In a closed pipe, the fundamental frequency (also known as the first harmonic) produces a wavelength that is four times the length of the pipe. To calculate the wavelength, we can use the formula:
λ = 4L
where λ represents the wavelength and L represents the length of the closed pipe.
Since the problem states that the fundamental note produced by the closed pipe is 128 Hz, we know that the frequency (f) is related to the speed of sound (v) and the wavelength (λ) by the equation:
v = fλ
In this case, we can assume that the speed of sound is approximately constant, so we can rearrange the equation to solve for the wavelength:
λ = v/f
Now, substituting the given frequency (f = 128 Hz) and assuming the speed of sound is approximately 343 meters per second (which is the speed of sound in dry air at room temperature), we can calculate the wavelength:
λ = (343 m/s) / (128 Hz) ≈ 2.68 meters
Therefore, the wavelength of the fundamental note produced by the closed pipe is approximately 2.68 meters.