# Science Questions

## How fast does my toothbrush vibrate?

Sun, 30th Mar 2008

Part of the show Tuberculosis and Magnetic Bacteria

### Question

I wanted measure how fast my sonic toothbrush actually brushes so I used a sound recorder to measure the sound it makes. I then looked at the waveform that the computer can show up to show how many oscillations per second. I counted 25 per tenth of a second which is only 15,000 cycles per minute but they claim on the packaging that it’s 30,000.

Ben: I’m not really sure I know this is the best way to measure it. If anybody knows get in touch: Chris what do you think?

Chris: I think you may be on to something. When I was driving around in Australia last year a group of school children tried to measure vitamin C in foodstuffs as their school science project. They took an off-the-shelf substance, food or drink cordial which is well known-very powerful brand, full of vitamin C. They thought, ‘we’ll use that as the control because we know that will have lots of vitamin C and if we can detect that we know our experiment’s working.’ They kept getting a negative result. It turned out that the company were lying and saying it was full of vitamin C and there was none in it. They had to pay a very big fine and change all their labelling. It could be that with this sonic toothbrush there’s a little bit of adventurous advertising going on. I think if anyone else has a sonic toothbrush and they would like to record it, analyse the waveform. If in fact you’ve done this, please do experiment and then tell us how many cycles a second is it producing? Is there some misleading advertising going on?

Ben: It would be fascinating to find out and we’re really pleased, Mark, that you’re getting into Kitchen Science in this way.

So what do you think?  Is this a good way to find out how fast a sonic toothbrush vibrates?

#### Make a comment

I suppose this could be explained by "marketingspeak". i.e. 15000 oscillations = 30000 brush movements, if you count each direction as a separate action...?

I wouldn't want to comment further without knowing exactly what your experimental setup looks like, and knowing a bit more about the mechanics of the toothbrush.

Broadly speaking, the method should have potential though. techmind, Sun, 6th Apr 2008

That was my conclusion as well daveshorts, Mon, 7th Apr 2008

Hi, Gents! Love the show. I'm a fan from Iowa in the US.

I agree with Ben that this seems suspect. First, this assumes that the sound emitted from the toothbrush is produced solely by the a 30kHz (or whatever) oscillation of the mechanism and nothing else (like constant, garden-variety friction). Few things emit what approaches a pure periodic sound, though. So whatever sound you get will likely be a composite waveform, created by all sorts of constructive and destructive interference. While we're at it, we're also assuming that the microphone used is capable of capturing a 30kHz sound, which probably isn't the case. Since the upper frequency limit of human hearing is around 20kHz, most consumer (and even commercial) mics don't accurately capture sounds much above 20kHz. Even if they did, the frequency and amplitude of this component of the emitted sound would probably be buried in the waveform.

Cool idea, but too many flawed assumptions.

Thanks for all of your great work! arioso, Fri, 11th Apr 2008

Sounds like a plausible argument; thanks everyone. chris, Thu, 17th Apr 2008

If you are recording the waveform digitally then you have to sample at twice the maximum frequency you want to record. Your sound card will certainly not be doing this, if it's an off the shelf audio card. What has probably happened is that your 'sub-sampling' has produced a beat frequency (artifact) at some audio frequency. Buy a system which can record ultrasound and you may get the right answer. One question; did you hear that pitch of sound from your toothbrush that the recording picked up? lyner, Thu, 17th Apr 2008

He may have been able to record the toothbrush okay, if the frequency is, as we suspect, 15kHz - because most soundcards offer up to 48k sample rates; so he was probably ok. Even with 44100, which is standard, it would have eben alright.

If the frequency genuinely was 30kHz then, as you say, it won't be a real answer.

Chris chris, Fri, 18th Apr 2008

In principle you're all right - you need to sample at at least twice the frequency you're trying to measure. Normal PC soundcards sample at 44.1kHz, so 20kHz is about the absolute upper limit you can measure. Many ordinary cheap microphones will rapidly lose sensitivity above much above 15kHz too.

But in this question we were considering frequencies of 15000 or (maybe 30000) oscillations per minute, whereas frequencies are normally measured in cycles per second (Hz).

So despite the 'sonic' name (which can trigger thoughts of 'ultrasonic'), the frequencies we're looking at here are really quite modest (a few hundred Hertz), so sampling shouldn't be an issue.
techmind, Fri, 18th Apr 2008

Well spotted tm. Fools rush in etc.
Sonic only means you can hear it - I can hear mine too!
500Hz isn't very high. lyner, Fri, 18th Apr 2008