Transcription of Transverse waves on a string - Harvard University
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Transverse waves on a string - Harvard University
Chapter 4 Transverse waves on a stringDavid Morin, the previous three chapters, we built up the foundation for our study of waves . In theremainder of this book, we ll investigate various types of waves , such as waves on a string ,sound waves , electromagnetic waves , water waves , quantum mechanical waves , and so Chapters 4 through 6, we ll discuss the properties of the two basic categories of waves ,namelydispersivewaves, andnon-dispersivewaves. The rest of the book is then largely aseries of applications of these results. Chapters 4 through 6 therefore form the heart of non-dispersive system has the property that all waves travel with the same speed,independent of the wavelength and frequency. These waves are the subject of this andthe following chapter (broken up into longitudinal and Transverse waves , respectively). Adispersive system has the property that the speed of a wavedoesdepend on the wavelengthand frequency. These waves are the subject of Chapter 6.
displacements of the string (we’ll be quantitative about the word \small" below). Let x be the coordinate along the string, and let ˆ be the transverse displacement. (There’s no deep reason why we’re using ˆ for the displacement instead of the » we used in Chapter 2.) Our goal is to flnd the most general form of ˆ(x;t).
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