# Does resonance have limit?+Fluid

• tksxkdhkd11
In summary, the resonator resonated and near the open end of the resonator, I could feel wind. The strength of the wind was constant, even though the amplitude of the soundwave was constant. This suggests that the resonator is resonating at its resonance frequency.
tksxkdhkd11
I made a helmholtz resonator by myself and played its resonace frequency sound to it. Obviously, the resonator resonated and near the open end of resonator, I could feel wind.
So I placed candle near the opening to see the strength of wind. Surprisingly, If decibel of soundwave was constant, the candle's movement was constant. Which means, the angle of tilted fire was constant.
What I thought was that when a material is resonating, It's amplitude of vibration continues to increase although the external soundwave's amplitude is constant. Isn't it true? If it is true, Why was the strength of wind constant? ( the lump of air near opening of Helmholtz resonator also goes under harmonic motion.)( For sure, the lump of air oscillate at resonance frequency.)

Isn't wind strength a velocity of fluid? So if wind strength is constant, it means that frequency and velocity of lump of air is constant. right??

other than that, is it the flow rate(N) that affects movement of fire or velocity of fluid?

You are right that the mathematical solution of an equation like ##x'' + \omega^2 x = F \cos \omega t## increases without limit, but a real resonator always loses energy for some reason. It is described better by an equation like ##x'' + 2\beta\omega x' + \omega^2 x = F \cos \omega t## where ##\beta## is a measure of the amount of energy loss.

For a Helmholtz resonator, there are two main causes of energy loss:
(1) The resonator radiates sound energy into the air. Note, that fact is not mentioned in many introductions to sound, when discussing things like the boundary conditions for open and closed pipes! It is the physical reason for the "end correction" of the length of an open pipe resonator.
(2) The viscosity of the air causes energy loss at the surface of the resonator, where the air velocity is always zero.

The size of (1) depends mainly on the cross section area of the neck of the resonator. (2) depends on the total surface area of the resonator.

Thanks! there's something confusing though;; When length of Open pipe increase, It is sure that the resonance frequency decreases due to friction. However, isn't the effective length, or end correction for Helmholtz Resonator L+1.4r??
What I think is because the "end correction" range increase as length increase, Although natural frequency decreases, because the amplitude of oscillation is greater, the velocity of air will be great. Am I correct? I am not sure whether longer effective length can be viewed as larger amplitude;;

## 1. Does resonance have a limit?

Yes, resonance does have a limit. Resonance occurs when an object or system vibrates at its natural frequency, but this vibration can only occur within a certain range of frequencies. Going beyond this range can result in damping and a decrease in resonance.

## 2. How does resonance work?

Resonance is a phenomenon that occurs when an object or system vibrates at its natural frequency in response to an external force. This external force can be in the form of sound waves, mechanical vibrations, or electromagnetic waves. When the frequency of the external force matches the natural frequency of the object or system, resonance occurs.

## 3. Can resonance cause damage?

Yes, resonance can cause damage if the amplitude of the vibrations is too high. For example, in bridges and buildings, if the frequency of the wind or an earthquake matches the natural frequency of the structure, it can cause excessive vibrations and potentially lead to structural damage.

## 4. Is resonance only limited to solid objects?

No, resonance can occur in both solid and fluid mediums. In fact, resonance in fluids, such as air or water, is the basis for many musical instruments like flutes and clarinets. Resonance can also occur in other fluid systems, such as in the human body where ultrasound is used for medical imaging.

## 5. How can resonance be controlled?

Resonance can be controlled by changing the frequency of the external force or by altering the natural frequency of the object or system. For example, in musical instruments, changing the length or thickness of a string can change its natural frequency and thus the pitch of the sound produced. In engineering, dampers can be used to absorb and dissipate energy to prevent excessive vibrations and potential damage.

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