Question

A diagnostic sonogram produces a picture of internal organs by passing ultrasound through the tissue. In one application, it is used to fid the size, location, and shape of the prostate in preparation for surgery or other treatment. The speed of sound in the prostate is 1540 m/s, and a diagnostic sonogram uses ultrasound of frequency 1.40 MHz. The density of the prostate is 1060 kg/m3.
1)

What is the wavelength of the sonogram ultrasound? (Express your answer to three significant figures.)

2)What is Young’s modulus for the prostate gland? (Express your answer to three significant figures.)

Answer 1

Answer:

1) $\lambda = 11\times 10^{-4} m$

2)$2.51\times 10^9 Pa$

Explanation:

Given data:

speed of sound v  = 1540 m/s

frequency f  = 1.40 MHz = 1.40 \times 10^6 Hz

density $\rho = 1060 kg/m^3$

1) we know that

$v = f\lambda$

$\lambda = \frac[v}{f} = \frac{1540}{1.40\times 10^6}$

$\lambda = 11\times 10^{-4} m$

2) we know that

$v= \sqrt{\frac{modulus}{density}}$

$v^2 = \frac{\gamma}{\rho}$

$\gamma = v^2 \rho$

$\gamma = 1540^2 \times 1060 = 2.51 \times 10^9 Pa$