Resonance frequencies question (first and second resonance frequencies)

In summary, resonance frequencies are the natural frequencies at which an object or system vibrates with the highest amplitude, determined by its physical properties. These frequencies can have both positive and negative effects, such as amplifying vibrations or causing structural damage. The first resonance frequency is the lowest and the second is the next highest frequency at which resonance can occur. Calculation of resonance frequencies depends on the object's properties and can be controlled by adjusting them or using damping materials.
  • #1
supernova1203
210
0
Trying to figure out how to go about solving this question, using these forumlas i tried to solve it but i didnt get the right answers

for frequency 1 i went with

f1=v/2L

for frequency 2 i went with

f2=v/L


any ideas on how to solve this?
 

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  • #2
The question says the whistle is closed at one end.

You had the right idea about how to answer the question, but you used the wrong formulas.
 

1. What are resonance frequencies?

Resonance frequencies are the natural frequencies at which an object or system vibrates with the highest amplitude. These frequencies are determined by the physical properties of the object or system, such as its mass, stiffness, and damping. When an external force is applied at these frequencies, it can cause the object or system to vibrate with a larger amplitude, which is known as resonance.

2. How do resonance frequencies affect objects and systems?

Resonance frequencies can have both positive and negative effects on objects and systems. On one hand, they can be used to amplify vibrations, which can be beneficial in music and communication technologies. On the other hand, resonance frequencies can cause unwanted vibrations that can lead to structural damage or failure in buildings, bridges, and other structures.

3. What is the difference between first and second resonance frequencies?

The first resonance frequency is the lowest frequency at which an object or system can resonate. It is also known as the fundamental frequency. The second resonance frequency is the next highest frequency at which resonance can occur. In general, the higher the resonance frequency, the less energy is required to produce resonance.

4. How are resonance frequencies calculated?

The calculation of resonance frequencies depends on the physical properties of the object or system. In simple cases, such as a mass on a spring, the resonance frequency can be calculated using the equation f = 1/(2π√(k/m)), where f is the resonance frequency, k is the spring constant, and m is the mass. In more complex cases, such as structures with multiple modes of vibration, computer simulations or experimental methods may be used to determine resonance frequencies.

5. How can resonance frequencies be controlled or avoided?

Resonance frequencies can be controlled or avoided by adjusting the physical properties of the object or system. For example, changing the mass or stiffness of a structure can shift its resonance frequencies. In some cases, damping materials can be added to reduce the effects of resonance. Computer simulations and experimental testing can also help identify potential resonance frequencies and inform design choices to avoid them.

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