Is a resonant frequency any of the harmonics?

[AAAA]

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

 

[haruspex]

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

I agree with you. Or you could read the question as "how long does the pipe need to be", suggesting a minimum length.

 

[AAAA]

Thanks for your help! :)