A 30 cm long organ pipe is filled with air and is open at one end and closed at the other. The speed of sound in air at 0°C is 331 m/s. What is the wavelength of the fundamental mode?
Question
A 30 cm long organ pipe is filled with air and is open at one end and closed at the other. The speed of sound in air at 0°C is 331 m/s. What is the wavelength of the fundamental mode?
Solution
The fundamental mode of a pipe closed at one end (also known as the first harmonic) 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 forms a standing wave that is essentially half of a wavelength.
Step 1: Identify the length of the pipe The length of the pipe is given as 30 cm, which is 0.3 m.
Step 2: Determine the relationship between the length of the pipe and the wavelength For a pipe closed at one end, the length of the pipe is equal to half the wavelength of the fundamental mode. Therefore, the wavelength (λ) is twice the length of the pipe.
Step 3: Calculate the wavelength Using the relationship from step 2, we can calculate the wavelength as follows: λ = 2 * length of the pipe λ = 2 * 0.3 m λ = 0.6 m
So, the wavelength of the fundamental mode for a 30 cm long organ pipe filled with air, open at one end and closed at the other, is 0.6 m.
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