Because the speed of ultrasound in bone is about twice the speed in soft tissue, the distance to a structure that lies beyond a bone can be measured incorrectly. If a beam passes through 4cmof tissue, then 2cmof bone, and then another 1cmof tissue before echoing off a cyst and returning to the transducer, what is the difference between the true distance to the cyst and the distance that is measured by assuming the speed is always 1540m/s? Compared with the measured distance, the structure is actually

(a) 1cmfarther

(b) 2cmfarther

(c) 1cmcloser

(d) 2cmcloser

Short Answer

Expert verified

The correct option is a.

Step by step solution

01

Measure the total time

The beam goes 2cminto the bone and 5cminto the tissue with a velocity of 1540cmin the tissue and 3080min the bone. The total time is given by

t=0.05m1540ms+0.02m3080m/st=3.89×10-5s

The measured distance will be

d=vtd=1540×3.89×10-5d=0.06md=6cm

02

Calculate the difference

The total distance is 7cmwhile the measured distance is 6cm. The difference will be

Δd=7-6Δd=1cm

Hence, the correct option is a.

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