각 문항과 함께 풀이 내용이 있습니다. 참조하세요.CHAPTER 13Having β2 change sign at the midpoint, yields a zero ∆τ , and so the pulse emerges from theoutput unchanged! Physically, the pulse acquires a positive linear chirp (frequency increaseswith time over the pulse envelope) during the first half of the channel. When β2 switches sign,the pulse begins to acquire a negative chirp in the second half, which, over an equal distance,will completely eliminate the chirp acquired during the first half. The pulse, if originallytransform-limited at input, will emerge, again transform-limited, at its original width. Moregenerally, complete dispersion compensation is achieved using a two-segment channel whenβ2L = −β2 L, assuming dispersion terms of higher order than β2 do not exist.14
CHAPTER 55.7. Assuming that there is no transformation of mass to energy or vice-versa, it is possible towrite a continuity equation for mass.a) If we use the continuity equation for charge as our model, what quantities correspond to Jand ρv? These would be, respectively, mass flux density in (kg/m2 − s) and mass densityin (kg/m3).b) Given a cube 1 cm on a side, experimental data show that the rates at which mass isleaving each of the six faces are 10.25, -9.85, 1.75, -2.00, -4.05, and 4.45 mg/s. If weassume that the cube is an incremental volume element, determine an approximate valuefor the time rate of change of density at its center. We may write the continuity equationfor mass as follows, also invoking the divergence theorem:5.8. The conductivity of carbon is about 3 × 104 S/m.a) What size and shape sample of carbon has a conductance of 3 × 104 S? We know thatthe conductance is G = σA/, where A is the cross-sectional area and is the length. Tomake G = σ, we may use any regular shape whose length is equal to its area. Examplesinclude a square sheet of dimensions × , and of unit thickness (where conductance ismeasured end-to-end), a block of square cross-section, having length , and with crosssectiondimensions √ × √, or a solid cylinder of length and radius a = /π.b) What is the conductance if every dimension of the sample found in part a is halved?In all three cases mentioned in part a, the conductance is one-half the original value ifall dimensions are reduced by one-half. This is easily shown using the given formula forconductance.5.9a. Using data tabulated in Appendix C, calculate the required diameter for a 2-m long nichromewire that will dissipate an average power of 450 W when 120 V rms at 60 Hz is applied to it:The required resistance will be
CHAPTER 33.1. An empty metal paint can is placed on a marble table, the lid is removed, and both parts aredischarged (honorably) by touching them to ground. An insulating nylon thread is glued tothe center of the lid, and a penny, a nickel, and a dime are glued to the thread so that theyare not touching each other. The penny is given a charge of +5 nC, and the nickel and dimeare discharged. The assembly is lowered into the can so that the coins hang clear of all walls,and the lid is secured. The outside of the can is again touched momentarily to ground. Thedevice is carefully disassembled with insulating gloves and tools.a) What charges are found on each of the five metallic pieces? All coins were insulatedduring the entire procedure, so they will retain their original charges: Penny: +5nC;nickel: 0; dime: 0. The penny’s charge will have induced an equal and opposite negativecharge (-5 nC) on the inside wall of the can and lid. This left a charge layer of +5 nC onthe outside surface which was neutralized by the ground connection. Therefore, the canretained a net charge of −5nC after disassembly.b) If the penny had been given a charge of +5 nC, the dime a charge of −2 nC, and the nickel