Simple Harmonic Motion/Fundamental Frequency

[Iman06]

Homework Statement

A tuba is a instrument that can be modeled after a closed tube and has a length of 4.9m. A frequency of 122.5hz produces resonance in the Tuba. Is this the fundamental frequency of the instrument? If not, what harmonic is it?

Homework Equations

f=λv
4l=λ(open closed tube)
v= 343m/s

The Attempt at a Solution

So for this problem, I used the equation 4l=λ to find the necessary wavelength for the length which I got as .089m. I then compared it to the actual(?) wavelength of the instrument based on the frequency and velocity, which I got as .3571m. The question is, what am I actually doing? I have no idea. Can someone at least clear up what exactly to do first?

 

[kuruman]

Hi iman06 and welcome to PF.

4l=λ(open closed tube)

This equation doesn't say much. There is a more complete equation that gives the fundamental and higher harmonics for a tube closed at one end. Figure out (or look up) what it is, then calculate a few frequencies for the length that is given to you and see if there is a match to the given 122.5 Hz.

 

[scottdave]

Like, how do the harmonic frequencies relate to the fundamental frequency?

How did you arrive at 0.089 meter for lambda?

 

[collinsmark]

Homework Equations

f=λv

This equation is wrong. By that I mean if 'f' is frequency, 'λ' is wavelength, and 'v' is the speed of sound, then the above equation is wrong.

4l=λ(open closed tube)
v= 343m/s

The Attempt at a Solution

So for this problem, I used the equation 4l=λ to find the necessary wavelength for the length which I got as .089m.

Okay, using "4l=λ" is a way to find the tube's fundamental wavelength, but you didn't do that quite right. I have no idea where the 0.089 m comes from.

 

[scottdave]

This equation is wrong. By that I mean if 'f' is frequency, 'λ' is wavelength, and 'v' is the speed of sound, then the above equation is wrong.

I missed that one. Must've been tired. Just look at the units or dimensions to figure what the equation should be.

Ill take this opportunity to mention my Insights article.https://www.physicsforums.com/insights/make-units-work/

 

[kuruman]

I missed that one. Must've been tired. Just look at the units or dimensions to figure what the equation should be.

I missed it also. I looked at the right side first (as I always do when I read an equation) and thought that I was looking at λν (lambda nu). At that point the "f" on the left side didn't register in my mind. The LaTeX nu ($\nu$) looks closer to nu than the nu provided in the PF symbols' menu which looks exactly like vee. I guess this confusion between vee and nu is the reason why "f" is preferred to denote frequency.