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Figure 1-1: Diagram illustrating a longitudinal wave using a coiled spring (slinky) attached to a wall, shown in two panels demonstrating both the static structure and the dynamic motion of a longitudinal wave. The top panel shows a black coiled spring anchored to a black wall bracket on the left, with a gray illustrated hand on the right gripping the end of the spring, depicting how the wave is generated by pushing and pulling the spring. Two regions of the spring are labeled: “Compression,” indicating a section where the coils are pressed tightly together, and “Refraction” (labeled beneath a section where the coils are spread further apart). In the bottom panel the same spring setup is shown again, with additional labels and arrows illustrating the wave’s motion dynamics. On the right side near the hand, a label reads “Coils Vibrate Left and Right” with a double-headed blue arrow indicating the side-to-side oscillation of the spring’s coils. Above the wall end on the left, a label reads “Source Moves Left and Right” with a similar double-headed blue arrow, indicating that the wave source itself oscillates back and forth. Below the spring, a large pink/salmon arrow labeled “Direction of Wave” points to the left, indicating the overall direction of wave propagation, which is parallel to (along the same axis as) the back-and-forth coil vibrations.
Figure 1-2: At the top, a horizontal grayscale gradient bar alternates between dark (black) and light (white) bands, representing regions of compression (dark, high pressure/density) and rarefaction (light, low pressure/density) in the physical medium. Labels beneath this bar read “Rarefaction” and “Compression,” and an arrow above labeled “Propagation” points to the left, indicating the direction the wave is traveling. Below the grayscale bar, a black sinusoidal (sine) wave curve is drawn, representing the pressure variation of the sound wave plotted against position, oscillating above and below a horizontal blue dashed line labeled “Zero” (representing average/ambient pressure). The wave completes approximately four full oscillation cycles across the diagram. Key labeled features on the sine wave include: Wavelength: A bracket spanning from one wave crest to the next, indicating the distance of one complete cycle. Pressure Maximum: An arrow pointing to a wave crest (peak), corresponding to a dark compression band above, where the medium experiences the highest pressure/density. Pressure Minimum: An arrow pointing to a wave trough, corresponding to a light rarefaction band above, where the medium experiences the lowest pressure/density. 1 Cycle: A bracket beneath one full oscillation (crest to trough to the next equivalent point), indicating one complete wave cycle. Amplitude: On the right side of the diagram, a vertical double-headed arrow between the zero line and the peak height, labeled “Amplitude,” indicating the maximum displacement of the wave from its equilibrium (zero) position.
Figure 1-3: A two-part diagram illustrating transverse wave terminology. The top diagram, “Amplitude of Transverse Wave” has a horizontal line labeled “Mean Position of the Particles” that runs through a sine-like wave with two crests above and two troughs below the line. Dashed vertical arrows extend from the mean position line to each crest (pointing up) and each trough (pointing down), with a horizontal arrow labeled “Amplitude” pointing to one of these vertical dashed lines, indicating that amplitude is the distance from the mean position to the peak of a crest or the bottom of a trough. The bottom diagram, “Crests and Troughs of a Transverse Wave” is the same wave shape is shown over a dotted background representing particles, with the horizontal mean position line again labeled “Mean Position of the Particles.” Two peaks are labeled “Crest A” and “Crest C,” with three upward arrows beneath Crest A showing particle displacement above the mean position. Two valleys are labeled “Trough B” and “Trough D,” with three downward arrows above Trough B showing particle displacement below the mean position. Text beneath the diagram states: “Shown: A and C Are Crests, B and D Are Troughs.”
Figure 1-4: Diagram illustrating the inverse square law for light or wave intensity from a point source. A circular inset in the upper left labeled “Sphere Area 4πr²” presents the formula for intensity at the surface of a sphere: P / 4πr² = I, where P is “Source Power.” The main diagram shows a point source labeled “Source Power P” at the bottom left, from which light radiates outward in a cone shape, expanding to three increasingly distant grid planes representing cross-sections of the spreading energy at distances r, 2r, and 3r from the source. At distance r, a single grid square represents intensity I. At distance 2r, the area has expanded to a 2 by 2 grid of four squares (covering 4 times the area), with the intensity labeled I over 4. At distance 3r, the area has expanded further to a 3 by 3 grid of nine squares (covering 9 times the area), with the intensity labeled I over 9. Caption text below the diagram reads: “The energy that is twice as far from the source is spread over four times the area, which equates to one-fourth of the intensity.”
