Problem 27. The intensity of echoes depends on not only the nature of the bounda

Question

Problem 27. The intensity of echoes depends on not only the nature of the boundary they reflect from, but also the dis- tance to the boundary. Consider a boundary that reflects of the incident wave intensity. Compare the intensity of the echoes recorded by the detector for boundaries 10, 20, and 30 mm from the source. Assume an attenuation coefficient of 500 dB m-1. Ignore any inverse-square fall-off. Clini cal ultrasound imaging devices often use a technique called time gain compensation to selectively amplify later echoes, thereby correcting for the effect of attenuation that you just calculated. 50 %

Explanation / Answer

The intensity of the ultrasound is given by I=Ioexp(-mx), where Io is the initial intensity, m is the attenuation coefficient and x is the distance travelled by the wave.

Using this we can calculate, m=500 dBm-1

X=10mm = 0.01 m: I= Io exp(-500*0.01)=0.007Io

X=20mm=0.02m=: I=Ioexp(-500*.02)=0.00005Io

X=30mm=0.03m=I=Ioexp(-500*0.03)=0.0000003Io

We can take a ratio7000:500:3. I in all cases will be 50%of initial and hence same for all.

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