Open air columns/ resonant length help

In summary: A.In summary, if the speed of sound is 346m/s, the frequency of sound produced by the third resonant length is 213.6 Hz. If the chime were shorter, the frequency of sound produced by the third resonant length would be higher.
  • #1
Pruzhinkin
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0

Homework Statement



Hollow tube chimes are made of metal and are open at each end. One chime is 0.54 m long.
A) if the speed of sound is 346 m/s, what is the frequency of sound produced by the third resonant length?
B)What would happen to the frequency of sound produced by the third resonant length if the chime were shorter?

Homework Equations



L1 = lambda/2 or lambda = 2L
L2 = lambda
L3 = 3 * lambda/2 or lambda = 2L/ 3
f1 = v/ lambda

The Attempt at a Solution



A) Lambda = 2L = 2 x (0.54m) = 1.08 m
f1 = v/ lambda = 346m/s / 1.08m = 320.4 Hz
L3 = 3 * (1.08m)/2 = 1.62 m

answer is
f = 346 / 1.62 = 213.6 Hz

or am i supposed to used f3=3f1, or is that only for string resonance. If it is used here then f3 = 3 * 320.4 = 961.2 Hz?

B) Not quite sure here, I understand what happens if a wavelength, frequency, or speed of sound changes, but for some reason this escapes me. I think i just fell into some sort of stupor where my head barely thinks.

Thanks in advance guys!
 
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  • #2
I think the frequency is supposed to be 320.37Hz instead of 320.4Hz. From reading into this, it appears that i do need to use f3 = 3f1 or f3=3v/2L to find the third resonant length frequency, which would give me 961.11Hz. Is this correct?
Still not sure about B)
 
Last edited:
  • #3
If the frequency of the third resonant length means the frequency of the third harmonic (3 half-wavelength is there along the length of the chime), that 961 Hz is correct.

As for B: Think, what happens to the wavelength if the length of the chime decreases?

ehild
 
  • #4
B. The wavelength shortens and the frequency increases/ temperature of course stays the same! Did i get it right?
Thanks for verifying my answer for A.:)
 
  • #5
It is hidden but assumed that "everything the same around, just using a shorter chime". The speed of sound is the same, so you are right, frequency = speed of sound /lambda is higher for a shorter chime. ehild
 

1. What is an open air column?

An open air column is a type of resonator that is open at one end and closed at the other. It is commonly used in musical instruments such as flutes and clarinets. When air is blown into the open end, it creates standing waves that produce specific resonant frequencies.

2. What is the resonant length of an open air column?

The resonant length of an open air column is the length of the column that produces the fundamental frequency or the lowest resonant frequency. It is typically measured from the closed end of the column to the open end.

3. How is the resonant length of an open air column determined?

The resonant length of an open air column can be determined by using the formula L = (n + 1/4)λ, where L is the resonant length, n is the number of nodes or half wavelengths, and λ is the wavelength of the sound. This formula can also be used to find the resonant length for higher harmonics.

4. How does the resonant length affect the sound produced by an open air column?

The resonant length of an open air column determines the fundamental frequency and the harmonics that can be produced. Changing the resonant length by altering the length of the column or covering the open end can change the pitch and sound quality of the instrument.

5. How can the resonant length of an open air column be adjusted?

The resonant length of an open air column can be adjusted by changing the length of the column or by covering the open end partially or completely. This can be done by using keys or holes in the instrument, or by using external objects such as fingers or mutes. By adjusting the resonant length, different notes and pitches can be produced.

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