1) (50 pts) In the first day demonstration, you observed that the resonant frequency of a 750 ml wine bottle was lower than the resonant frequency of a 1000 ml soda bottle.
Assuming that the diameters of the opening were the same, explain how the wine bottle could have a lower frequency. Reference the Helmholtz resonator equation in your answer.
2) (50 pts) In Module 2.4 there was a pendulum lab.
a. In the online pendulum lab, you changed mass, displacement angle, length and gravity. Which of the above variables had no effect on the period? Explain why using the pendulum formula.
b. One of the options in the pendulum lab was the gravity of Jupiter. Explain how that would affect the period compared to Earth’s gravity. Explain why using the pendulum formula.
Extra credit (20 pts) – Choose one:
Design an experiment that would show how changes in opening area would affect the frequency of a Helmholtz resonator.
Referencing question 1 above, one dimension (variable) caused the wine bottle to be lower in pitch than the soda bottle.
If the frequency of the wine bottle was 100 Hz and the frequency of the soda bottle was 200 Hz, what would be the ratio of the wine bottle dimension to the soda bottle dimension? Explain your reasoning and show your calculations.