Week 8

The second dock design was retrieved this morning. Unfortunately, the slot for the phone was too small and had to be cut away to fit the phone. Because of this, the horn path was disrupted, and sound did not travel as designed. For this reason, precise tests were not performed. However, subjective testing was promising. Music was played on the phone, which was then placed in the case, then the dock, while the phone volume remained constant. It was clear that the music was significantly louder when the phone was in the dock than when it was in the case alone. This test showed that the horn model is more effective than the bowl model utilized in the previous dock design. The second dock is shown below.

Dock 2

Dock 2 with case

The main accomplishment of this dock design was that it proved that a large horn can be printed with the available equipment. Building on this success, another dock was designed in CAD with features that should amplify the music according to last week's mathematical modeling. The CAD designs for the third dock design are shown below. The most important feature is the parabolic funnel shape that extends out to the mouth where sound is released. Mathematical modeling and empirical data show that this design will amplify sound. Other changes to the second dock design include a larger slot for the phone, and a more forward center of mass, since the weight of the phone tended to tip the previous dock.

CAD model of dock 3

Internal view of dock 3, demonstrating horn

Due to the fine edge at the mouth of the horn, the print has a high degree of technical difficulty and is somewhat likely to fail. To improve the chances of success, the horn will be printed in two pieces, as a semicircle is far easier to print than a circle. Supports will also be added to the inside of the dock, though it will be tedious and difficult to remove them from the neck. If this print fails, the size of the horn will be reduced to give more thickness to the mouth. Obviously this will have a negative impact on the sound amplification ability of the dock, but may be a necessary sacrifice.

The equation L=(log(A)-log(a))*4000/(f*0.4343) expresses the ideal value of one of the variables given the other 3 to maximize the amplitude of sound waves through a horn, where "L" is neck length of the horn, "A" is area of the mouth, "a" is area of the throat, and "f" is the frequency of the sound waves. The areas of the mouth and throat of the horn are 75 mm and 35 mm, respectively. The neck length is about 150 mm and will be able to be more precisely measured after the dock is printed. Using the previously mentioned equation, the ideal frequency for a horn of these dimensions is 20kHz. This value is well outside the frequencies generally found in music. In fact, 20kHz is about the highest frequency a human ear can detect. However, this does not mean the horn will be ineffective; the equation only tells which frequency will experience the greatest amplitude due to the horn. The horn will still amplify frequencies found in music. The reason the dimensions of the horn in the third design are not optimized to amplify typical music frequencies is because the main objective of this print is to confirm that a horn this intricate can be printed. If successful, the dimensions will be adjusted to optimize amplification for musical frequencies.