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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 $2d$ .
12: Gravitational Lenses
https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Big_Ideas_in_Cosmology_(Coble_et_al.)/12%3A_Gravitational_Lenses
Chapter 12 delves into the phenomenon of gravitational lensing. Light from distant sources is deflected by the curved spacetime around massive objects, providing astrophysicists with the ability to ma...Chapter 12 delves into the phenomenon of gravitational lensing. Light from distant sources is deflected by the curved spacetime around massive objects, providing astrophysicists with the ability to map out mass, both seen and unseen. In the first part of the chapter you will examine the geometric properties of simple gravitational lenses. In the second part, you will use astrophysical gravitational lenses as instruments for studying dark matter, weighing galaxy clusters, and extra-solar planets.
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.
5.4: Evolution of Galaxies and the Universe Itself
https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Big_Ideas_in_Cosmology_(Coble_et_al.)/05%3A_Moving_Through_Time/5.04%3A_Evolution_of_Galaxies_and_the_Universe_Itself
We previously introduced the idea of the light-minute, the light-hour, and the light-year as distance measurements. This method works because the speed of light is constant. We can use the constancy o...We previously introduced the idea of the light-minute, the light-hour, and the light-year as distance measurements. This method works because the speed of light is constant. We can use the constancy of the speed of light to measure distances this way for any time period we like. However, the constancy of light speed means that light is not only a useful tool for measuring distances; light can also be used as a sort of time machine.
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.
15.0: The Cosmic Microwave Background Introduction
https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Big_Ideas_in_Cosmology_(Coble_et_al.)/15%3A_The_Cosmic_Microwave_Background/15.00%3A_The_Cosmic_Microwave_Background_Introduction
Since its discovery in 1965, the cosmic microwave background (CMB) has provided some of the most important observational constraints for our theories of the nature and evolution of the Universe. The C...Since its discovery in 1965, the cosmic microwave background (CMB) has provided some of the most important observational constraints for our theories of the nature and evolution of the Universe. The CMB is a glow of microwave light coming from every direction in the sky. Together with the abundances of the lightest elements and the Hubble expansion, it is one of the key observational pillars supporting the Big Bang theory.

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