How Do Resonance Frequencies Change with Sphere Position and Design?

In summary, by varying the distance between the lid and the sphere and using a slotted sphere, we were able to observe the periodic variation of ∆f and how the orientation of the slots affects the resonance frequency.
  • #1
arielle
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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! (:
 
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  • #2
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.
 

FAQ: How Do Resonance Frequencies Change with Sphere Position and Design?

What is a resonator?

A resonator is a device that is used to produce and amplify vibrations or sound waves by making use of the phenomenon of resonance. It typically consists of a chamber or cavity in which sound waves can bounce around and amplify, creating a louder and more defined sound.

What is the purpose of a resonator in a lab experiment?

In a lab experiment, a resonator is used to study the properties of resonance and how it can be manipulated. It can also be used to measure the frequency and amplitude of sound waves in different materials, and to analyze the effects of different shapes and sizes of resonators on sound waves.

How does a resonator work?

A resonator works by creating a standing wave pattern within the chamber or cavity. This standing wave pattern is created when the frequency of the sound wave matches the natural frequency of the resonator, causing it to vibrate at a higher amplitude. This amplifies the sound and creates a louder and more defined tone.

What are some common types of resonators used in lab experiments?

Some common types of resonators used in lab experiments include Helmholtz resonators, cavity resonators, and tube resonators. These can be made out of different materials and have different shapes and sizes, allowing for a variety of experiments and measurements to be conducted.

What are the applications of resonator lab experiments?

Resonator lab experiments have various applications in fields such as acoustics, physics, and engineering. They can be used to study the properties of sound waves, measure the frequency and amplitude of different materials, and design and test new resonator systems for practical applications such as musical instruments, speakers, and communication devices.

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