Determing frequency shift of an ultrasound

[grigri9]

Homework Statement

A Doppler blood flow unit emits ultrasound at 5.0 MHz.

What is the frequency shift of the ultrasound reflected from blood moving in an artery at a speed of 0.20 m/s?

Express your answer using two significant figures.

Homework Equations

f' = f0(v/v-Vs)
frequency shift = f' - f0

f0 = 5*10^6 Hz
v = 1500 m/s (assumed)
Vs = 0.20 m/s

The Attempt at a Solution

Plugging in the numbers we get the following equation for frequency shift:

(5*10^6)*[1500/(1500-0.2)]-5*10^6

Which comes out to approx 666 Hz. or 6.7 *10^2 Hz using 2 significant figures. However, this problem comes from an online homework set and according to that 6.7 *10^2 is not the correct solution.

Does anyone have an idea of what I am doing wrong? Thanks in advance for any and all help!

 

[rl.bhat]

Hi grigri9, welcome to PF.
We have here a case of the "listener" (the blood corpuscles) moving away from a stationary source, and thus the frequency, f corpuscle that will be reflected by the corpuscles will be
f corpuscle = f(transmitted)[(Vs - Vb)/Vs

For the reflected waves, reflection, the corpuscles are the source and the "listener" is the receiver. The frequency at the receiver will be
f(receiver) = f(corpuscles)*Vs/(Vs + Vb)

from which we get
f(receiver) = f(transmitted)*(Vs-Vb)/(Vs+Vb)