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.
 Fall '11
 CalculusII
 Force

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