SPH3U multi-step question on electromagnetic waves

Question

You have two options that you are trying to select between when deciding upon who to use as your internet service provider.

Option 1 - Fiber optic cable

Option 2 - Connection from your antenna to a satellite (orbit at about 500km) above your home

 You are going to send a signal using both methods from your beach front cottage in Bobcaygeon to a server in Miami (then the signal will return to you to make it a round trip). The method that returns the signal to you faster will be the one that you purchase. The signal will be an EM wave. 

a) Explain how the pulse will make the journey with each method (this will require research, make sure to include any resources that you used (url is fine)).

b) Assuming that the satellite signal travels through the air the entire time and the fiber optic signal is travelling through glass, calculate the time that it would take for the pulse to return to you using each method (show all of your work and explain your thinking).

Answer 1

a) We use the units of the international system: MKSA, i.e. m, kg, s, A, mol, K, Cd.

Optical fiber connection: electromagnetic wave speed c = 200,000 km/s (because the optical fiber is made of glass). Distance between Bobcaygeon (Ontario) and Miami (USA) d = 2,500 km, so the round trip is 2d = 5,000 km.

Satellite connection: electromagnetic wave speed c' = 300,000 km/s (in air). Distance covered by the waves between Bobcaygeon, the satellite, Miami d' = 2,550 km (with Pythagorus), so the round trip is 2d' = 5,100 km.

b) Fiber optic connection:

We use the formula c = D/t with c = 200,000 km/s and D = 2d = 5,000 km.

Thus: t = 2d/c = 5,000/200,000 = 0.025 s = 25 ms.

Satellite connection:

We use the formula c' = D'/t' with c' = 300,000 km/s and D' = 2d' = 5,100 km.

Thus: t' = 2d'/c' = 5,100/300,000 = 0.017 s = 17 ms.

We therefore prefer the operator who offers satellite connection, which is 1/3 faster.

Note: Although faster, the satellite connection is more sensitive to interference and external disturbances, as it is not “wired” like the fiber optic connection.