Final answer:
The reflection of the ultrasound signal occurred at a depth close to 4.46 cm in the fat tissue, which is calculated by halving the distance obtained using the one-way time derived from the given round-trip time delay and the known speed of ultrasound in fat tissue.
Step-by-step explanation:
The question asks us to determine the depth at which a reflection occurred for an ultrasound wave traveling through fat tissue, given a time delay of 0.13 ms for the reflected wave. To find the depth, we use the formula distance = speed × time, knowing that ultrasound travels through fat tissue at approximately 1,450 meters per second. As the wave has to travel to the reflecting surface and back, the actual depth will be half the distance calculated using the time delay.
The calculation would look something like this: 0.13 ms is the round-trip time, so the one-way time is 0.13 ms / 2, which is 0.065 ms or 0.065 × 10-3 seconds. Using the speed of sound in fat, depth = 1,450 m/s × 0.065 × 10-3 s = 0.09425 m or 9.425 cm. However, we need to halve this distance because the time measured is for a round trip. Therefore, the depth is 9.425 cm / 2 = 4.7125 cm, which is closest to option d) 4.46 cm.