When one reflector is twice as deep as another reflector, the pulses time-of-flight is _______ for the deeper reflector.

When one reflector is twice as deep as another reflector, the pulses time-of-flight is _______ for the deeper reflector.

• A. The same
• B. Half as long
• C. Twice as long
• D. Four times as long

Answer: (C)

Time-of-flight grows with the distance the pulse travels, and in a uniform medium it travels down and back up at the same speed. The round-trip time is t = 2d / v. If the deeper reflector has depth 2d, the round-trip time becomes t' = 2(2d) / v = 4d / v, which is twice the original time t = 2d / v. So the deeper reflector’s time-of-flight is twice as long. The other options would require different depth changes: the same would mean no depth change, half as long would mean shallower depth, and four times as long would require quadrupling the depth.

Time-of-flight grows with the distance the pulse travels, and in a uniform medium it travels down and back up at the same speed. The round-trip time is t = 2d / v. If the deeper reflector has depth 2d, the round-trip time becomes t' = 2(2d) / v = 4d / v, which is twice the original time t = 2d / v. So the deeper reflector’s time-of-flight is twice as long. The other options would require different depth changes: the same would mean no depth change, half as long would mean shallower depth, and four times as long would require quadrupling the depth.