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

[sbayla31]

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\lambda

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

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

The Attempt at a Solution

I can sub the lengths into the latter two equations:

0.72m =(n/2)\lambda

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

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

I don't know what to do next
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)?

 

[tiny-tim]

hi sbayla31!

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

 

[Sourabh N]

The Attempt at a Solution

I can sub the lengths into the latter two equations:

0.72m =(n/2)\lambda

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

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

I don't know what to do next
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.

 

[sbayla31]

hi sbayla31!

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

Hmm. Does this have anything to do with the 9th harmonic of a closed tube? Or am I totally off?

 

[tiny-tim]

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?

 

[Liquidxlax]

what is the wavelength of that note?

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