Figure 1-6: Diagram comparing specular and diffuse reflection across three panels. Left panel, titled “Specular: One Direction” shows a single arrow that strikes a flat horizontal surface at an angle and reflects away as a single arrow in one defined direction, illustrating that specular reflection sends light in a single, predictable direction. The middle panel, titled “Diffuse: Multiple Directions, Low Amplitude (Scattering)” shows an arrow that strikes a flat horizontal surface and scatters into several smaller arrows pointing in multiple different directions, illustrating that diffuse reflection scatters light across many directions with reduced intensity. The right panel shows a single bold downward arrow that strikes a central point, from which eight small arrows radiate outward in all directions, further illustrating the concept of scattering from a single point of contact.
Figure 1-7: Diagram titled “Transducer” illustrating wave behavior at an impedance boundary, shown in two panels. Panel a) shows a blue downward arrow labeled “Incident Wave” striking a horizontal boundary line separating “Impedance Z₁” (above) from “Impedance Z₂” (below). At the boundary, a portion of the wave reflects back upward as a smaller blue arrow labeled “Reflected Wave,” while another portion continues downward through the boundary as a larger blue arrow labeled “Transmitted Wave,” illustrating partial reflection and transmission at an impedance mismatch. Panel b) shows a blue downward arrow labeled “Incident Wave” striking a horizontal boundary with small black triangular bumps (representing a rough or textured surface). At this boundary, the wave scatters into multiple small arrows pointing in different upward/outward directions, while a portion still transmits straight through as a downward arrow below the line.
Figure 1-8: Two-panel diagram illustrating refraction, shown through a physics schematic and an ultrasound imaging analogy. The left panel is a diagram showing the boundary between a gray “Glass” medium (lower left) and “Air” (upper right), separated by a horizontal dashed blue line labeled “Boundary,” with a vertical dashed line labeled “Perpendicular Line” at the point of incidence. An “Incident Ray” travels diagonally downward through the air and strikes the boundary at angle θᵢ, measured from the perpendicular line. Upon crossing into the glass, the ray bends and continues as a “Refracted Ray” traveling downward and to the left at a different angle, illustrating how light changes direction when passing between media of different optical densities. The right panel is an illustration of an ultrasound transducer (depicted as a handheld probe with a cord) emitting a cone-shaped ultrasound beam (shown in light blue) downward into a cross-section of tissue (shown in pink with small oval shapes representing cellular structures). The beam bends slightly within the tissue, with an angle θ marked at the point of bending, and dotted arrows indicate the beam’s path of travel through the tissue layer. This panel draws a parallel between optical refraction and the refraction of ultrasound waves as they pass through biological tissue.
Figure 1-9: Two-panel image illustrating a mirror artifact in ultrasound imaging, shown through a schematic diagram and an actual clinical scan. The left panel, a schematic diagram shows two pink, curved muscle shapes labeled “Muscle” at the top, with three solid black lines converging downward from the muscle regions to a central purple heart-like shape, labeled “True Aorta” via a line pointing to the central path. Two dashed lines diverge from the muscle regions outward to two gray circles on either side, labeled “False Images.” The right panel is a clinical color Doppler ultrasound image with a fan-shaped scanning field. At the top, an orange and yellow curved structure represents the transducer footprint or near-field tissue. A white-outlined rectangular region of interest labeled “LLL” contains the color Doppler overlay: a blue-colored structure labeled “IVC” (inferior vena cava) on the left and two orange/red/yellow colored structures both labeled “A” (representing the aorta and its mirror artifact) on the right, illustrating a real vessel alongside a duplicated artifactual image, similar to the false images described in the schematic. Technical parameters in the upper left read “TIS: 0.7” and “TIB: 0.7,” with “5fps” and “13cm” labeled at the bottom right indicating frame rate and depth.
Figure 1-10: The top panel shows a pale yellow tissue block containing a single dark red vertical structure (representing a strong reflector, such as a vessel wall or fascial layer). An ultrasound transducer on the right emits an orange beam that travels left through the tissue, reflects off the red structure, and returns to the transducer (shown as a double-headed orange arrow). A red horizontal arrow points rightward from the structure toward the transducer, indicating the direction of the returning echo. Below the tissue block, a single red triangle marks the resulting position of this single reflector as it would appear on the ultrasound display. The bottom panel shows the same tissue block now containing three dark red vertical structures with alternating orange and yellow bands between them, representing multiple reflective layers. The transducer’s beam interacts with all three structures, each sending an echo back (shown by three red rightward arrows of increasing length matching depth). Below the tissue block, three red triangles of increasing size are shown, illustrating that each reflective boundary produces its own artifact or echo signal on the display, with deeper or stronger reflectors producing larger triangular markers.
