Harmonics of a closed-closed tube

In summary, n is a value used to represent the mode or multiple of the fundamental frequency in a physical resonator. It is important to note that the frequencies of overtones may not always be exactly harmonically related due to factors such as 'end effect' and effective length of the oscillating object. For a closed-closed tube, the fundamental frequency is determined by the half wavelength between the two ends, with the first overtone occurring at near twice the frequency and the second overtone occurring at twice the frequency. This can be calculated using the equation f = c/2x, where c is the speed of sound in the tube and x is the effective length.
  • #1
abbeygeib
1
0
I don't understand how to get n... if that doesn't make sense i can explain more... I have the length and velocity... from there i just don't understand what n even is or means...
 
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  • #2
n is the mode or the multiple of the fundamental frequency. If you want the third harmonic, n=3.
 
  • #3
It should really be referred to as the second (U)overtone(/U) for a physical resonator because the frequencies of overtones may not be exactly harmonically related. Look at the spec of Quartz crystals for use in oscillators and you'll see what I mean; It's all to do with 'end effect' and effective length of the oscillating object, in wavelengths. Having said this, for a closed-closed tube, the end effect will be v. small.

The fundamental frequency will be the frequency at which there is a half wavelength between the two ends - allowing a node at each end*. The first overtone will be when there is a node in the centre (i.e. at near twice the frequency) and the second will be when there are two nodes - asoasf.

* fundamental f =c/2x
where c is the speed of sound in the tube and x is the effective length
 

1. What is the definition of "harmonics of a closed-closed tube"?

The harmonics of a closed-closed tube refer to the specific resonant frequencies that are produced when a sound wave is trapped inside a tube that is closed at both ends.

2. How are the harmonics of a closed-closed tube different from other types of tubes?

The main difference is that a closed-closed tube only allows for certain resonant frequencies to be produced, while other types of tubes, such as open-closed or open-open tubes, have a wider range of possible resonant frequencies.

3. What factors affect the harmonics of a closed-closed tube?

The length and diameter of the tube, the speed of sound in the medium inside the tube, and the temperature of the medium can all affect the harmonics of a closed-closed tube.

4. How do the harmonics of a closed-closed tube relate to musical instruments?

The harmonics of a closed-closed tube are responsible for the different pitches produced by musical instruments such as flutes, clarinets, and organ pipes. By changing the length or diameter of the tube, musicians can alter the harmonics and create different notes.

5. Can the harmonics of a closed-closed tube be used in other applications besides music?

Yes, the principles of harmonics in closed-closed tubes can be applied in various fields such as acoustics, engineering, and physics. They are used in technologies such as organ pipes, air columns in wind instruments, and even in industrial processes like ultrasonic cleaning.

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