In deriving the governing equation for a vibrating string, there are several assumptions that are made. One of the assumptions that I had a hard time understanding was the following. Once the string is split into n particles, the force of tension on each particle from the particles in the right and the left is assumed to be proportional to the ratio of the vertical displacement to the horizontal displacement. Could you please explain to me how this assumption is correct. What are the reasons behind it. Thanks.