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# Uncertainty of the speed of a wave watch

1. Hey, well basically, I chose Melde's experiment for my AS level physics coursework, measuring the first five standing wave patterns for various tensions. i recorded the value of both frequency and wavelength in order to calculate v via v=f*wavelength.

Example results :

Tension
1N Frequency (Hz) 17.5 26.2 35.2 44.3 53.8
Wavelength (m) 1 0.675 0.5 0.41 0.345
Velocity (ms?¹) 17.5 17.685 17.6 18.163 18.561 Average velocity 17.9018ms^-1

My problem is that, i'm unsure how i would calculate the uncertainty present in the average of v. If freq. has an uncertainty of +- 0.05hz and wavelength +- 0.01m. Would i find the min and max values for both and calculate min and max values for the velocity at that frequency. Repeating for each different column, then finding an average max and avg min for the speed, subtracting the two and halving to find the +- uncertainty.

Would i then use this uncertainty on the original avg vel. eg 17.9+-0.5ms^-1
or would i calculate the mean of the two max and min values of v to get a different average? Although if i did that then doesn't it render my first results useless?

Hopefully that makes sense. Probably not though xD

Regards.
2. Find the percentage uncertainty in both the wavelength and the frequency. Use the biggest percentage to calculate the uncertainty in the velocity
3. If the uncertainty in f really is ±0.05 Hz that is an error of less than 1% (0.05 in 17.5 is 0.28%)
If the uncertainty in wavelength really is ±0.01m then that is about 3% max (0.01 in 0.345)
This gives a maximum uncertainty in v of between 3 and 4%.
That is a little under 3%
So there seems to be consistency.
By far the larger source of possible error in this experiment is the measurement of the wavelength. (See also below*)
However, it looks a bit suspicious as the value of v seems to be increasing as you increase the number of antinodes.
Can you be certain that this apparent increase is just due to random experimental error, or due to something else? Would not the values of v lie randomly about the mean value, rather than seeming to show a (slightly) increasing trend?

There's something that puzzles me about these results.
You say they are the first 5 standing wave patterns.
In this case, shouldn't the first one be the fundamental (lowest) frequency?
The others are then all a multiple (2f, 3f, 4f, 5f etc) times this?
In your results this doesn't happen. The others are not a whole multiple of the 1st. (17.5, 26.2, 35.2, 44.3, 53.8)
It looks like the fundamental is around 9Hz and these are all multiples of that. Did you measure the case with one loop, a single antinode in the centre of the wave? This would have been the 1st (fundamental) frequency.
By the way, this would not affect your results or calculation, but would need to be commented on.

* There could be a small systematic error in the results. This is due to the fact that the end of the string where the resonator is, is not quite a node. After all, a node is a place of zero displacement, and the resonator is moving there, so how can it be a true node? In reality, so long as the amplitude of the resonator is small it doesn't cause a problem. Even so, it means that the measurement of the wavelength is always out by a small amount for each vibration mode. As the wavelengths get smaller, this small difference gets proportionally larger. This could account for the fact that your velocity values seem to increase as you increase the frequency.
Of course, there could be other reasons.
Most text book conveniently ignore this!
4. Ahh thanks, yeah it does look a tad suspect xD although this was just a sample of many results and on others it seemed to stay fairly consistent, i also repeated the experiment using a set length of 1m between vibration generator and pulley. which effectively got rid of uncertainty in wavelength. and all those results showed no increase in v along with increase in anti-nodes. must have just been the ones i sampled xD

Yeah sorry should have been clearer, ignored the fundamental, (which was around 9Hz or something) and just measured from the first standing wave which creates a full wavelength.

I have thought about the fact the node at the generator isn't perfectly still but my teacher said it was negligible to the experiments data (although i will probably mention it at some point)

Thanks
5. (Original post by WE3MAN)
Ahh thanks, yeah it does look a tad suspect xD although this was just a sample of many results and on others it seemed to stay fairly consistent, i also repeated the experiment using a set length of 1m between vibration generator and pulley. which effectively got rid of uncertainty in wavelength. and all those results showed no increase in v along with increase in anti-nodes. must have just been the ones i sampled xD

Yeah sorry should have been clearer, ignored the fundamental, (which was around 9Hz or something) and just measured from the first standing wave which creates a full wavelength.

I have thought about the fact the node at the generator isn't perfectly still but my teacher said it was negligible to the experiments data (although i will probably mention it at some point)

Thanks
Yes the error due to the node not being exactly at the end is probably negligible.

One thing I would add is that the error in the frequency is going to be greater than your stated value if that value is simply the precision of the scale or readout of the generator. In order to get the standing wave condition you adjust the frequency until you see the antinodes. However there will certainly be a degree of play here where you can increase and decrease the frequency a small amount and still get a good standing wave. You need to estimate this amount of give and take in locating the point where you get resonance, and using it as a + or - in the reading.

If you have measured the fundamental where you get a half wavelength, you should include this in your data, or be prepared to give a good reason why you have ignored it.

Good luck.
6. May I ask what medium the wave is going through and at what temperature?

I am confused at how you got the wavelength of 17.5Hz to be 1 0.675m.

Is this about a sound wave or is this about a different wave?

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