In other words sx x sx s in the limit where x is

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Unformatted text preview: ∂y ￿ − ∂x ￿ x+∆x ∆x ￿￿ ∂y ￿ ∂x ￿ x a But S(x + Δx)–S(x) is just the amount S changes when we change x. In other words, S(x + Δx) – S(x) = ΔS. In the limit where Δx is very, very small, then, the definition of a derivative gives us: µ ∂2y = F ∂ t2 On the left: that’s a derivative! 36 Fig. 15.13 So we have a formula for the way the slope of a tiny bit of string changes as you look at different points along the wave. Let’s write that out in full. Hey, it’s the Wave Equation! Compare to what we had before: So " Speed of a wave on a string. or F = tension. μ = mass per unit length " (linear mass density). 38 37...
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This note was uploaded on 03/11/2013 for the course PHYS 101 taught by Professor Calculusii during the Fall '11 term at University of Alberta.

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