Question

During an ultrasound, sound waves are sent by a transducer through muscle tissue at a speed of 1,300 m/s. Some of the sound waves are reflected from a metal fragment 5.0 cm into the muscle tissue. How long did it take the transducer to detect the reflected waves from the metal fragment after they were first emitted?

0.26 seconds
39 seconds
4.6 E−5 seconds
7.7E−5 seconds

Answer 1

Answer:

(d) 7.7E−5 seconds

To calculate the time it takes for the reflected waves to return to the transducer, we can use the formula:

time = distance / speed

The distance the sound waves travel is twice the depth of the metal fragment, since they have to travel to the fragment and then back to the transducer. Therefore, the distance traveled by the sound waves is:

distance = 2 x 5.0 cm = 0.1 m

The speed of the sound waves in muscle tissue is 1,300 m/s. Therefore, the time taken for the waves to travel this distance is:

time = distance / speed = 0.1 m / 1,300 m/s = 7.7E−5 seconds

Therefore, the transducer takes 7.7E−5 seconds to detect the reflected waves from the metal fragment after they were first emitted.

The correct answer is (d) 7.7E−5 seconds.

Answer 2

To calculate the time it took for the reflected waves to be detected, we can use the formula:

time = distance / speed

where distance is the round-trip distance traveled by the sound waves (i.e., twice the distance from the transducer to the metal fragment) and speed is the speed of sound in muscle tissue.

The round-trip distance traveled by the sound waves is:

2 * 5.0 cm = 10.0 cm = 0.1 m

The speed of sound in muscle tissue is given as 1,300 m/s.

Therefore, the time it took for the reflected waves to be detected is:

time = distance / speed = 0.1 m / 1,300 m/s = 7.7E−5 seconds

So the answer is 7.7E−5 seconds (option D).