Wavelengths for a standing wave on a string (13-18)

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Question

Wavelength of a standing wave on the string

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Review

Here \(\lambda\) represents the wavelength of both the standing wave and also the original wave we created on the string. So according to Equation 13-18, a whole number \(n\) of half-wavelengths must fit onto the string to generate the standing wave pattern described by Equation 13-16. Figure 13-14 shows the patterns for \(n = 1\) (for which half of a wavelength fits), \(n = 2\) (for which two half-wavelengths, or one full wavelength, fits), and \(n = 3\) (for which three half-wavelengths, or one and a half full wavelengths, fits). Each of these patterns is called a \(\textbf{standing wave mode}\).