Wave Equation
Suppose, the motion of the string discussed previously , is restricted to the x-y plane only (Fig. 5.2). Considering motion of the element PQ, net force, Fy in y- direction is
Fig. 5.2 Forces acting on an elemental length of a string
Fy = T sin θ2 - T sin θ1 |
(5.27) |
where T is the tension in the string. Further, θ being small
|
(5.28) |
and,
|
(5.29) |
From Eqs. (5.27-5.29), we get
|
| (5.30) |
By Newton's law of motion,
|
(5.31) |
where m is the mass of the string per unit length.
| (5.32a)
(5.32b) |
