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7.4: Chapter Checklist
https://phys.libretexts.org/Bookshelves/Waves_and_Acoustics/The_Physics_of_Waves_(Goergi)/07%3A_Longitudinal_Oscillations_and_Sound/7.04%3A_Chapter_Checklist
A system analogous to that in problem 7.3 is a tube of air with a piston at the top and the bottom open, as shown in Figure $7.9$ : If the cross sectional area of the tube is $A$ , what is the anal...A system analogous to that in problem 7.3 is a tube of air with a piston at the top and the bottom open, as shown in Figure $7.9$ : If the cross sectional area of the tube is $A$ , what is the analog in this system of the spring constant, $K$ , in problem 7.3?
4.1: Symmetries
https://phys.libretexts.org/Bookshelves/Waves_and_Acoustics/The_Physics_of_Waves_(Goergi)/04%3A_Symmetries/4.01%3A_New_Page
When the two modes are in phase for one of the blocks so that the block is moving with maximum amplitude, the modes are $180^{\circ}$ out of phase for the other block, so the other block is almost s...When the two modes are in phase for one of the blocks so that the block is moving with maximum amplitude, the modes are $180^{\circ}$ out of phase for the other block, so the other block is almost still. The complete transfer of energy back and forth from block 1 to block 2 is a feature both of our special initial condition, with block 2 at rest and in its equilibrium position, and of the special form of the normal modes that follows from the reflection symmetry.
8.3: Light
https://phys.libretexts.org/Bookshelves/Waves_and_Acoustics/The_Physics_of_Waves_(Goergi)/08%3A_Traveling_Waves/8.03%3A_Light
In particular, if one of the mirrors is moved a distance $d$ (it might be part of an experimental setup designed to detect small motions, for example), the relative phase of the two components reach...In particular, if one of the mirrors is moved a distance $d$ (it might be part of an experimental setup designed to detect small motions, for example), the relative phase of the two components reaching the screen changes by $2kd$ where $k$ is the angular wave number of the plane wave, because the path length of the reflected wave has changed by $2d$ .
13.10: 13-8- Holography
https://phys.libretexts.org/Bookshelves/Waves_and_Acoustics/The_Physics_of_Waves_(Goergi)/13%3A_Interference_and_Diffraction/13.10%3A_13-8-_Holography
If we now make a positive slide from the plate and shine through it a laser beam with the same frequency, $\omega$ , the wave “gets through” where the light intensity on the plate was large and is ab...If we now make a positive slide from the plate and shine through it a laser beam with the same frequency, $\omega$ , the wave “gets through” where the light intensity on the plate was large and is absorbed where the intensity was small. The important thing to note about the complex conjugate wave is that it represents a beam traveling in a different direction from either the signal or the reference beam, because the complex conjugation has changed the sign of $k_{x}$ and $k_{y}$ .
11.9: Chapter Checklist
https://phys.libretexts.org/Bookshelves/Waves_and_Acoustics/The_Physics_of_Waves_(Goergi)/11%3A_Two_and_Three_Dimensions/11.09%3A_Chapter_Checklist
In other words, if $\psi(x, y, t)$ is the $z$ displacement of the membrane as a function of $(x, y)$ , then the force (in the $z$ direction) on a small chunk of the boundary stretching from the...In other words, if $\psi(x, y, t)$ is the $z$ displacement of the membrane as a function of $(x, y)$ , then the force (in the $z$ direction) on a small chunk of the boundary stretching from the point $(0, y)$ to $(0, y + dy)$ is $d F=-d y \gamma \frac{\partial}{\partial t} \psi(0, y, t) .$ where $\rho_{P}$ is the density of the paint-thinner, $\rho_{W}$ is the density of the water, and $\tau_{S}$ is the surface tension of the boundary between the water and the paint-thinner.
10: Antennas and Radiation
https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_and_Applications_(Staelin)/10%3A_Antennas_and_Radiation
Thumbnail: Animation of a half-wave dipole antenna transmitting radio waves, showing the electric field lines. (Public Domain; Chetvorno via Wikipedia)
Front Matter
https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_and_Applications_(Staelin)/00%3A_Front_Matter
7.2: A Mass on a Light Spring
https://phys.libretexts.org/Bookshelves/Waves_and_Acoustics/The_Physics_of_Waves_(Goergi)/07%3A_Longitudinal_Oscillations_and_Sound/7.02%3A_A_Mass_on_a_Light_Spring
and the displacement of the mass is determined by the displacement of the end of the spring, $x(t) \equiv \psi(\ell, t)=A \sin k_{n} \ell \cos \omega_{n} t .$ To find the force on the mass, consider...and the displacement of the mass is determined by the displacement of the end of the spring, $x(t) \equiv \psi(\ell, t)=A \sin k_{n} \ell \cos \omega_{n} t .$ To find the force on the mass, consider the massive spring as the continuum limit as $a \rightarrow 0$ of masses connected by massless springs of equilibrium length $a$ , as at the beginning of the chapter.
6.3: Using Computation to Simulate Centripetal Force
https://phys.libretexts.org/Courses/Berea_College/Introductory_Physics%3A_Berea_College/06%3A_Applying_Newtons_Laws/6.03%3A_Using_Computation_to_Simulate_Centripetal_Force
Simulate centripetal motion in trinket with visual python
3.1: Motion with Constant Speed
https://phys.libretexts.org/Courses/Berea_College/Introductory_Physics%3A_Berea_College/03%3A_Describing_Motion_in_One_Dimension/3.01%3A_Motion_with_Constant_Speed
Since the position as a function of time for the ball plotted in Figure $\PageIndex{1}$ is linear, we can summarize our description of the motion using a function, $x(t)$ , instead of having to tab...Since the position as a function of time for the ball plotted in Figure $\PageIndex{1}$ is linear, we can summarize our description of the motion using a function, $x(t)$ , instead of having to tabulate the values as we did in Table 3.1.1. The velocity, $v_{x}$ , is simply the difference in position, $∆x$ , between any two points divided by the amount of time, $∆t$ , that it took the object to move between those to points (“rise over run” for the graph of $x(t)$ ):
26.1: Functions of Real Numbers
https://phys.libretexts.org/Courses/Berea_College/Introductory_Physics%3A_Berea_College/26%3A_Calculus/26.01%3A_Functions_of_Real_Numbers
Unfortunately, it becomes difficult to visualize functions of more than 2 variables, although one can usually look at projections of those functions to try and visualize some of the features (for exam...Unfortunately, it becomes difficult to visualize functions of more than 2 variables, although one can usually look at projections of those functions to try and visualize some of the features (for example, contour maps are 2D projections of 3D surfaces, as shown in the $xy$ plane of Figure A1.1.2).

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