Final answer:
The wavelength of a sound wave in a pipe closed at one end is λ = 4L, with frequency calculated by f = v/λ. For a pipe open at both ends, the resonant frequencies are given by fn = nv/2L, where n signifies harmonics.
Step-by-step explanation:
The formula for the wavelength of a sound wave in a pipe that is closed at one end is λ = 4L, where λ is the wavelength and L is the length of the pipe. In such a pipe, the standing wave has a node at the closed end and an antinode at the open end.
For a simple tube closed at one end, the fundamental frequency has this wavelength, and the frequency is related to the wavelength and the speed of sound by the equation f = v/λ. In contrast, for a tube open at both ends, the resonant frequencies are given by fn = nv/2L, where n represents the harmonics (n = 1, 2, 3, ...).
The wavelength formula for an asymmetrical pipe depends on whether the pipe is open at both ends or open at one end and closed at the other.
If the pipe is open at both ends, the wavelength formula is λ = 2L / n, where λ is the wavelength, L is the length of the pipe, and n is the harmonic number.
If the pipe is open at one end and closed at the other, the wavelength formula is λ = 4L / n.