An organ pipe is open at both ends. It is producing sound at its sixth harmonic, the frequency of which is 257 Hz. The speed of sound is 343 m/s. What is the length of the pipe
The open pipe has to be of length lambda/2, and odd number.
Fundamental L= fundamentallambda/2
second harmonic L= 3*fundamentallambda/2
third L = 5*fundamentallambda/2
etc.
fundamentallambda= speedsound/freq
To find the length of the organ pipe, we need to calculate the fundamental wavelength (λ) first, and then use the formula for the length of an open pipe, which is L = (2n - 1) * λ/2, where n is the harmonic number.
To calculate the fundamental wavelength, we can use the formula: λ = speed of sound / frequency.
Given that the frequency is 257 Hz and the speed of sound is 343 m/s, we can calculate the fundamental wavelength as follows:
λ = 343 m/s / 257 Hz
≈ 1.336 m
Now, to determine the length of the pipe using the formula mentioned earlier:
L = (2n - 1) * λ/2
Since the pipe is producing sound at the sixth harmonic, n = 6. Plugging in the values:
L = (2 * 6 - 1) * 1.336 m / 2
= 11 * 1.336 m / 2
≈ 7.348 m
Therefore, the length of the organ pipe is approximately 7.348 meters.