Week 2

After examining existing phone case amplifiers on the market, Week 1 models of the case were modified. Most models featured a design in which the sound from the iPhone speaker was channeled through a funnel of increasing girth before opening to release the sound, as in Figure 1. 

Source: https://images-na.ssl-images-amazon.com/images/I/71-oe7QD9eL._SL1500_.jpg

Figure 1

Existing market product

Though no mathematical equation has been found to explain the relationship between shape and sound intensity, it became clear that a funneling "horn" shape was an accepted model for sound magnification. Further research will be conducted to find mathematical evidence to support this theory and optimize the space. An equation was found, however, to explain a material's ability to transfer sound. The speed of sound, c, through a material can be expressed with Hook's Law as the square root of the quotient of bulk modulus elasticity, E, and density, ρ, in the following equation:

c = (E/ρ)^1/2

Thus, by maximizing bulk modulus elasticity (a material's ability to withstand volume change under pressure) and minimizing density, a greater sound projection can be achieved. Materials research conducted revealed that aluminum is a quintessential material for sound transfer, as it has a high E/ρ ratio. Since the phone case will be 3D printed, an aluminum-infused PLA was found online that would be compatible with the printers in the innovation studio. A roll with enough PLA to easily print a case and dock can be purchased for 30 dollars. This material would be ideal for the case and dock, but special clearances will have to be obtained to use it in the lab's printers. Also, aluminum's low specific heat may be problematic, as the phone may easily overheat in its case. A rigid metal would also likely be a poor shock absorber, endangering the phone in the event of a drop. The construction of a case made of multiple materials will be considered for improved shock absorbance and heat transfer.

CAD for the case has begun. The first printed model of the phone case is expected by Monday, April 16. A 2D CAD drawing of the phone case is shown in Figure 2.

Figure 2

2D CAD drawing