Strings are mostly used in musical instruments and many other applications of domestic and industrial in nature. A string of length L is shown in Figure 10.4(a), which is subjected to tension T. Let at time t = 0, the string is pulled in the lateral direction (y direction) as shown in figure 10.4 (b) and left. Hence the lateral deflection u along the string is a function of the space variable x and time t i.e.,

 

If the lateral deflection is small, the change in tension T due to the deflection is negligible. Figure 10.4(c) shows the free body diagram of an elemental length dx of the string. When the string is vibrating, in the y direction inertia force is acting. Considering the forces in the vertical direction, applying Newton 's second law one may have

                                                    (10.1)