To determine the longest wavelength for standing sound waves in a tube open at both ends, we can use the formula:
λ = 2L/n
where: λ is the wavelength, L is the length of the tube, and n is the harmonic number (1, 2, 3, ...).
In this case, the tube is 102.0 cm long, and it is open at both ends. Since it is open at both ends, the first harmonic (n = 1) will have an antinode at each end of the tube.
The longest wavelength occurs when n is the smallest possible value, which is n = 1. Plugging the values into the formula, we have:
λ = 2L/n = 2(102.0 cm) / 1 = 204.0 cm.
Therefore, the longest wavelength for standing sound waves in a 102.0 cm long tube that is open at both ends is 204.0 cm.