Q: Suppose you send an incident wave of specified shape, gI (
Suppose you send an incident wave of specified shape, gI (z-v1t), down string number 1. It gives rise to a reflected wave, hR(z+v1t), and a transmitted wave, gT (z-v2t). By imposing the boundary conditi...
See AnswerQ: (a) Formulate an appropriate boundary condition, to replace Eq
(a) Formulate an appropriate boundary condition, to replace Eq. 9.27, for the case of two strings under tension T joined by a knot of mass m. (b) Find the amplitude and phase of the reflected and trans...
See AnswerQ: Suppose string 2 is embedded in a viscous medium (such as
Suppose string 2 is embedded in a viscous medium (such as molasses), which imposes a drag force that is proportional to its (transverse) speed: / (a) Derive the modified wave equation describing the m...
See AnswerQ: Equation 9.36 describes the most general linearly polarized wave on
Equation 9.36 describes the most general linearly polarized wave on a string. Linear (or “plane”) polarization (so called because the displacement is parallel to a fixed vector nˆ) results from the com...
See AnswerQ: Write down the (real) electric and magnetic fields for a
Write down the (real) electric and magnetic fields for a monochromatic plane wave of amplitude E0, frequency ω, and phase angle zero that is (a) traveling in the negative x direction and polarized in...
See AnswerQ: Show that the differential equations for V and A (Eqs.
Show that the differential equations for V and A (Eqs. 10.4 and 10.5) can be written in the more symmetrical form where
See AnswerQ: Confirm that the retarded potentials satisfy the Lorenz gauge condition. [
Conï¬rm that the retarded potentials satisfy the Lorenz gauge condition. [Hint: First show that where ∇denotes derivatives with respect to r, and ∇(...
See AnswerQ: (a) Suppose the wire in Ex. 10.2
(a) Suppose the wire in Ex. 10.2 carries a linearly increasing current I (t) = kt, for t > 0. Find the electric and magnetic fields generated. (b) Do the same for the case of a sudden burst of current:...
See AnswerQ: A piece of wire bent into a loop, as shown in
A piece of wire bent into a loop, as shown in Fig. 10.5, carries a current that increases linearly with time: I (t) = kt (−∞ Calculate the retarded vector potentia...
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