Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.
• For the standing wave of Eq. (7.118) calculate the string’s transverse velocity at any fixed position x. [That is, differentiate (7.118) with respect to t, treating x as a constant.] At certain times the string’s displacement is zero for all x, and an instantaneous snapshot of the string would show no wave at all. Sketch the string at such a moment, and indicate, with several small arrows, the velocity of several points on the string at that moment.
y(x, t) = A sin kx cos ωt (7.118)
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