Can you please provide suggestions on how I can improve this EEI and whether my ideas are right? Please also correct any errors if noted? ...

Can you please provide suggestions on how I can improve this EEI and whether my ideas are right? Please also correct any errors if noted? 

Introduction: http://www.enotes.com/homework-help/can-you-please-provide-suggestions-how-can-improve-485907 

Discussion

An experiment was conducted over a four week period, in order to test frequency changes with different volumes of water and frequency changes among different types of wine glasses. It was hypothesised that (1) adding water to a wine glass lowers its frequency (2) small wine glasses produce a higher pitch. Four different wine glasses were used: Big red wine glass, medium red wine glass, medium white wine glass, and a champagne glass. With each wine glass, three trials of the resulting frequencies at different volumes were collected and analysed. The results obtained show that frequency increases as the size of the glass decreases and decreases as more water is added to the glass thus confirming the hypothesis.  

Graph 1 shows that the frequencies of the wineglass with water at the bottom stayed the same in the beginning. This is because the bottom of the wineglasses has the smallest radius and is also supported by a stem. This reduces the distance that the glass can vibrate, thus reducing the duration of one wave. From the equation F=1/T, a decrease in the time of one wave cycle (T) produces an increase in the frequency. With increasing percentages of volume of water, the space for the glass walls to vibrate increases. In other words, T increases and thus the frequency decreases. This “space” is from the shape of the glass where the radius of the top of the glass is much larger than the radius at the bottom of the glass. Also, the glass walls are thinner at the top, giving the glass a more elastically property, making the walls vibrate more at the top of the glass.

The further up the water was, the easier the vibration waves were to be seen. The waves were seen close to the glass walls, and standing water patterns can be observed. They occur 90 degree to each other as seen in figure 1: the circle is the glass, it is the cross (+) that copies the movement of the finger when playing. These wave patterns are the nodes of this motion described in the introduction.  Another explanation to why frequency decreases as more water is added is that as water is added, the amount of vibrating material increases, slowing down the vibrations. Since there is more material to vibrate, a lower frquency is produced.

Graph 1 also proves the hypothesis that smaller wine glasses (having a smaller radius) produce higher frequencies. This can be noted at the beginning of the graph where (in order from smallest radius to the largest, see figure 3) the champagne glass had a frequency of 1171.88Hz, medium white wine glass had a frequency of 1015.63, medium red glass with a frequency of 761.72 and big red wine glass with a frequency of 664.06. This can also be explained by the equation F=1/T, where T increases as the radius increase and thus F decreases.

According to A.P. French, if (f0/f)^2 is plotted against against (1-d/H*) ^4, a straight line must be produced. The data was plotted and graphed in French’s equation. French states that an ideal wineglass gives perfect linear line when its data point are plotted on a graph. Therefore, it is expected that the graph for glasses that don’t change shape (champagne glass in this experiment) will be linear, and parabolic for those that change shape in an outward or inward fashion (large red wine glass, medium red and medium white wine glass in this case). This is because the same amount of water can be added to the champagne to increase the note by one note. However, for glasses that change shape outwardly, more water must be added every time to increase the note by one step.

The data points for glasses that change shape in this experiment displayed a slightly almost curved trend line, where the gradient increases with x-values.  Those results can be explained using French’s equation:

Where there equation is in the form of y=c +mx (m=gradient) 

Looking at the gradient of French’s equation, only the variables R (radius of water) and a (glass thickness) have not been controlled. Density of glass and liquid in this experiment remained constant since temperature of water used did not vary greatly and B is a constant French used. For R, with an increase in the percentage of the water volume, R increased because of the shape of the wineglass used. For a, with an increase in the percentage of the water volume, a decreases the further up the glass walls also because of the shape of the wineglass used. Therefore, R/a is an increasing value with an increase in the water volume percentage, thus giving the increasing gradient of the trend line in graph 2 and it also explains the slightly curved shape of those graphs.

The graph also shows how much the linear line does not fit the general equation of French’s. The big red wine glass had an RMSE of 0.1328, themedium red has an RMSE of 0.3844, medium white with an RMSE of 0.09268 and the champagne with an RMSE of 1.966. The Root Mean Square Error (RMSE) is a measure of how far away, on average, the data points are from the fitted curve. Smaller is better and thus the results are valid.Although the RMSEs are not large values, they are enough to show the varying factors that are involved in this experiment, like the thickness and the radius of the glass at the water level.

In each glass, the radius varies at different heights. The champagne glass, however, was the closest to the ideal cylindrical glass that P.A. French used. Therefore, the expected RMSE should be the smallest value when compared to the other glasses’ RMSE. However, this was not true (see graph 2). The expected order from the lowest RMSE to the highest (due to the varying radius within in each glass) is: champagne, medium white wine glass, medium red wine glass and big red wine glass. However, the results obtained shows that the order from the lowest RMSE to the highest is: Medium white wine glass, big red wine glass, medium red wine glass and champagne. This could have resulted from the following barriers:

All wine glasses has a peak (intensity) bigger than the microphone. Therefore, the first peak was taken off from the FFT graph. However, for the champagne glass, it had an intensity lower than that of the microphone, therefore the second peak had to be taken. However, difficulties were encountered when finding the second peak and thus could be a source of error which affected the champagne’s RMSE.

Another source of error is from the background noise. When measuring the frequency, the environment was not quiet which may have affected the frequency recorded, especially since the champagne produces very low pitches. However, a cardboard was used on one side of the microphone to reduce background noise interfering with the pitch of the wine glasses.

