Final answer:
To find the diameter of the gallbladder, the distances to the reflecting surfaces from ultrasound echoes at differing times are calculated using the speed of sound in soft tissue. These distances provide the necessary information to determine the diameter when subtracted from each other.
Step-by-step explanation:
The question revolves around the use of diagnostic ultrasound in medical imaging. In the provided scenario, a technician observes two ultrasound echoes from the patient's gallbladder, with the first echo at 78 microseconds (μs) and the second at 136 μs. To find the diameter of the gallbladder, one must first calculate the distance to each reflecting surface and then use those distances to determine the overall size of the gallbladder.
The speed of sound in soft tissue is approximately 1540 m/s. Knowing this, we can calculate the distance traveled by the ultrasound for both echoes:
- Distance = Speed × Time
- Since the ultrasound has to travel to the reflecting surface and back, the actual depth is half the calculated distance.
For the first echo:
- Time = 78 × 10^-6 seconds
- Distance traveled one way = (1540 m/s × 78 × 10^-6 s) / 2
For the second echo:
- Time = 136 × 10^-6 seconds
- Distance traveled one way = (1540 m/s × 136 × 10^-6 s) / 2
By calculating these distances and subtracting the smaller from the larger, we obtain the diameter of the gallbladder.