During an ultrasound, sound waves are sent by a transducer through muscle tissue at a speed of 1300 m/s. Some of the sound waves are reflected from a metal fragment in the muscle and are detected by the transducer 1.5 x 10−4 seconds after they were first emitted. What is the depth of the metal fragment in the muscle tissue?

Distance of metal fragment is 0.0975 m

Explanation:

As we know that the ultrasound will move towards the metal fragment and reflected back to the transducer

So the time interval in which sound will go to the metal fragment and come back is given as

now we know that the speed of the wave in the metal is

v = 1300 m/s

now we know that total distance traveled by the ultrasonic wave is given as

so the depth of metal fragment is half of total distance because in the ultraviolet sound move to and from between transducer and metal fragment so its distance is given as

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.