In an open-ended tube, the wavelengths of the harmonics (or resonant frequencies) are related to the length of the tube. The relationship can be expressed as:
λ = 2L/n
where λ is the wavelength, L is the length of the tube, and n is the harmonic number.
Given that the first harmonic wavelength (n = 1) is 35 cm, we can rearrange the equation to solve for the length of the tube:
L = λ * n/2
L = 35 cm * 1/2 L = 17.5 cm
Now, we can use this length to find the wavelength of the 7th harmonic (n = 7):
λ = 2L/n λ = 2 * 17.5 cm / 7 λ = 35 cm / 7 λ = 5 cm
Therefore, the wavelength of the 7th harmonic in the open-ended tube is 5 cm.