By Fleisch, Daniel A.; Kinnaman, Laura
"Waves are an incredible subject within the fields of mechanics, electromagnetism, and quantum idea, yet many scholars fight with the mathematical elements. Written to counterpoint path textbooks, this booklet makes a speciality of the subjects that scholars locate so much tricky. keeping the hugely renowned procedure utilized in Fleisch's different Student's publications, the ebook makes use of simple language to provide an explanation for primary rules in an easy and transparent means. workouts and fully-worked examples aid readers try out their realizing of the options, making this a terrific booklet for undergraduates in physics and engineering attempting to become familiar with this not easy topic. The booklet is supported through a collection of on-line assets to be had at www.cambridge.org/9781107643260. those contain interactive ideas for each workout and challenge within the textual content and a chain of video podcasts within which the authors clarify the real strategies of each component to the book"-- Read more...
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Additional info for A student’s guide to waves
Find the frequency and angular frequency of the following waves. 02 s. 5 ns. (c) A sound wave with period of 1/3 ms. 2. Find the period of the following 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?
So, if you made a plot of the values of y as the wave passes over your location, those values would decrease from the value of point 2 to the value of point 1, as shown in the lower portion of Fig. 8. Thus the slope you measure over time (at a given location) has two differences from the slope you measure over distance (at a given time). The first difference is that the magnitude of the slope will be different (since the run in the distance plot is x but the run in the time plot is t). The second difference is that the sign of slope over distance is positive, but the sign of the slope over time is negative.
Use the power-series representation of sin θ , cos θ , and eiθ to prove the Euler relation eiθ = cos θ + i sin θ . 9. Show that the wavefunction f (−x − 1) is shifted in the negative xdirection relative to the wavefunction f (−x). 10. Find the phase speed and the direction of propagation of each of the following waves (all units are SI). (a) f (x, t) = 5 sin(3x) − t/2. (b) ψ(x, t) = g − 4x − 20t. (c) h(y, t) = 1/[2(2t + x)] + 10. 2 The wave equation There are many equations that describe wave behavior and the relationship between wave parameters, and you may well find such equations referred to as “the wave equation”.