(*This program is about finding the roots of the equations stored in \ table t1. Now i am trying to find the roots of these equation in one \ single run.*) ClearAll["Global`*"] a = 1/(2*b^3) t1 = Table[ a*(((Sin[b*(1 - i)]*Sin[b*i])/Sin[b]) - (( Sinh[b*(1 - i)]*Sinh[b*i])/Sinh[b])), {i, 0.01, 0.5, 0.01}]; t1[[1]] (* ( Csc[b] Sin[0.01 b] Sin[0.99 b] - Csch[b] Sinh[0.01 b] Sinh[0.99 b])/(2 b^3) *) f[x_] := t1[[50]] /. b -> x; p = Plot[{f[x], 0.}, {x, 0.1, 50}, PlotPoints -> 350] 
intersections = Graphics`Mesh`FindIntersections[p] // Chop (* {{7.8527, 0}, {14.136, 0}, {20.4191, 0}, {26.7031, 0}, {32.9867, 0}, {39.2698, 0}, {45.5524, 0}} *) Labeled[Show[p, Frame -> True, Axes -> False, Epilog -> {PointSize[.025], Red, Point[intersections]}], Style[#, 20] &@Column[N[intersections, 10], Frame -> All], Right] 
I tried by doing manually it works but it is too time-consuming. I want to somehow put in a loop such that first few roots of the equations in the table can be found.
