BIO Ultrasound in Medicine. A 2.00-MHz soundwave travels through a pregnant woman’s abdomen and is reflected from the fatal heart wall of her unborn baby. The heart wall is moving toward the sound receiver as the heart beats. The reflected sound is then mixed with the transmitted sound, and 72 beats per second are detected. The speed of sound in body tissue is 1500 m/s. Calculate the speed of the fatal heart wall at the instant this measurement is made.

Frequency emitted is $2.00\text{\hspace{0.17em}MHz}$

Sound’s speed is$1500\text{\hspace{0.17em}m}/\text{s}$

Number of beats per second are $72$

The frequency of the sound wave is defined as the number of oscillation produced per unit time. It is given as-

$\mathbf{f}\mathbf{=}\frac{v}{\lambda }$

where, v is the velocity ,$\mathit{\lambda }$ is the wavelength androle="math" localid="1655818635098" $\mathit{f}$ is the frequency of sound wave.

The frequency of the ultrasound waves is by using equation $f=2.40\times {10}^6\text{\hspace{0.17em}Hz}$.The wavelength of the wave is $\lambda =\frac{v}{f}$

Range of the frequencies is$f_1=1.00\text{\hspace{0.17em}MHz}$ to$f_2=20\text{\hspace{0.17em}MHz}$ . The corresponding wavelengthrole="math" localid="1655818948502" $f_2$ to is smaller than the corresponding wavelength to$f_1$ , according the equationrole="math" localid="1655819020395" $\mathrm{v}=\mathrm{\lambda f}$ as v does not change in the same medium. So,

${\lambda }_2=\frac{1.5\times {10}^3\text{\hspace{0.17em}m/s}}{\begin{array}{c}20.0\times {10}^6\text{\hspace{0.17em}Hz}\\ =0.075\times {10}^{-3}\text{\hspace{0.17em}m}\\ =0.075\text{\hspace{0.17em}mm}\end{array}}$

${\lambda }_1=\frac{1.5\times {10}^{3}m/s}{\begin{array}{c}1.00\times {10}^{6}Hz\\ =1.5\times {10}^{-3}m\\ =1.5mm\end{array}}$

Therefore, the corresponding wavelengths are$0.75mm$ to $1.5mm$.