An echo returns after 130 μs in tissue; what is the depth of the reflector?

An echo returns after 130 μs in tissue; what is the depth of the reflector?

• A. 5.0 cm
• B. 3.9 cm
• C. 15.0 cm
• D. 10.0 cm

Answer: (D)

Measuring depth from echo time relies on the speed of sound in tissue and the fact that the pulse travels to the reflector and back. The depth is given by d = (c × t) / 2, where c is the speed of sound in tissue (about 1540 m/s) and t is the round-trip time. Here, t = 130 μs = 0.00013 s. So d = (1540 m/s × 0.00013 s) / 2 ≈ (0.2002 m) / 2 ≈ 0.1001 m ≈ 10.0 cm. So the reflector is about 10 cm deep. Quick check: a depth of 5.0 cm would correspond to about 65 μs, 3.9 cm to about 50 μs, and 15.0 cm to about 195 μs, which don’t match 130 μs.

Measuring depth from echo time relies on the speed of sound in tissue and the fact that the pulse travels to the reflector and back. The depth is given by d = (c × t) / 2, where c is the speed of sound in tissue (about 1540 m/s) and t is the round-trip time.

Here, t = 130 μs = 0.00013 s. So d = (1540 m/s × 0.00013 s) / 2 ≈ (0.2002 m) / 2 ≈ 0.1001 m ≈ 10.0 cm.

So the reflector is about 10 cm deep. Quick check: a depth of 5.0 cm would correspond to about 65 μs, 3.9 cm to about 50 μs, and 15.0 cm to about 195 μs, which don’t match 130 μs.