# Homework Help: Ultrasound reflected from an oncoming bloodstream

1. Dec 12, 2004

### j2dye

Ultrasound reflected from an oncoming bloodstream that is moving at 31 cm/s is mixed with the original frequency of 1.3 MHz to produce beats. What is the beat frequency? (Velocity of sound in blood = 1540 m/s.)

I know that there are two doppler shifts; one where the source is fixed and the other where the observer is fixed.

So i'm supposed to use the doppler shift equation to solve for this:

f1=f((V + Vo) / (V - Vs))

but I dont know what numbers to plug into which variables.

After I find the frequency of the doppler shifted echo all I have to do is subtract it from the original frequency of 1.3 MHz, right?

2. Dec 12, 2004

### Andrew Mason

You have used the doppler expression where the source and observer are both moving relative to the medium. You also have to keep in mind that there is a reflection so there are two doppler shifts.

Use the moving observer form:
$$f_{blood} = f_{source}(\frac{v_{sound}+ v_{blood}}{v_{sound}})$$

to find the apparent frequency that the blood receives. The blood then acts as a moving source and reflects this back to the observer so used the moving source form:

$$f_{observer} = f_{blood}(\frac{v_{sound}}{v_{sound} - v_{blood}})$$

You are correct that the beat frequency is the difference between the original and the reflected sound.

AM