PHYSICS harmonics + standing waves

[br2pi5]

Hello! Just wanted to confirm equations!

both open ends--> wavelength = 2L/n (n being # of nodes)
both closed ends --> wavelength = 2L/n (n being #antinodes)
one open, one closed --> wavelength = 4L/n (n being only odd positive integers, no even # harmonics)

Is this correct? If so, how would I tackle a problem like the one in KA (attached)? Since it only said open or closed, I thought it meant both open and both closed, thus using the same equation of 2L/n (different n's).

OPEN n=4, wavelength = 2L/4 and frequency = 4v/2L
CLOSED n=3, wavelength = 2L/3 and frequency = 3v/2L
how is this a factor of 2? I'm definitely doing something wrong....

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[JustinM88]

^My work. Actually didn't need the diagrams, just the formulas. We're just using those 3 formulas^ and rearranging stuff to get frequency (f) into each equation and comparing those (the v is the same for each pipe, so that variable doesn't change anything).

 

[br2pi5]

^My work. Actually didn't need the diagrams, just the formulas. We're just using those 3 formulas^ and rearranging stuff to get frequency (f) into each equation and comparing those (the v is the same for each pipe, so that variable doesn't change anything).

so I can better understand it visually, on your first diagram, you only have 2 nodes and 2 antinodes right? I might not be reading it correctly though

 

[JustinM88]

so I can better understand it visually, on your first diagram, you only have 2 nodes and 2 antinodes right? I might not be reading it correctly though

Right. I wish it was as easy as “3rd harmonic has 3 nodes” but it doesn’t work like that for a closed pipe

 

[br2pi5]

Right. I wish it was as easy as “3rd harmonic has 3 nodes” but it doesn’t work like that for a closed pipe

would you mind taking me through your thought process when answering the question?

 

[JustinM88]

would you mind taking me through your thought process when answering the question?

Red boxes are the main equations I used.

Let me know if ya want me to clarify anything here^

 

[br2pi5]

Red boxes are the main equations I used.

Let me know if ya want me to clarify anything here^

so n= nodes and not what I previously thought, that n meant something different for either a closed-closed or open-open or open-closed pipe? (from first post)

 

[JustinM88]

so n= nodes and not what I previously thought, that n meant something different for either a closed-closed or open-open or open-closed pipe? (from first post)

I believe n represents which harmonic it is (ie. 1st, 2nd, 3rd, etc).
(I too used to think n referred to the nodes/antinodes but more recently realized it’s not that)

 

[br2pi5]

I believe n represents which harmonic it is (ie. 1st, 2nd, 3rd, etc).
(I too used to think n referred to the nodes/antinodes but more recently realized it’s not that)

Hi justin! how would you do this question?

 

[JustinM88]

Hi justin! how would you do this question?

Heres one way:

 

[br2pi5]

Heres one way:

Got it, also I just realized it's a system of equations type of problem so I could set the Ls equal to each other (except one has the (n+2)) and solve for n.

 

[JustinM88]

Got it, also I just realized it's a system of equations type of problem so I could set the Ls equal to each other (except one has the (n+2)) and solve for n.

Nice! Was trying to do the system of equations thing at first but didn’t think of doing the n + 2 thing