[b]Animation:[br][/b]Use the "start," "pause," and "stop" buttons to control the animation. Pressing "start" will show the incident (red) wave traveling to the right, interacting with the different media.[br][br][b]Materials: [br][/b]Select the materials of the three media with the drop-down menus near the top of the screen. You can choose between seven different materials. The material-dependent properties are listed in a table below the simulation. Quantities which depend on parameters of the simulation (e.g. wavelength) are listed in-simulation.[br][br][b]Pulses:[br][/b]Pulses originate at the "origin of pulse" point. Their form is that of a perfect sine wave that travels to the left or right, depending on if the wave is transmitted or reflected. The frequency of the waves can be adjusted with the slider labeled "f". The number of wavelengths in each pulse can also be specified.[br][br][b]Wavelength:[br][/b]The wavelength of a wave is a function of its velocity and the frequency. Since [math]v=\lambda f[/math], the wavelength is [math]\lambda=\frac{v}{f}[/math]. The wave velocity is a material-dependent constant.[br][br][b]Spatial pulse length (SPL)[br][/b]The SPL is given by the number of wavelengths in each pulse times the wavelength:[br][math]SPL=\left(\text{Number of wavelenths}\right)\lambda[/math].[br][br][b]Acoustic impedance:[br][/b]Acoustic impedance is a measurement of how well a material "resists" sound waves traveling. In terms of the density [math]\rho[/math] of the material and the speed of the waves [math]v[/math] in the medium, the impedance is[br][math]z=\rho v[/math].[br][br]The SI unit of acoustic impedance is the Rayl (1 Rayl = 1 kg/(s*m[sup]2[/sup])).[br][br][b]Reflection and transmission:[br][/b]Waves incident on each barrier will be partially transmitted and partially reflected, depending on the acoustic impedance of the material. If the "to scale" option is unchecked, all reflection and transmission coefficients will be set to unity, meaning that all waves, regardless of true intensity, will be shown with an amplitude of 1. If the "to scale" box is checked, the amplitudes of the transmitted and reflected waves will be accurately shown, assuming that the amplitude of the incident wave is unity.[br][br]The transmission and reflection coefficients are given in terms of the acoustic impedance values by[br][br][math]r=\frac{\left(z_1-z_2\right)}{\left(z_1+z_2\right)}[/math] and [math]t=\frac{2\sqrt{z_1z_2}}{z_1+z_2}[/math].[br][br][b]Wave separation:[br][/b]In the simulation, the separation between the two echoed waves is shown by [math]\Delta x[/math], the distance between the centers of these two pulses.[br][b][br]Interference:[br][/b]Waves will reflect from the two barriers and interfere with each other. The minimum distance apart that the centers of the pulses can be in order to be registered as two separate pulses of a detector is called the [i]axial resolution[/i], given by [math]\frac{1}{2}SPL[/math]. Since the detector is located in medium 1 (left), this refers to the spatial pulse length in medium 1. If the pulses are closer than half of the spatial pulse length, they interfere and appear to be a single pulse to the detector. If they are farther apart, the two pulses can be distinctly detected.[br][br][b]The detector:[br][/b]The black box near the bottom of the screen is a detector for returning pulses. As each distinct pulse passes, the counter will increase by one. You can move the position of the detector so that it is in the path of the incoming pulses.[br][br][b]Attenuation:[br][/b]Different materials absorb sound in different amounts. This is called [i]attenuation[/i], and is also dependent on the frequency. Attenuation is represented by the absorbtion coefficient [math]\alpha[/math], in terms of [math]a[/math] and [math]b[/math] (material-dependent constants) and frequency [math]f[/math] by[br][br][math]\alpha=af^b[/math].[br][br]A good approximation for ultrasound imaging purposes is [math]b\approx1[/math]. Given a value of [math]\alpha[/math], we find the value [math]\mu_A[/math] by[br][br][math]\mu_A=\frac{\alpha}{20log_{10}e}\approx\frac{\alpha}{8.69}[/math].[br][br]Using this value, the attenuation is modeled exponentially by[br][math]A\left(x\right)=A\left(0\right)e^{-\mu_Ax}[/math]. [br][br]In the simulation, attenuation is activated by the "attenuation" checkbox. If unchecked, waves are not assumed to be absorbed in any of the media.[br][br][b]Other adjustments:[br][/b]The left and right barriers, origin of the pulse, and y-axes for the reflected waves can be adjusted using the black dots.

Created by Lewis Hicks and Priya Jamkhedkar for the Portland State University Physics Department, 2021.