By Fleisch, Daniel A.; Kinnaman, Laura
"Waves are an enormous subject within the fields of mechanics, electromagnetism, and quantum concept, yet many scholars fight with the mathematical facets. Written to counterpoint path textbooks, this ebook makes a speciality of the themes that scholars locate so much tough. preserving the hugely well known method utilized in Fleisch's different Student's publications, the e-book makes use of undeniable language to give an explanation for primary principles in an easy and transparent method. workouts and fully-worked examples aid readers attempt their knowing of the ideas, making this a great e-book for undergraduates in physics and engineering attempting to familiarize yourself with this hard topic. The booklet is supported by way of a set of on-line assets to be had at www.cambridge.org/9781107643260. those comprise interactive strategies for each workout and challenge within the textual content and a sequence of video podcasts within which the authors clarify the $64000 recommendations of each element of the book"-- Read more...
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Extra info for A student’s guide to waves
23, but it’s easier to compare waves by plotting them on the same graph, as in Fig. 24. 22 Waveforms of Eq. 40) at time t = 0. first (y1 ) wavefunction has been plotted using a dashed line to distinguish it from the second (y2 ) wavefunction. When comparing waveforms on a timedomain plot such as Fig. 24, you may encounter terminology such as “y2 is leading y1 ” or “y1 is lagging y2 ”. Many students find this confusing, since in this plot it appears that y1 is somehow “ahead” of y2 (that is, the peaks of y1 appear to the right of the peaks of y2 ).
24. 22 Waveforms of Eq. 40) at time t = 0. first (y1 ) wavefunction has been plotted using a dashed line to distinguish it from the second (y2 ) wavefunction. When comparing waveforms on a timedomain plot such as Fig. 24, you may encounter terminology such as “y2 is leading y1 ” or “y1 is lagging y2 ”. Many students find this confusing, since in this plot it appears that y1 is somehow “ahead” of y2 (that is, the peaks of y1 appear to the right of the peaks of y2 ). To see the flaw is this logic, remember that time is increasing to the right in this plot, so the peaks of y2 occur before (that is, to the left of ) the peaks of y1 .
Adding these two same-direction phasors produces a resultant phasor (which we label eiθ + e−iθ ) that also points along the positive real axis and has a magnitude (length) of 2 (since eiθ and e−iθ both have a magnitude of 1). Hence the expression (eiθ + e−iθ )/2 has a magnitude of 1, which is the value of cos θ for θ = 0. Now look at the phasors eiθ and e−iθ for θ = 30◦ . The phasor eiθ points above the real axis by 30◦ , and the phasor e−iθ points below the real axis by 30◦ . 73. 866, which is the value of cos θ for θ = 30◦ .