By Fleisch, Daniel A.; Kinnaman, Laura
"Waves are a tremendous subject within the fields of mechanics, electromagnetism, and quantum concept, yet many scholars fight with the mathematical elements. Written to enrich path textbooks, this booklet specializes in the themes that scholars locate such a lot tough. conserving the hugely renowned strategy utilized in Fleisch's different Student's courses, the e-book makes use of undeniable language to provide an explanation for basic rules in an easy and transparent manner. routines and fully-worked examples aid readers try out their figuring out of the ideas, making this a terrific e-book for undergraduates in physics and engineering attempting to become familiar with this tough topic. The booklet is supported by way of a collection of on-line assets on hand at www.cambridge.org/9781107643260. those contain interactive strategies for each workout and challenge within the textual content and a chain of video podcasts during which the authors clarify the real techniques of each element of the book"-- Read more...
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Extra resources for A student’s guide to waves
A) A mechanical wave with frequency of 500 Hz. 09 × 1014 Hz. 1 rad/s. 3. (a) What is the speed of an electromagnetic wave with wavelength of 2 meters and frequency of 150 MHz? 5 kHz, if the speed of sound is 340 m/s? 4. 5 μs at a fixed location? (b) What is the difference in phase of a mechanical wave with period of 2 seconds and speed of 15 m/s at two locations separated by 4 meters at some instant? 5. If vector D = −5ˆı − 2jˆ and vector E = 4jˆ, find the magnitude and direction of the vector F = D + E both graphically and algebraically.
Notice that both of these phasors rotate anti-clockwise at the same rate (since they have the same ω), maintaining the phase difference between them (π/2 in this case). If you were to add these two phasors together, the resultant would be another phasor rotating at the same frequency and maintaining constant length, but its projection onto the vertical axis would grow larger and smaller (and become negative) as y1 and y2 rotate. 3 in the next chapter. Another important concept that students sometimes find confusing is the meaning of “negative frequency”.
4 If θ decreases (becomes less positive or more negative), the phasor rotates in the clockwise direction. One reason why phasors are extremely useful in the analysis of waves is shown in Fig. 15. As shown in the right portion of the figure, as the phasor rotates, the projection of the phasor onto the imaginary axis traces out a sine wave as θ increases. And, as shown in the bottom portion of the same figure, the projection of the phasor onto the real axis traces out a cosine wave as θ advances.
A student’s guide to waves by Fleisch, Daniel A.; Kinnaman, Laura