Chapter 12.4, Problem 28R

To determine

To Calculate: The number of fibres needed to form a cable.

Answer to Problem 28R

  $3185$

Explanation of Solution

Given:

Diameter of optical fiber, $d=0.3\text{mm}$

Side of square cross-section of cable, $a=1.5\text{cm}$

Formula Used:

Area of circle, $A=\frac{\pi d^2}{4}$

Here, d is the diameter.

Area of square, $A\text{'}=a^2$

Here, a is the side of the square.

Conversion units:

  $\begin{array}{l}{\text{1mm =10}}^{\text{-3}}\text{m}\\ {\text{1 cm =10}}^{\text{-2}}\text{ m}\end{array}$

Calculations:

Number of fibres can be calculated as follows:

  $\begin{array}{l}N=\frac{A\text{'}}{A}\\ N=\frac{a^2}{\pi d^2/4}\\ N=\frac{4a^2}{\pi d^2}\end{array}$

Substitute the values and solve:

  $\begin{array}{l}N=\frac{4a^2}{\pi d^2}\\ N=\frac{4{\left(1.5\times {10}^{-2}\right)}^2}{\pi {\left(0.3\times {10}^{-3}\right)}^2}\\ N=3184.7\approx 3185\end{array}$

Conclusion: 

Thus, the number of fibres needed to form a cable is $3185$ .