A problem listed for a given section requires an understanding of that section and earlier sections, but not of later sections. Within each section, 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.
• (a) At any fixed point x = x0, the traveling wave y(x, t) = A sin(kx − ωt) can be expressed as y(x0, t) = A sin(ωt + ϕ). Find ϕ. (b) For x0 = 0, what is ϕ? (c) By how much must one change x0 [from its value in part (b)] so that ϕ is π larger than in part (b)? Express your answer in terms of λ.
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