Velocity of air, period, flutes and resonant frequencies

[ajd17]

Hi,

We were talking about the speed of air expelled from the mouth as it passes over the embouchure hole of a flute, and I'm having trouble understanding part of the concept. At one point, in the notes, I have if the velocity of the airstream is greater than the period of the flute cavity's resonance frequency, then the deflections created by the airstream will not help the high frequency oscillations self-reinforce. Later the prof says if the resonant frequency in the flute's cavity is below the airstream resonant frequency, then this is the optimum speed for driving the resonance.

I like numbers as ways of explaining but I am not a mathematician, so if someone would give me an example of airstream velocity and the period of a frequency where the velocity of the airstream is higher, that would be great. I'm stuck at the understanding that velocity is m/s, while period is measured in seconds, or frequency is measured in cycles per second. If someone would be so kind as to show me how to make the correlation between the two (formulas??), that would be appreciated.

And no, this is not a homework question, although understanding this will help me when it comes time for the final.

Thanks,
ajd

 

[eljose79]

Dear ajd,

Thank you for your question about the relationship between the velocity of an airstream and the resonant frequency of a flute cavity. This is a complex concept, but I will do my best to explain it in simpler terms and provide an example to help clarify.

First, let's define some terms. The velocity of an airstream is the speed at which the air is moving, usually measured in meters per second (m/s). The resonant frequency of a flute cavity is the natural frequency at which the air inside the cavity vibrates, usually measured in cycles per second or Hertz (Hz).

Now, let's consider the statement "if the velocity of the airstream is greater than the period of the flute cavity's resonance frequency, then the deflections created by the airstream will not help the high frequency oscillations self-reinforce." This means that if the airstream is moving too fast, it will not be able to interact with the resonance of the flute cavity and help to amplify the sound. In other words, the airstream will not be in sync with the natural frequency of the cavity and will not contribute to the resonance.

To better understand this, let's look at an example. Let's say the resonant frequency of a flute cavity is 100 Hz. This means that the air inside the cavity naturally vibrates at 100 cycles per second. Now, if we have an airstream with a velocity of 200 m/s, we can use a simple formula to calculate the period of the airstream's frequency:

Period = 1/frequency

In this case, the period would be 1/200 = 0.005 seconds. This means that the airstream completes one cycle in 0.005 seconds. However, since the resonant frequency of the flute cavity is 100 Hz, the period of the cavity's frequency would be 1/100 = 0.01 seconds. This means that the cavity completes one cycle in 0.01 seconds. As you can see, the period of the airstream's frequency is half of the period of the cavity's frequency.

This is where the concept of resonance comes in. When the period of the airstream's frequency is equal to the period of the cavity's frequency, they are in sync and the airstream can interact with the cavity's resonance, amplifying the sound. However, if the airstream's frequency is too fast, the periods will not match up

 

[charng]

I would like to clarify the relationship between velocity of air, period, flutes, and resonant frequencies. The velocity of air refers to the speed at which air moves, usually measured in meters per second (m/s). The period of a frequency is the time it takes for one complete cycle of a wave to occur, and it is often measured in seconds (s). Frequency, on the other hand, is the number of cycles of a wave that occur in one second, and it is measured in Hertz (Hz).

In the context of flutes and resonant frequencies, the velocity of the airstream is important because it affects the resonance of the flute's cavity. Resonance occurs when an object vibrates at its natural frequency in response to an external force, in this case, the airstream passing over the embouchure hole of a flute. The resonance frequency of a flute's cavity is determined by its size and shape.

Now, to address your confusion about the relationship between velocity and period, let's use an example. Let's say the velocity of the airstream is 10 m/s and the period of the resonant frequency of the flute's cavity is 0.01 s. This means that the airstream is moving at a much faster rate (10 m/s) than the period of the resonant frequency (0.01 s). In this case, the airstream will not be able to reinforce the high frequency oscillations of the flute's cavity because it is moving too quickly. This is what was meant by the statement "if the velocity of the airstream is greater than the period of the flute cavity's resonance frequency, then the deflections created by the airstream will not help the high frequency oscillations self-reinforce."

On the other hand, if the resonant frequency of the flute's cavity is lower than the frequency of the airstream, then the airstream will be able to drive the resonance of the flute's cavity at its optimum speed. This is because the airstream is moving at a rate that is closer to the period of the resonant frequency, allowing for better reinforcement of the oscillations.

I hope this explanation helps you understand the relationship between velocity, period, and resonant frequencies in the context of flutes. As for formulas, there are several equations that can be used to calculate these values, but they may not be necessary for a basic understanding of the concept. If you