# Homework Help: Device that detect waves in a frequency range and beats

Tags:
1. Jun 28, 2016

### Soren4

1. The problem statement, all variables and given/known data
You have a device that can measure sound waves only if the frequency of the wave is in the range $0.8 kHz- 20 kHz$. You have a whistle that produces sound waves at $21.5kHz$. You ride a bike moving away from a wall, at the same time you blow the whistle and hold the device in your hand. What is the velocity you must have in order to make the device measure the minimum beat frequency that it can detect?

2. Relevant equations
Doppler effect and beats

3. The attempt at a solution
I premit I don't have any problem with the Doppler effect, the only problem here is to understand what to look for if I'm asked the "minimum beat frequency" that can be detected by the instrument. If $f_1$ is the frequency of the whistle and $f_2$ is the frequency modified by the reflection on the wall at a certain velocity, which condition between the following two is correct?
• $|f_2-f_1| > 0.8 kHz$
• $\frac{f_2+f_1}{2} <20kHz$
$|f_2-f_1|$ is the beat frequency, while $\frac{f_2+f_1}{2}$, as explaied at https://en.wikipedia.org/wiki/Beat_(acoustics) , is the frequency of the wave resulting from the interference of the two.

Now, in my view, what really counts is $\frac{f_2+f_1}{2}$, because that's the "real" frequency of the resulting wave, and I know that the device has a limitation on the frequency of the wave, but I'm not convinced about it. Which of the two would be correct, and (possibly) why?