The air in an adjustable pipe open at one end and closed at the other resonates at the fundamental frequency when the pipe has length L0. The pipe is then adjusted such that it is twice its original length. What is the wavelength of the air in the pipe at the new fundamental frequency?A.L0B.2L0C.4L0D.8L0
Question
The air in an adjustable pipe open at one end and closed at the other resonates at the fundamental frequency when the pipe has length L0. The pipe is then adjusted such that it is twice its original length. What is the wavelength of the air in the pipe at the new fundamental frequency?A.L0B.2L0C.4L0D.8L0
Solution
The fundamental frequency, also known as the first harmonic, of a pipe that is open at one end and closed at the other is when there is a node (point of no displacement) at the closed end and an antinode (point of maximum displacement) at the open end. This means that the length of the pipe, L0, is equal to one-fourth of the wavelength of the sound wave.
When the length of the pipe is doubled to 2L0, the pipe still has a node at the closed end and an antinode at the open end. Therefore, the length of the pipe is still equal to one-fourth of the wavelength of the sound wave.
So, if 2L0 = 1/4 wavelength, then the wavelength = 4 * 2L0 = 8L0.
So, the answer is D. 8L0.
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