Search
- https://phys.libretexts.org/Bookshelves/Waves_and_Acoustics/The_Physics_of_Waves_(Goergi)/07%3A_Longitudinal_Oscillations_and_Sound/7.04%3A_Chapter_ChecklistA 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?
- https://phys.libretexts.org/Bookshelves/Waves_and_Acoustics/The_Physics_of_Waves_(Goergi)/04%3A_Symmetries/4.01%3A_New_PageWhen 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.
- https://phys.libretexts.org/Bookshelves/Waves_and_Acoustics/The_Physics_of_Waves_(Goergi)/08%3A_Traveling_Waves/8.03%3A_LightIn 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 \(2d\).
- https://phys.libretexts.org/Bookshelves/Waves_and_Acoustics/The_Physics_of_Waves_(Goergi)/13%3A_Interference_and_Diffraction/13.10%3A_13-8-_HolographyIf 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 \(k_{y}\).
- 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_Springand 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.
- https://phys.libretexts.org/Bookshelves/Waves_and_Acoustics/The_Physics_of_Waves_(Goergi)/12%3A_Polarization/12.03%3A_Wave_Plates_and_PolarizersOne reason that polarization is important is that the polarization state of an electromagnetic wave can be easily manipulated. Two of the most important devices for such manipulation are polarizers an...One reason that polarization is important is that the polarization state of an electromagnetic wave can be easily manipulated. Two of the most important devices for such manipulation are polarizers and wave plates.
- https://phys.libretexts.org/Bookshelves/Waves_and_Acoustics/The_Physics_of_Waves_(Goergi)/01%3A_Harmonic_Oscillation/1.04%3A_Complex_NumbersTo divide a complex number \(z\) by a real number \(r\) is easy, just divide both the real and the imaginary parts by \(r\) to get \(z/r = a/r + ib/r.\) To divide by a complex number, \(z'\), we can u...To divide a complex number \(z\) by a real number \(r\) is easy, just divide both the real and the imaginary parts by \(r\) to get \(z/r = a/r + ib/r.\) To divide by a complex number, \(z'\), we can use the fact that \(z'^* z' = |z'|^2\) is real.
- https://phys.libretexts.org/Bookshelves/Waves_and_Acoustics/The_Physics_of_Waves_(Goergi)/05%3A_Waves/5.04%3A_New_PageThen the system looks like the diagram in Figure \( 5.11\), where the oscillators move up and down in the plane of the paper: Let us find its normal modes. The answer is that we must have the first im...Then the system looks like the diagram in Figure \( 5.11\), where the oscillators move up and down in the plane of the paper: Let us find its normal modes. The answer is that we must have the first imaginary bead on either side move up and down with the last real bead, so that the coupling string from bead 0 is horizontal and exerts no transverse restoring force on bead 1 and the coupling string from bead 5 is horizontal and exerts no transverse restoring force on bead 4: \[A_{0}=A_{1} ,\]
- https://phys.libretexts.org/Bookshelves/Waves_and_Acoustics/The_Physics_of_Waves_(Goergi)/01%3A_Harmonic_Oscillation/1.05%3A_Exponential_SolutionsThe amplitude, A, and phase, θ, are the polar coordinate representation of the same complex (1.96) shows that c and d are also the coefficients of cos ωt and sin ωt in the real part of the product of ...The amplitude, A, and phase, θ, are the polar coordinate representation of the same complex (1.96) shows that c and d are also the coefficients of cos ωt and sin ωt in the real part of the product of this complex number with −iωt e . This relation is illustrated in figure 1.9 (note the relation to figure 1.4).
- https://phys.libretexts.org/Bookshelves/Waves_and_Acoustics/The_Physics_of_Waves_(Goergi)/00%3A_Front_Matter/04%3A_PrefaceFor similar reasons, the discussion of two- and three-dimensional waves occurs late in the book, after you have been exposed to all the tools required to deal with one-dimensional waves. While the exa...For similar reasons, the discussion of two- and three-dimensional waves occurs late in the book, after you have been exposed to all the tools required to deal with one-dimensional waves. While the examples of waves phenomena that we discuss in this book will be chosen (mostly) from familiar waves, we also will be developing the mathematics of waves in such a way that it can be directly applied to quantum mechanics.
- https://phys.libretexts.org/Bookshelves/Waves_and_Acoustics/The_Physics_of_Waves_(Goergi)/13%3A_Interference_and_Diffraction/13.04%3A_Examples=\frac{1}{2 \pi} \int_{-a}^{a} d x e^{-i k_{x} x}=\left.\frac{1}{-2 i \pi k_{x}} e^{-i k_{x} x}\right|_{-a} ^{a}=\frac{\sin k_{x} a}{\pi k_{x}} . =\frac{e^{-i n b k_{x} / 2}\left(e^{i n b k_{x} / 2}-e...=\frac{1}{2 \pi} \int_{-a}^{a} d x e^{-i k_{x} x}=\left.\frac{1}{-2 i \pi k_{x}} e^{-i k_{x} x}\right|_{-a} ^{a}=\frac{\sin k_{x} a}{\pi k_{x}} . =\frac{e^{-i n b k_{x} / 2}\left(e^{i n b k_{x} / 2}-e^{-i n b k_{x} / 2}\right)}{e^{-i b k_{x} / 2}\left(e^{i b k_{x} / 2}-e^{-i b k_{x} / 2}\right)}=e^{-i(n-1) b k_{x} / 2} \frac{\sin n b k_{x} / 2}{\sin b k_{x} / 2} .
