# Sound problem: Beat frequency

1. Apr 30, 2004

### jjlittel

I have been trying this problem for a couple of days:

Ultrasound reflected from an oncoming bloodstream that is moving at 30 cm/s is mixed with the original frequency of 2.5 MHz to produce beats. What is the beat frequency? (Velocity of sound in blood = 1540 m/s.)

I tried this as a doppler effect problem where the frequency is
(original frequency)*{v/(v-velocity of source)}. I then subtracted that from the original frequency to find the beat frequency, and came up with 487.1 Hz, but that was not the right answer. For v, I used 1540 m/s, and velocity of source was 0.3 m/s. Is there something I am missing in my approach to the problem?

2. Apr 30, 2004

### gnome

I think you have to solve this with two shifts.

Consider a second observer riding along with the oncoming bloodstream. This observer is moving toward the original source & therefore perceives an increase in frequency. So the reflected wave starts out with a shifted frequency, which is then shifted again because it's source (the oncoming bloodstream) is moving toward the original observer.

3. Apr 30, 2004

### jjlittel

Thank you for the help, gnome. You were right about the second shift, and I finally got the answer, which was 974.2 Hz.