A 1300 nanometer wave traveling in a medium with a refractive index of 1.44 will have a velocity of approximately 0.6944 times the speed of light in a vacuum. To calculate the distance traveled in 100 nanoseconds, the formula distance equals velocity multiplied by time can be applied. Given the velocity, the wave would travel about 69.44 meters in that time frame. The discussion clarifies that knowing the wavelength is unnecessary for this calculation, as the velocity and time are sufficient. Overall, the focus is on understanding how refractive index affects light speed in a medium.