A narrow beam of ultrasonic waves reflects off the liver tumor, in a way that en

Question

A narrow beam of ultrasonic waves reflects off the liver tumor, in a way that enables us to probe the location of the tumor.

a) If the speed of the wave is 10% less in the liver than in the surrounding medium, determine the depth of the tumor.

b) Ultrasonic waves used for medical diagnostics have a frequency of 2 MHz. And the speed of sound in biological tissue is 1500 m/s. How deep would the tumor have to be for the reflected waves to result in destructive interference?

A narrow beam of ultrasonic waves reflects off the liver tumor, in a way that enables us to probe the location of the tumor. If the speed of the wave is 10% less in the liver than in the surrounding medium, determine the depth of the tumor. Ultrasonic waves used for medical diagnostics have a frequency of 2 MHz. And the speed of sound in biological tissue is 1500 m/s. How deep would the tumor have to be for the reflected waves to result in destructive interference?

Explanation / Answer

n = c/v = c/0.9c = 10/9

sin50 = n*sinc

c = 43.55

tan C = x1/d = x2/d

x1 = d*tanC.....x2 = d*tanC

x1+x2 = 12 = 2d*tanC

d = 12/(2*tanC) = 6/tanC = 6.309 cm

b)

path difference = Lambda/2

2t = v/2f

t = v/4f = 1500/(4*2*10^6)= 187.5e?6 m

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