Resonance and rules for mathematical equations

[Spookie71]

Homework Statement

What is the wavelength of the lowest note that can resonate within an air column 42 cm in length and closed at both ends.

Homework Equations

Given: l = 42 cm
n = 1

Required: $$\lambda$$

Analysis: l = $$\frac{n\lambda}{2}$$

therefore $$\lambda$$ = $$\frac{2l}{n}$$

I don't know how this came to be, could someone please explain.

I've just gone back to high school after 15 years and would appreciate if you could also forward me on to some good links for rules for mathematical equations such as these.

Thanks
Scott

 

[learningphysics]

The steps to go from:

$$l = \frac{n\lambda}{2}$$ to $$\lambda = \frac{2l}{n}$$ ?

start at:

$$l = \frac{n\lambda}{2}$$

first multiply both sides by 2.

that gives:

$$2l = 2\times \frac{n\lambda}{2}$$

on the right side, the 2 in the numerator cancels with the 2 in the denominator, so

$$2l = n\lambda$$

Then divide both sides by n.

$$\frac{2l}{n} = \frac{n\lambda}{n}$$

on the right side, the n in the numerator cancels with the n in the denominaotr. so,

$$\frac{2l}{n} = \lambda$$

Then just switch sides.

$$\lambda = \frac{2l}{n}$$

 

[Spookie71]

Thanks Learningphysics for helping

Scott

 

[learningphysics]

Thanks Learningphysics for helping

Scott

No prob. Sounds like you're looking for a refresher on algebra.

This seems to be a complete algebra course online:

http://www.themathpage.com/alg/algebra.htm

sosmath has quite a few examples:

http://www.sosmath.com/algebra/solve/solve0/solve0.html

Here's another page where you can practice:

http://www.coolmath.com/algebra/algebra-practice-solving.html

Hope this helps.