If the round-trip time doubles, the reflector distance changes by what factor?

If the round-trip time doubles, the reflector distance changes by what factor?

• A. The distance remains the same
• B. The distance increases by four
• C. The distance doubles
• D. The distance decreases by half

Answer: (C)

The key idea is that the round-trip time is directly proportional to how far the sound travels. In ultrasound, the pulse goes to a reflector and back, so the round-trip distance is 2 times the reflector distance, and the time taken is T = (2D) / c, where c is the speed of sound in the tissue. If the round-trip time doubles, then (2D) must double while c stays the same, which means D must double as well. So the reflector distance increases by a factor of two. The other possibilities don’t fit because they would require different changes in time: remaining the same would need the time unchanged, quadrupling the distance would need quadrupling the time, and halving the distance would require halving the time.

The key idea is that the round-trip time is directly proportional to how far the sound travels. In ultrasound, the pulse goes to a reflector and back, so the round-trip distance is 2 times the reflector distance, and the time taken is T = (2D) / c, where c is the speed of sound in the tissue.

If the round-trip time doubles, then (2D) must double while c stays the same, which means D must double as well. So the reflector distance increases by a factor of two.

The other possibilities don’t fit because they would require different changes in time: remaining the same would need the time unchanged, quadrupling the distance would need quadrupling the time, and halving the distance would require halving the time.