How Do Resonance Frequencies Change with Sphere Position and Design?

[arielle]

Lab part I: We had to work with resonators. Huge box! Lowered a solid glass sphere into the box and measured the distance from the lid to the sphere. Varied the distance and measured the resonance frequency at the varies distances.

Q: ∆f =f(at distance x) - fr , fr = resonance frequency of the box without sphere.
You will find that ∆f varies periodically with x. (1) why? (2) What is the r/s between period in ∆f and λ of resonant f.

Attempt: I was thinking...prob has to do with mode?
Anyway the graph I got was a sine curve.

Part II:
Q: we used a slotted sphere. i.e a sphere with lots of slots. using a polar graph paper we managed to measure the angle of the tilt of the sphere. It is said that when the slots are orthogonal to the axis of resonator, then the slotted sphere acts like a solid sphere. When slots are parallel to axis, it causes small shift from resonant f. (1) why?

Attempt:Graph I got was a sine curve with little spikes at the tip, as the sine curve reaches the minimum and goes back up, it dips a little and goes up again.
Thank you! (:

 

[jbsteele]

Answer: 1. The reason why ∆f varies periodically with x is that the frequency of the resonance is directly related to the distance between the lid and the sphere. The frequency is inversely proportional to the distance between the two, meaning that as the distance increases, the frequency decreases. Therefore, when plotted on a graph, you would get a sine curve. 2. The relation between the period in ∆f and the λ (wavelength) of the resonant frequency is that the period is equal to the wavelength divided by 4. This is because a full wave is composed of four quarters, which explains the relationship between the period and the wavelength. 1. When the slots are orthogonal to the axis of the resonator, the slotted sphere acts like a solid sphere because the slots do not affect the overall shape or size of the sphere. Therefore, it behaves just like a solid sphere and does not cause any shifts in the resonance frequency. However, when the slots are parallel to the axis, they create small shifts in the resonance frequency because they disrupt the shape and size of the sphere, thus altering the resonance frequency.