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**1. The problem statement,λ all variables and given/known data**

A drum skin is stretched over one end of a pipe, creating a resonant air column with one open end and one fixed end. How long must the pipe be to achieve a resonant frequency of 280.0 Hz? (Use 343 m/s for the speed of sound.)

## Homework Equations

V = fλ

## The Attempt at a Solution

My assumption is that a resonant air column means that

*any*of the harmonics for a fixed and open end could be used in order to solve for pipe length.

**1. Solve for wavelength:**

V = fλ

343/280 = λ

1.225m = λ

**2. Solve for "pipe length"**

Knowing that the first harmonic is a 1/4 λ for a fixed and free end system, I divided 1.225 by 4 to get ~0.30m, which the book states is correct. But if that works for a resonant air column, the rest of the harmonics should as well. So I multiplied 1.225 by 3/4 to get ~0.92m. The book also states this is correct, but these are the only two lengths the book shows

However, could I not keep going to other harmonics to get greater and greater lengths? For example, the 3rd harmonic, I multiply 1.225 by 5/4 to get ~1.5m, which the book does not list. But is this not also correct?

Thanks for your help