ELECTRIC OSCILLATIONS AND ELECTRIC WAVES. 199 



angles to the #-axis in Figs. 136 and 137), and we will assume that 

 the string is perfectly flexible.* Under these conditions the 

 ^-component of the tension of the string is always and every- 

 where equal to a constant T. 



vTK 



b\ 



Fig. 136. 



x * dx 



Fig. 137. 



X-OX18 



Let the curve ccc, Fig. 136, be the configuration of the string 

 at a given instant /, that is, ccc is what a photographer would 

 call a snapshot of the moving string. The shape of the curve 

 ccc defines the ordinate y as a function of x, and the steepness 



dy 

 of the curve ccc at a point is the value of -7- at that point. 



Consider the very short portion ab of the string. The length 

 of this portion of the string when the string lies along the #-axis 

 (in equilibrium) is dx, and the mass of the portion is m*dx 

 grams, where m is the mass of one centimeter of the string in 

 grams. An enlarged view of the very short portion of the string 

 is shown in Fig. 137. The adjacent parts of the string pull on 

 the portion ab; and the forces R and R' thus exerted on ab 

 are parallel to the string at a and at b respectively. The x- 

 component of R is the force T to the left, and the re-component 

 of R f is the force T to the right. Therefore the downward 

 force D is equal to T tan B, and the upward force U is equal 

 to T tan B' ; and the net upward force U D which acts on 

 the portion ab of the string is equal to !T(tan B' tan 6). But 



dy 

 tan B is equal to the value of -7- at a and tan 0' is equal 



dy 

 to the value of at 6. Therefore the difference, tan 0' tan 0, 



* This means that the only thing that keeps the string straight is its tension. 



