A planetary science laboratory has compiled the following data for four different disturbances triggered simultaneously at one end of a 2.0 km test track.
Disturbance
Medium present in test track
Measured arrival time at far end
P
evacuated tube (pressure ≈10−7 atm)
6.7 µs
Q
same evacuated tube filled with argon gas at 1 atm
5.9 s
R
steel rail bolted to track floor
0.33 s
S
optical fiber mounted alongside rail
10 µs
Assume the speed of light in vacuum is 3.0×108m/s and the refractive index of the fiber is 1.5. Argon supports sound at 330m/s.
(a) For each disturbance (P, Q, R, S) classify the underlying wave as mechanical or electromagnetic. Support each classification with quantitative reasoning based on the data.
(b) For disturbance R, derive an expression for the tension FT required in a different steel cable of linear mass density μ to achieve the same propagation speed observed in the steel rail. State all assumptions clearly.
(c) The lab plans to replace the evacuated section of the tube with nitrogen gas at 0.50 atm. Predict qualitatively how the arrival time of a sound disturbance analogous to Q will change, and justify your prediction in terms of wave-medium interactions.
(d) Critically evaluate the advantages and limitations of using electromagnetic versus mechanical waves for high-precision timing experiments over kilometer-scale distances, drawing on evidence from parts (a) through (c).