A beam of 1.0 MHz ultrasound begins with an intensity of 1000 W/m². After traveling 12 cm through tissue with no significant reflection, the intensity is about

A. 750 W/m²

B. 500 W/m²

C. 250 W/m²

D. 125 W/m²

Option C

Explanation:

Given:

- Depth of tissue d = 12 cm

- frequency of ultrasound f = 1 MHz

- Input Intensity I_i = 1000 W/m^2

- attenuation coefficient soft tissue a = 0.54

Find:

- Out-put intensity at the required depth

Solution

- The amount of attenuation in (dB) with the progression of depth is given by:

Attenuation = a*f*d

Attenuation = 0.54*12*1

Attenuation = 6.48 dB

- The relation with attenuation and ratio of input and output intensity is given by:

Attenuation = 10*log_10 (I_i / I_o)

6.48 dB = 10*log_10 (I_i / I_o)

I_i / I_o = 10^ (0.648)

I_o = 1000 / 10^ (0.648)

I_o = 225 W/m^2

- Hence the answer is option C: I_o = 250 W/m^2