Other sources of error include the measuring straw used to find the distance of the height of the different water levels. Its accuracy was only to cm values. Also, the experimenter had to hold the straw while reading the water level height and thus the position of the straw may not have been the same each time. This can be another source of error.

It was also observed that the champagne glass does not sing with the same finger force applied to it as the force applied to the other wine glasses. It vibrated the most. When the straw was placed in the wine glass, it also started to move around, following the direction of the finger.

Several recommendations have been made to enhance this experiment. Firstly, improve the accuracy of results, it is suggested that a better measure equipment should be used to get more accurate results for the height of the water at different levels. Despite the RMSE errors, the results are valid as the trends (see graph 1 and 2) confirm research data and the conclusions drawn from similar investigations. Another recommendation is to completely block out background noise by conducting the experiment in a quietenvironment.

Conclusion

This experiment proves the hypothesis that adding water to a wineglass reduces its frequency and a small wineglass produces the highest pitch.  These results confirm the hypothesis and are consistent with background research as well as results from a separate, similar investigation.  Despite errors encountered, the results are valid as the trends (see graph 1 and 2) confirm research data and the conclusions drawn from similar investigations. (Morgan Johnstone, James Stallkamp, Fabianny Anez, n.d.)

Asked on by rainbow224

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gsenviro | College Teacher | (Level 1) Educator Emeritus

Posted on

In general, the writing and organization are good. However, evaluation would have been much easier if the plots had been provided (perhaps as image attachments).

Some of the corrections you may want to make:

"With each wine glass, three trials of the resulting frequencies at different volumes were collected and analysed" should be "With each wine glass, three trials each were conducted at different volumes and resulting frequencies were recorded and analyzed" (assuming that corresponding to each water volume for each glass, you did three frequency measurements, or in other words, triplicate sampling).

Sizes of the glasses need to be mentioned somewhere, especially to help the non-specialists, i.e. people who are not very familiar with the sizes of the different glasses used in your work. Also, when you say size, do you mean the distance between glass tip and stem (i.e. the bowl height) or radius? Please be clear on this.

Replace "The further up the water was, the easier the vibration waves were to be seen. The waves were seen close to the glass walls, and standing water patterns can be observed" with "The further up the water was, the easier the vibration waves were to observe. The waves were seen close to the glass walls, and standing water patterns were observed."

You write "They occur 90 degree to each other as seen in figure 1: the circle is the glass, it is the cross (+) that copies the movement of the finger when playing." What occurred at 90 degrees to each other? Also, you may want to use the term "orthogonal" to describe things that are at 90 degrees to each other. The information "the circle is the glass" should be provided in the figure caption.

"These wave patterns are the nodes of this motion described in the introduction" should read: "These wave patterns are the nodes of this motion, as described in the introduction section."

You write "Another explanation to why frequency decreases as more water is added is that as water is added, the amount of vibrating material increases, slowing down the vibrations. Since there is more material to vibrate, a lower frquency is produced." This should read "Another explanation as to why...." Also, part of this sentence seems copied and pasted from another source. You need to cite the source and in case you are citing it verbatim, kindly paraphrase.

"This can be noted at the beginning of the graph where (in order from smallest radius to the largest, see figure 3) the champagne glass had a frequency of 1171.88Hz, medium white wine glass had a frequency of 1015.63, medium red glass with a frequency of 761.72 and big red wine glass with a frequency of 664.06." You need to provide the frequency units with all the values here.

"According to A.P. French, if (f0/f)^2 is plotted against against (1-d/H*) ^4, a straight line must be produced." Kindly specify the meaning of different variables, such as f0, f, etc.

"This is because the same amount of water can be added to the champagne to increase the note by one note. " It would be a good idea to replace that with "This is...the champagne glass to...."

"The data points for glasses that change shape in this experiment displayed a slightly almost curved trend line, where the gradient increases with x-values." I would argue that "slightly almost" is very confusing choice of words. Consider revision.

"The graph also shows how much the linear line does not fit the general equation of French’s." This is a somewhat awkward choice of words. You may want to state that your results do not confirm to the trend stated by French.

RMSE need to be defined and its non-abbreviated form written at its first appearance.

"Other sources of error include the measuring straw used to find the distance of the height of the different water levels." The phrase "distance of the height" is confusing. I believe you mean the distance between the water surface and rim of the wineglass.

You have mentioned that French used a cylindrical glass and the glasses used in your study were non-cylindrical. In such an experimental design, one should not expect the same trends to be observed. Thus, it is hardly surprising that you did not observe the linear trends. The comparison of your work with that of French is somewhat difficult.

"Firstly, improve the accuracy of results, it is suggested that a better measure equipment should be used to get more accurate results for the height of the water at different levels." This should be replaced with "Firstly, to improve..., ...more accurate equipment...."

Also, only one suggestion to improve the results has been made; you may want to add more.

"These results confirm the hypothesis and are consistent with background research as well as results from a separate, similar investigation." I believe you meant "existing" instead of background research. Also, if a "separate, similar" work has produced similar results, you may want to cite them properly.

My main concern from the work is the effect of glass shape on results and the applicability of French's results for comparison, given that a current study used different glass shapes than French. 

I would suggest going through your work once more and looking for other typos or minor corrections. You should also try to improve the work by incorporating the effect of glass shape on your results.

Good luck.

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