Matakuliah
Tahun
: K0124 / Matematika Teknik II
: 2006/2007
PERTEMUAN 14
VIBRATING STRING EQUATION
1
2
2 y
2  y
a
2
t
x 2
This equation is applicable to the small transverse vibrations of a taut,
flexible string, such as violin string, initially located on the x axis and set
into motion.
2
The function
y(x, t) is the displacement of any point x of the string at
time t. The constant a2 = T /  , where T is the (constant)
tension in the string and  is the (constant) mass per unit
length of the string.
3
It is assumed that no external forces act on the string but
that it vibrates only due to its elasticity.
4
The equation can easily be generalized to higher
dimensions as for example the vibrations of a membrane or
drum head in two dimensions.
5
In two dimensions, for example, the equations is
2
2

2z

z

z
2
 a  2  2 
2
t
y  .
 x
y
Y =(x, t)

6
TERIMA KASIH
7