1/sqrt(2) is part of the definition of bandwidth, being the factor or ratio of the system's amplitude to the signal amplitude. The frequency where this relationship holds is the bandwidth. The value of 1/sqrt(2) is 0.7071 or about 71% of the signal amplitude. It's probably associated with the root mean square (RMS) of 1/2 and 1/2 (sqrt((1/2)^2+(1/2)^2)). Considering the sine wave as the simplest wave, the average amplitude on the positive side is 1/2 (because the maximum value of sine is 1 and the minimum is 0 on the positive side) and on the negative side is -1/2 (min is -1 max is 0) (1/2)^2+(-1/2)^2=2/4=1/2, the square root of which is 1/sqrt(2) or sqrt(2)/2.