# I Uncertainty of frequency

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1. Mar 16, 2016

### gagzi bear

what can be the uncertainty of the frequency that humans can hear ?
I'm aware that there are many ways,but i tried google-ing to find them but i couldnt.
if you could help me it would be great.

Last edited: Mar 16, 2016
2. Mar 16, 2016

### drvrm

i think you mean "hear" rather than here.
in that case the 'sensitivity" of our human instrument "ear' defines the range of differentiating the frequency and the error thereof.

The normal human ear can detect the difference between 440 Hz and 441 Hz. It is hard to believe it could attain such resolution from selective peaking of the membrane vibrations.

3. Mar 16, 2016

### gagzi bear

thanks for pointing out the mistake its hear.
but experimentally when I was finding the speed of sound i found 587.2Hz as a result im looking for the uncertainty i can use to add to the graph.
since we heard the frequency i thought uncertainty should bee the human hearing difference

4. Mar 16, 2016

### nasu

How did you measure the frequency? If you don\t describe your actual context, you will get irrelevant answers.

5. Mar 16, 2016

### rumborak

I think an absolute number won't make much sense, since almost everything regarding hearing works on a logarithmic scale. (e.g. the Mel scale: https://en.m.wikipedia.org/wiki/Mel_scale )

6. Mar 16, 2016

### sophiecentaur

The (western) musical scale has adjacent notes with a frequency ratio of the twelfth root of 2. That makes about 6% difference for a semitone. People with a 'good ear' can discriminate to within much less than a semitone (and even have a permanent memory of a note, when they have 'perfect pitch'). If you work with a figure of about 1% frequency discrimination memory you wouldn't be far wrong. That figure will only apply for mid range notes. Low and high frequency discrimination is nothing like as good. Listening to two notes at the same time, it is easy to detect a beat between them and that could be much better discrimination (well under a Hz difference for two (near) 1kHz tones.

How is it done in the cochlea? The crude model is that each of the resonating hairs in the cochlea will respond to a narrow range of frequencies and that the pitch is perceived in terms of which hair vibrates most. This link, and a load more links (google terms like frequency discrimination cochlea) suggest that it's much cleverer than that because we are aware of the time variation of the frequency components of what we hear, too.

7. Mar 16, 2016

### gagzi bear

hi i was doing the speed of sound using resonance tube and we kept n constant and changed length and and found frequency.
Tone gen app for iPhone was used to find frequency.we can change it to find the best resonance and record the frequency that gave the best.

8. Mar 16, 2016

In tuning a stringed (fretted) musical instrument, you can get two notes to match well within one Hz of each other by listening to the beat (difference) frequency that occurs when the two notes are almost identical in frequency. Octave strings can also be tuned by getting one note (e.g. the high E) to resonate when the lower octave (e.g. the low E) is bowed or plucked. A resonance tube may have a very narrow range over which it resonates, but I have limited quantitative info on how narrow the resonance may be.

9. Mar 17, 2016

### sophiecentaur

It's worth mentioning that time and frequency (effectively the same thing, in measurement terms) can be measured to a greater accuracy than any of the other quantities that we measure in Physics. It makes no real difference what actual frequency you are talking about because it's all a matter of ratios. It amazing just how easy it is to equip yourself with a rubidium controlled frequency standard source with an accuracy of better than 1 part in 1011. (Just a few hundred GBP second hand on eBay!!!) Moreover, you don't need a special climate controlled room to operate it. You keep it on a bench and it will reach 'almost' its steady frequency in a matter of minutes.

Last edited by a moderator: May 7, 2017