Q77PP - University Physics with Modern Physics

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) $\mathbf{1}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}$ .

Step-by-Step Solution

Answer

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

STEP 1: Given data

Distance of object from transducer is $10 cm$ .

STEP 2: 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.

STEP 3: Number Of Pulses Per Second

The pulses travel distance $10 cm$  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  $v=1540 m/s$.

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

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  $7700{\text{\hspace{0.17em}s}}^{-1}$.