Final answer:
The wavelength of the m=6 harmonic for a pipe open at both ends can be calculated using the formula λ = 2L/m. Assuming the speed of sound is the same in the tube and a string with the same length, the harmonics of the tube and the string would have the same frequencies if both the tube and string have symmetric boundary conditions.
Step-by-step explanation:
A pipe open at both ends supports standing waves with nodes at each end and antinodes at the center. For such a pipe, the wavelength for any harmonic m can be found using the formula λ = 2L/m, where L is the length of the pipe and m is the harmonic number. In the case of the m=6 harmonic, we simply put the values into the equation and solve for the wavelength (λ) of the standing wave that would be supported in such a configuration, knowing the speed of the wave (v) in the medium.
Since the wavelength and speed are related by the formula v = fλ, where f is the frequency, and given that the speed of sound v is consistent, we can conclude that the harmonics of the string and the tube would have the same frequency if the tube is also open at both ends and has a length L. However, if the tube has one end closed, the pattern of harmonics changes and they would not correspond directly to those of the string. The fundamental frequencies for both the open and closed tubes and the resulting harmonics are determined by their boundary conditions.