Question

If the deepest structure you wish to image is $\mathbf{10}\mathbf{.}\mathbf{0}\mathbf{cm}$ from the transducer, what is the maximum number of pulses per second that can be emitted? (a) $\mathbf{3850}$; (b) $\mathbf{7700}$; (c) $\mathbf{15400}$; (d) $\mathbf{1}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}$ .

Short answer

The correct answer is (b)$7700{\text{\hspace{0.17em}s}}^{-1}$ .

Step-by-step solution

Given data

Distance of object from transducer is $10cm$.

The Frequency

The number of pulses generated every second, is called frequency. Which is given as $\mathbf{f}\mathbf{=}\frac{1}{t}$

Here, t is the time period of a pulse.

Number Of Pulses Per Second

The pulses travel distance $10cm$ then back to the transducer due to the reflection, so the total distance is $d=20cm$. We are given the velocity through the tissue by $v=1540m/s$.

$\begin{array}{c}f=\frac{1}{t}\\ =\frac{v}{d}\end{array}$

Plug the values for $v$ and $d$ to get $f$-

$\begin{array}{c}f=\frac{1520\text{\hspace{0.17em}m/s}}{0.20\text{\hspace{0.17em}m}}\\ =7700{\text{\hspace{0.17em}s}}^{-1}\end{array}$

Therefore, the maximum number of pulses is $7700{\text{\hspace{0.17em}s}}^{-1}$.