(b) So my second thought was a digital camera. This may also be better because I can then save the pictures to a disk and look them up at home where I would have more time. I used a friend take pictures of the oscilloscope while I was resonating the wine glass.
However encountered another problem when I got home and brought up the images on my computer; the images were not very focused and I could not see the small markers between squares on the oscilloscope so could not accurately read off measurements. The next day I would have to overcome this problem. I needed more light on the screen of the oscilloscope. The flash on the camera was no use as it reflected back from the screen.
Solution: To light the screen by shining a small concentrated light onto it.
Day 3
Aim
To overcome the lighting problem and collect some results.
Achievements
I used two small lamps, directed at the screen of the oscilloscope to illuminate it, hopefully making the small markings readable on the digital photos. However, this was still unsuccessful so I decided to try and use the natural light from the window as the rest of the room was quite dark and enclosed. I set up my experiment again, making slight adjustments due to the different space available and the direction the oscilloscope must be facing. This diagram illustrates the new set up:
I took one photo while resonating the wine glass and looked at it on a computer to check the image came out clearly enough and the markings could be seen. Success!! I also found this set up was preferable to the last as I could resonate the wine glass and take a photo at the same time so would not need anyone to aid me.
Additional Equipment
- digital camera
- pile of books
- beaker hold water to dip finger in
- floppy disks
Method
- Wet finger
- Run around rim of wine glass applying more or less pressure and at a varying speed until a pure note can be produced
- Take 3 photos using the digital camera of the oscilloscope screen
- Add 10cm3 of water to the glass and repeat method
Method for Obtaining Results
This photo shows how I measured my results.
The time period I measured was in milliseconds and to obtain the frequency I just did one divided by this number so as to see how many waves there would be in one second. I used the photos obtained by the digital camera to measure the time period between waves on my computer at home. I took 3 pictures of the wave produced at each 10cm3 volume interval because I realised it would be difficult to read the exact measurement and some human error would be involved. An average of 3 ensures a fairer representation as one result could be a freak. The problem of this however, is that if a freak result were one of the 3, it would distort the average anyway.
Results
As this graph does not pass through the y axis at a lower point and gradually get higher I decided to change the volume measured from the amount of water left in the glass to the amount of air left in the glass. This way I could more clearly demonstrate my findings.
The results shown in the scatter graph, I believe, show a definite trend. There is quite a strong correlation; however, it could be argued whether a line of best fit would be a curved or straight line. What is certain is that as the volume of water in the glass increases, the frequency decreases. My prediction was correct.
Analysis
To ascertain how much possibility there was of this being a straight line. I have used a statistical method to analyse correlation. This involves taking the x and y values and formulating them into and equation which shows the strength of a correlation.
Unfortunately I had to remove the row of 110 cm3 of air because of a lack of results. This would affect the result I obtained for correlation. -1<r<1 , -1 being a perfectly straight negative correlation and 1 being a perfectly straight positive correlation and 0 showing no correlation at all for example, as would be the case in a circle. The number of 0.6 shows that the line created is a positive correlation and that it is not particularly strong. There is therefore a strong argument towards the fact that this line should be curved (ignoring all errors).
Explanation
The reason that the water changes the frequency of the sound waves produced is that as a resonant wave moves around the glass, it drags the water molecules with it, creating a wave of water that you can see near the edge of the glass. The dragging water molecules increase mass and reduce the energy of the wave travelling through the glass. When the energy is reduced, so is the frequency of the wave in the glass.
Errors
There could be a relationship between the pressure forced upon the glass by my finger and the voltage signal produced. This would mean the varying pressure of my finger would cause errors in the results. However, if this were true I would have had to have kept a reasonably similar pressure for all the results as they didn’t fluctuate greatly.
Another slight inaccuracy could be in the readings taken from the oscilloscope. As I can only judge the readings to 0.5ms human error is unavoidable. The scale provided on the oscilloscope is only a general guidance.
T= + 0.05m/s, so margin of error for f= 1/T +0.05
Error bars can be seen in all graphs so as to indicate the margin of human error in the results.
