sciencecapsules

  Throw a stone on the sheet of water in a pond.  Circular waves are created and spread throughout the water surface.  The waves travels as crests and troughs.  We are going to model this waves mathematically.       In a right angled triangle, opposite side divided by hypotenuse gives the sine of the angle x   as illustrated in the figure.     Trigonometry says:  As the angle goes from zero degree to 90 degree, the sine value goes from 0 to 1.  When the angle increases to 180 degree, the sine goes down to 0.  As the angle further increases to 270 and to 360 degree,  the sine goes to -1 and then back to 0.  So when the angle makes one rotation, the sine makes one wavy motion as given in the figure.      So sine function is very suitable to represent a wave.   Y = sin x        As the x goes from 0 to 360 degree or in radian 0 to 2 pi, Y oscillates between +1 to -1 in wavy fashion.(PI = 3.14....) Y = A.sin x      Here A represents the amplitude, the top of th