What is the correct frequency for a 20 cm pipe with open and closed ends?

[Karol]

Homework Statement

What is the base frequency of a 20 cm pipe which is open on both ends.
Again but closed on one end.

Homework Equations

u=velocity, \lambda=wave length: \lambda=\frac{u}{f}
Velocity in air=348[m/sec]

The Attempt at a Solution

I understand these are standing waves in air.
In an open end there is a peak, so the first wavelength is \lambda=2\cdot 20=40[cm]
$0.4=\frac{348}{f_1}\rightarrow f_1=870[Hz]$
The answer should be 1140[Hz]
In the closed on one end condition, in the open end there is a peak and in the closed end a node, so the wavelength is \lambda=4\cdot 20=80[cm]
$0.8=\frac{348}{f_1}\rightarrow f_1=435[Hz]$
The answer should be 570[Hz]
Both answers differ from the right ones by the same factor

 

[NascentOxygen]

Puzzling.