# Influence of acceleration in acoustic doppler's effect experiment

Recently I've done an acoustic doppler's effect experiment for physics lab assignment. The setup was two microphones in a straight line, movable object with sound source and a pc with the usual sound editing software.

The object gained its speed using a rubber that shoots the sound source (2) in a straight line (1) along the two microphones (3).

Firstly I set the microphones $0.8~\text{m}$ apart, and launched the source. Then I checked the time between two microphone max amplitudes and got the ~ $7.4~\text{m}/\text{s}$ speed.

Second part follows the same recorded information. I picked the part of the function where source is moving towards the object and made a furje analysis, got the peak frequency of $4078$ $\text{Hz}$,then did the same with moving away ($4017~\text{Hz}$). Frequency of source standing still was $4047~\text{Hz}$. When I had these numbers I used the standard doppler effect formula and calculated the speed of source considering these frequencies, and it was ~ $2,59~\text{m}/\text{s}$ .

As the speed I measured directly and the speed I got from doppler's formula were so different I repeated the experiment few times yet getting the same answer all three times.

I was thinking the difference was because of the acceleration, obviously rubber shooting an object does not give constant velocity needed for doppler's effect formula. Saying that, guidelines in lab experiment manual suggested to presume that speed is constant. Still, the $5~\text{m}/\text{s}$ difference seems a bit odd.

Maybe anyone has an idea how to explain the difference between different methods of finding source speed, or see a major flaw in experiment set-up.

If you need any additional information let me know.

Edit: Thanks for the response. Still can't figure out what couses such difference, though leaning towards acceleration as the main couse of problem. Maybe someone else has some more ideas ?

## 1 Answer

Here are some ideas to be considered:

• What was the position of the source, microphones and starter at the beginning of the experiment? To get a reasonable data the source should be already moving when passing the first microphone.
• Do you have a signal long enough (in time) Fourier analysis to be precise? Did you try that on more frequencies? If you don't have a long window, bins of the FFT could be e.g. of 20 Hz!
• Have you tried to vary the microphones distance? What has that done to the uncertainty? The longer (with moreless constant speed), the better!
• Could there be any kind of delay in microphone-PC communication? (Least probable case.)
• Thank you for the input. - If we would use my given image as reference, I streched the ruber with source to around position (1) before releasing it, so it went through both microphones while moving. -For FFT I picked, for example, when source was heading towards second microphone until its max amplitude. The time between two microphones was around 0.1s, sampling rate was 192000Hz. Not sure if that's long enough time. But logically speaking the frequency changes made sense. I couldn't have tried another frequency of the source because it was really just an object with a switch for sound. – Laury Sep 13 '15 at 16:18
• To answer the third point, I did try to change the distance between microphones, yielding the same results. – Laury Sep 13 '15 at 16:19