Chapter 12, Problem 56P

To determine

To Calculate: The expected beat frequency.

Answer to Problem 56P

  $f_{\text{beat}}=136.36\text{ Hz }$ .

Explanation of Solution

Given:

Blood flow speed, $\left(v_{\text{blood}}\right)$

  $=2\text{ cm/s }=0.02\text{ m/s}$ .

Device emits frequency, $\left(f\right)$

  $=3.5\text{ MHz }=3.5\times {10}^6\text{Hz}.$

Speed of sound in human tissue, $\left(v_{\text{sound}}\right)$

  $=1540\text{ m/s}$ .

Formula used:

  $f_{\det ector}^{}=f\frac{\left(1-\frac{v_{\text{blood}}}{v_{\text{sound}}}\right)}{\left(1+\frac{v_{\text{blood}}}{v_{\text{sound}}}\right)}$

  $f_{\text{beat}}=f-f_{\text{detector}}$

Here, $f,f_{\text{detector}.},f_{\text{beat}}$ are the frequencies of device, detector, and beat respectively.

  $$

Calculation:

A Doppler flow meter is a device that is used to measure the speed of blood flow.

First, determine the frequency of blood flow,

  $f_{\text{blood}}=f\left(1-\frac{v_{\text{blood}}}{v_{\text{sound}}}\right)$

  $f_{\text{blood}}=3.5\times {10}^6\left(1-\frac{0.02}{1540}\right)\text{ Hz}$

  $f_{\text{blood}}=3499954.54\text{ Hz}$

Now, find the frequency of the detector,

  $f_{\text{detector}}^{}=f_{blood}\frac{\left(1-\frac{v_{\text{blood}}}{v_{\text{sound}}}\right)}{\left(1+\frac{v_{\text{blood}}}{v_{\text{sound}}}\right)}\text{ Hz}$

  $f_{\text{detector}}^{}=3499954.54\frac{\left(1-\frac{0.02}{1540}\right)}{\left(1+\frac{0.02}{1540}\right)}\text{ Hz}$

  $f_{\text{detector}}^{}=3499863.63\text{ Hz}$

Subtract the frequency of detector value from the original frequency value to calculate the beat frequency.

  $f_{\text{beat}}=f-f_{\text{detector}}\text{ Hz}\text{.}$

  $f_{beat}=136.36\text{ Hz }$

Conclusion:

The expected beat frequency is 136.36 Hz if the blood flowing through a large leg artery at $2\text{ cm/s}.$