Day 4
Aim
To investigate how the size of the glass affects its frequency.
Achievements
I found 3 glasses of varying sizes shown in the picture below and measured the maximum water capacity.
Glass 1
I first tested glass one in the same way as my initial investigation except this time I measured the frequency every 20cm3 just to gain a general picture of the type of frequencies it was capable of.
Results
The results show the trend of a curved line, similar to that of the first wine glass. As the volume increases the frequency becomes lower; a deeper sound. This was recognisable while doing the experiment toward the end of filling the glass. I believe it is the shape of the glass which affects the results.
Day 5
Aim
To complete my investigation into how the size of a wine glass could affect its frequency at different volumes.
Achievements – Glass 2 and 3
I collected results for the 2nd and third glasses featured in my previous photograph. I took results every 20 cm3 of water for the second glass but took results every 10cm3 for the third glass as it was so small. Taking results every 20cm3 would have given too few results to make an accurate judgement.
Results from Glass 2
This again shows a curved trend. As the volume of water increases, the frequency decreases.
Results for Glass 3
On this scatter graph, a curved line of best fit will fit quite well with only a couple of possible freak results which I have circled.
Combined Results
This scatter graph shows a comparison of the results for each glass. The different shaped curves provide a representation of the shape of each glass. From the picture I can see that the original glass and glass 1 are of a similar shape and so they provide similar frequencies as shown in the graph. Glass 2 and 3 also have similar shapes and their frequencies are also similar. I believe that the shape of the glass has a strong relationship with the frequency produced at different intervals.
Analysis
I believe the shape of the graph directly relates to the shape of the glass. The main way that the frequency is changed is due to the fact that as the waves travel around the glass they drag water molecules. The more that is put into the glass, the greater the surface area that the water is in direct contact with the glass. The greater the surface area, the more molecules will be dragged around the glass with the vibrating wave. When no water is in the glass, the whole surface area of the glass makes direct contact the air thus no energy is lost. However, if a set amount of water removes a set amount of energy, ie. if they were directly proportional, the graph would show a straight line. Instead the curved line leads me to believe the amount of energy removed by the water is instead proportional to the amount of air left in the glass.
This diagram roughly demonstrates my idea. If x represents the amount of air in the glass, then as x becomes smaller, y (the amount of energy taken from the wave, become larger). The value of y I have given is only a rough guide. The real relationship could be any multiple of this of any power of x>0. The graph roughly shows what my general formula would look like as a set of results.
I have calculated a possible frequency as shown in table by using 1.4kHz – y. As the graph shows my theory works well with the graph taken from the practical results obtained.
Although I am able to explain my results in a general mathematical way, I am unfortunately unable to explain them in a physical or practical way.
Day 6
Aim
To use a different type of liquid in the glass to see if this affects the frequency. I have chosen fairy washing up liquid as it is of a different consistency to the water.
Method
I had to use a slightly different method to measure the fairy liquid as I realised that if I measured it in a measuring cylinder, the majority of the liquid would be left down the tube as I poured it out. Instead, I poured water in at intervals of 10cm3 into the glass and made markers at every stage. This way I could pour the fairy liquid directly into the glass without losing any or creating an inaccurate measurement of the volume.
Problems Encountered
Although I devised a method for creating a more accurate reading of the volume, I still encountered many problems will doing this experiment. For example, one problem was that as used water on my finger to create resonance, the water gradually ran down the side of the glass, half washing the markers off. On reconsideration, it would have been better to use a permanent pen for the markers, however, as this was a school glass, I didn’t really have a choice.
I also tried using fairy liquid on my finger tip to resonate the glass but found it wouldn’t work. I believe this is because the fairy liquid made rim of the glass too smooth so the jerky movement needed make wave vibrations in the glass could not be created. I researched this further and found my assumption was correct. There is no oil on a wet finger tip so it makes better contact with the glass.
Finally I could only collect results up to 150cm3 of water in glass due to the fact that at 160cm3 the fairy liquid kept getting stuck to my finger tip, making it impossible to create resonance.
