Could open tube and closed (at one end) tube produce the same frequency?

In summary, the two instruments produce different notes because the wavelength of the note is different for each.
  • #1
sbayla31
9
0

Homework Statement



Is it possible for a flute (tube open at both ends) 72 cm long and an oboe (tube open at one end) 64.8 cm long to produce the same note? Prove your answer.

Homework Equations



v=f[tex]\lambda[/tex]

L=(n/2)[tex]\lambda[/tex] (tube open at both ends)

L=((2n-1)/4)[tex]\lambda[/tex] (tube open at one end)

The Attempt at a Solution



I can sub the lengths into the latter two equations:

0.72m =(n/2)[tex]\lambda[/tex]

0.648m =((2n-1)/4)[tex]\lambda[/tex]

I know how to isolate [tex]\lambda[/tex] and then sub in v/f for [tex]\lambda[/tex] to find the frequency (the note).

I don't know what to do next :confused:
I know I could use a guess and check method, but I would prefer doing it mathematically.
Also, how do I find out what the resonant length is (n)?
 
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  • #2
hi sbayla31! :smile:

i suppose you've noticed that 64.8 = 0.9*72 ? :wink:
 
  • #3
sbayla31 said:


The Attempt at a Solution



I can sub the lengths into the latter two equations:

0.72m =(n/2)[tex]\lambda[/tex]

0.648m =((2n-1)/4)[tex]\lambda[/tex]

I know how to isolate [tex]\lambda[/tex] and then sub in v/f for [tex]\lambda[/tex] to find the frequency (the note).

I don't know what to do next :confused:
I know I could use a guess and check method, but I would prefer doing it mathematically.
Also, how do I find out what the resonant length is (n)?


The idea is, n is not same in the two equations. Use n and another variable (say m) and then divide. You'll find some value for the ratio n/m. All integer tuples (n,m) that satisfy the ratio, work.
 
  • #4
tiny-tim said:
hi sbayla31! :smile:

i suppose you've noticed that 64.8 = 0.9*72 ? :wink:

Hmm. Does this have anything to do with the 9th harmonic of a closed tube? Or am I totally off?
 
  • #5
sbayla31 said:
Is it possible for a flute (tube open at both ends) 72 cm long and an oboe (tube open at one end) 64.8 cm long to produce the same note? Prove your answer.

what is the wavelength of that note? :smile:
 
  • #6
tiny-tim said:
what is the wavelength of that note? :smile:

naughty naughty, i think you gave him to much information...
 

Related to Could open tube and closed (at one end) tube produce the same frequency?

1. Can an open tube and a closed tube produce the same frequency?

Yes, under certain conditions, an open tube and a closed tube can produce the same frequency.

2. What are the conditions for an open tube and a closed tube to produce the same frequency?

The length of the open tube must be twice the length of the closed tube, and the temperature of the air inside the tubes must be the same.

3. How does the length of the tubes affect the frequency produced?

The longer the tube, the lower the frequency produced. This is true for both open and closed tubes.

4. Is the frequency produced by an open tube and a closed tube exactly the same?

No, the frequencies may be very close but not exactly the same due to slight differences in air pressure and temperature inside the tubes.

5. Why is it important to have the same temperature inside both tubes for them to produce the same frequency?

Temperature affects the speed of sound, so if the temperatures are different, the speed of sound inside the tubes will be different and the frequencies produced will not be the same.

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