u
u
x1
x2
a
x3
wave at t1
wave at t2
wave at t3
x
x
b
u
A
u (x,t)
B
u(x,t+Δt)
C
sΔt
x
x
y
u
y=f(x)
f(x)
wave at time 0
f(x-st)
wave at time t
speed s
a
x
st
b
x
u (x,t)
1
0.5
0
4
3
t
2
1
0
u
-2
0
2
4
x
6
u (0,t)=0
8
10
u(L,t)= 0
u (x,t)
0
u
0
x
L
u
string is concave down
L
force
a
x
x
0
string is concave up
force
L
b
x
c
c
x1 P
a
x2
x
x1 P
b
x2
x
c
x1 Q
x2
x
x1 R
x2
x
c
D=1
D=3
0.3
0.3
t= 1
0.25
0.2
0.25
0.2
t= 3
0.15
t= 5
0.1
0.05
0
-5
t= 1
0.15
-4
-3
-2
-1
0
1
2
3
4
5
0.1
t= 3
0.05
t= 5
0
-5
-4
-3
-2
-1
0
1
2
3
4
5