In an underwater telephone cable the ratio of the radius of the core to the thickness of the protective sheath is denoted by x. The speed v at which a signal is transmitted is proportional to x²ln(1/x). Show that

where K is some constant, and hence deduce the stationary values of v. Distinguish between these stationary values and show that the speed is greatest when x = 1/√e.

Transcribed Image Text:

du d.x x [2 n (+)-1] = Kx In