Organ pipe A , with both ends open, has a fundamental frequency of 270 Hz. The t

Question

Organ pipe A, with both ends open, has a fundamental frequency of 270 Hz. The third harmonic of organ pipe B, with one end open, has the same frequency as the second harmonic of pipe A. How long are (a) pipe A and (b) pipe B? (Take the speed of sound to be 343 m/s.)

I found A to be 0.63m. For part B I got 0.508m but it's saying it's wrong, any help?

Here is the hint from WileyPlus: You need to use the formula for resonant frequencies in a pipe with two open ends and the formula for resonant frequencies in a pipe with only one open end. In the latter, only the odd harmonics are possible.

Explanation / Answer

Speed of the air in the pipe is 348 m/s
Wavelength A = 348/270 = 1.29 m
Length of pipe A = 0.644 m
2nd Harmonic of A has frequency 600 Hz
and wavelength 0.644 m
3rd harmonic of B has wavelength 0.644 m which is 4L/3
so the length of B is (3*0.64)/4 = 0.483 m

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