Consider a wave sent down a string in the positive direction whose equation is given is `y=y_(0)sin[omega(t-x/v)]` The wave is propagated along because each string segment pulls upward and downward on the segment adjacent to it a slightly larger value of `x` and, as a result does work upon the string segment to which wave is travelling. For example, the portion of string at point `A` is going upward, and will pull the portion at point `B` upward as well. In fact, at any point along the string, each segment of the string is pulling on the segment just adjacent and to its right, causing the wagve to propagate. It is by this process that the energy is sent along the string. Now we try to calculate how much energy is propagated down the stirng per second `T_(y)=tsintheta~~TtanthetaimpliesT_(y)=-T(dely)/(delx)` (The negative sign appears because as shown in the figure II, the slope is negative) the force will act through a distance `dy=v_(y)dt=(dely)/(delt) dt` Therefore work done by force in time `dt` is `dW=T_(y)dy=-T((dely)/(delx))((dely)/(delt))dtimpliesdW=(omega^(2)y_(0)^(2)T)/vcos^(2)[omega(t-x/V)]dt`.....(A) The average power transmitted down the string (i.e. the average energy transfer or sent down it per second) isA. `(2omega^(2)y_(0)^(2)T)/v`B. `(omega^(2)y_(0)^(2)T)/v`C. `(omega^(2)y_(0)^(2)T)/(2v)`D. `(omega^(2)y_(0)^(2)T)/(4v)`