4 Where Does the Wave Equation Come From?
29
Fig. 4.6 Closed linear chain of the length L = circumference of the circle for N = 16
Fig. 4.7 Linear chain of the length L for N = 4
is known as a linear chain; see Fig. 4.7. A force F acting on the end of a length
L results in a deflection s according to F = D s. As in the theory of elasticity, we
are interested in the relative elongation and write F = E e f f s/L with an effective
modulus of elasticity E e f f = D L. We also introduce an effective specific mass
density ρ e f f ,
ρ e f f =
m
L
,
Effective mass density
of the linear chain
E e f f = D L.
Effective modulus of elasticity
of the linear chain
⎫
⎪ ⎪ ⎬
⎪ ⎪ ⎭
(29)
29
Fig. 4.6 Closed linear chain of the length L = circumference of the circle for N = 16
Fig. 4.7 Linear chain of the length L for N = 4
is known as a linear chain; see Fig. 4.7. A force F acting on the end of a length
L results in a deflection s according to F = D s. As in the theory of elasticity, we
are interested in the relative elongation and write F = E e f f s/L with an effective
modulus of elasticity E e f f = D L. We also introduce an effective specific mass
density ρ e f f ,
ρ e f f =
m
L
,
Effective mass density
of the linear chain
E e f f = D L.
Effective modulus of elasticity
of the linear chain
⎫
⎪ ⎪ ⎬
⎪ ⎪ ⎭
(29)