Results
This scatter graph of preliminary results shows that the constituency of the liquid has made no difference to the change in frequency produced by the glass when resonated. However, there are a few discrepancies which I have circled. Therefore, I have decided to try different volumes of sugar in water to change the constituency many times as a final assurance.
Day 7
Aim
To test to see if adding sugar into water changes the frequency produced when resonated.
Method
I used glass 2 for this experiment as it is smaller so less sugar has to be added and I found it easier to produce a clear note with this particular glass. I left 70cm3 in the glass to keep the water as a constant and added 0.5g of sugar after each set of results, measured using a set of scales accurate to 2 decimal places. I also took into account the weight of the paper on which I put the sugar to be weighed before I tipped it into the glass. I took 3 photos of the wave produced at each interval.
Results
These results clearly show that the amount of sugar in the water does not affect the frequency produced by the glass when it is resonated. There is no change in frequency at all.
Day 8
Aim
To investigate how the speed of my finger around the rim of the glass affects the amplitude of the sound produced. I predict the sound will be louder as the speed increases. This is based on what I have noticed during the previous investigations.
Method
I used a record player turn table to obtain different speeds at which my finger could travel around the glass. I placed 5 markers onto the turn table and the speed of the marker would represent the speed of my finger around the glass. As the table turned I concentrated on one particular marker at a time and equated the motion of my finger around the glass with the motion of the marker around in a circle.
Calculating the results
I measured the speed of each marker by timing, with a stop clock, the number of seconds for the table to turn once. I then measured the distance of each marker from the centre of the turntable to obtain its radius and used the formula ∏d to calculate the circumference of the circle made by each marker. In this way I could find the distance it travels in one turn and using s=d , I could find the speed.
t
Results
These results do not seem to follow a particular pattern together, rather they seem to have two different patterns or a lot of freak results. One graph shows possible lines of best fit. I did notice that the two main different lines of best fit were created by the two different speed settings on the record player. The results taken when the turn table was set to 45 are circled in blue. I have decided to do the experiment again and see how the new results compare to these.
Day 9
Aim
To retake results form yesterday due to confusion.
Results
On one graph I have drawn possible trend lines but I don’t think there is a strong enough correlation to definitely say there’s a relationship between the speed my finger travels around the glass and the voltage signal produced. I again noticed that the two sets of results seemed to belong to the two different speed settings on the record player.
Possible Explanations
- It could be that it is easier to follow the markers on the inside/outside of the turn table and so this distorts the results. This is human error which is unavoidable in the type of uncontrolled environment in which my experiment was conducted.
- There could instead, be a relationship between the pressure forced upon the glass by my finger and the voltage signal produced. However, I cannot test this as I do not have the equipment.
- Although only slight, the error could be partly due to any inaccuracies in the readings taken from the oscilloscope. As I can only judge the readings to 0.5mv human error is avoidable. The scale provided on the oscilloscope is only a general guidance.
Other Strange Occurrences
On a few occasions a standing wave was produced on the screen. I believe this is not really to do with the reflection of sound waves from other objects to the microphone (see diagram)
This diagram shows what could have happened. Sound waves are vibrated out from the wine glass and travel in all directions. One wave can reach the microphone in phase and another could be reflected from an object to the microphone and be out of phase at is has travelled a longer distance.
As can be seen on the two pictures above, one wave appears to be brighter and clearer than the other. This could show that the line which traces the wave on the oscilloscope has just finished the first trace and gone back trace the next period of t. For this to be rectified, the dial on the oscilloscope would have to be changed to al the time that each square represents.
See tables 1,2,3 in appendix
See tables 5,6 and graph 3 in appendix
See tables 7,8 and graph 4 in appendix
See tables 9,10 and graph 5 in appendix
See table 11 and graph 6 in appendix
See table 12 and graph 7 in appendix
See tables 13, 14 and graph 7.5 in appendix
See tables 16, 17 and graph 8 in appendix
See tables 17, 18 and graph 10 in appendix
