opportunity for the reader to set up similar or completely new scenarios to get familiar with this remarkable tool and what it can reveal about wave behavior. This effort can be especially rewarding using the enhanced Ripple available at http://www.courses.fas.harvard.edu/~icgzmod/java_physics/ripple/, since more drawing options are avaialble and the scenarios you create can be saved. See Using Falstad Applets for more information.
Refraction: abrupt vs. gradual
Discussions of refraction are often introduced, and frequently finished, with examples involving sudden changes in impedance (called index of refraction in the case of light). Often a ray tracing approach is adopted, where one follows rays which move along the direction of travel of the waves (and perpendicular to the wave fronts, or rows of crests and troughs). No doubt refraction (and reflection) due to sudden changes is an important topic, but slower changes in the medium propagating the wave (e.g. temperature or wind speed gradients which affect sound speed) also lead to refraction of ray paths, and usually negligible reflection. Moreover the ray paths may curve gracefully rather than bend abruptly.
In the examples above (left in Ripple: Setup "Refraction"; right, setup "Temperture gradient 1") the blue indicates higher impedance (lower temperature). The higher impedance develops gradually on the right, abruptly on the left. The sudden change leads to partial reflection of a wave impinging from above and to the left, but the gradual change on the right is an anti-reflection coating in effect, and no discernable reflected wave is generated. Both cases bend (refract) the ray significantly.
Sound shadows: wall vs. refraction
To mask a sound source, would you rather be behind a solid wall, or depend on refraction to bend the sound up and away from you? As is made clear in the remarkable account of the silence near a raging Civil War battlefield, chapter 28, refraction leaves silent zones that are far quieter than the sound shadow behind even a very tall wall, where diffraction fills the shadow with sound which is only modestly attenuated compared to the original source.
In measurements using two probes in these Ripple simulations (using the enhanced version, here, which Paul Falstad kindly allowed the Harvard Instructional Computing Group to develop, starting with his foundation code in the original Ripple), the wall decreased the sound intensity about 22 dB (behind wall vs. between wall and source), while the temperature gradient (which gave a speed gradient) refraction reduced the sound intensity by 40 dB, a much more substantial reduction.
We show a montage Ripple scenarios used in Chapter 2: