Calculation of End Correction in an Open Organ Pipe

Introduction
An open organ pipe is a tube open at both ends that produces sound when an air column vibrates inside it. The length of the pipe, speed of sound and fundamental frequency are important parameters that determine the quality of sound produced. The end correction is a term used to account for the difference between the effective length of the pipe and its actual length.

Formula for End Correction
The formula for end correction in an open organ pipe is given by:

i = 0.6r

where i is the end correction, and r is the radius of the pipe.

Calculation of End Correction
Given,
Length of open organ pipe = 44 cm
Speed of sound = 340 m/s
Fundamental frequency = 340 Hz

The wavelength of the sound wave produced in the pipe can be calculated using the formula:

λ = 2L/n

where λ is the wavelength, L is the length of the pipe, and n is the harmonic number.

For the fundamental frequency, n = 1. Therefore,

λ = 2 x 44 cm / 1 = 88 cm

The speed of sound can also be expressed as:

v = fλ

where v is the speed of sound, f is the frequency, and λ is the wavelength.

Substituting the values,

340 m/s = 340 Hz x 0.88 m

The effective length of the pipe can be calculated using the formula:

L' = L + i

where L' is the effective length of the pipe, and i is the end correction.

Rearranging the formula, we get:

i = L' - L

Substituting the values,

i = 0.88 m - 0.44 m = 0.44 m

The radius of the pipe is not given, so we cannot calculate the exact value of the end correction. However, using the formula i = 0.6r, we can say that the end correction is proportional to the radius of the pipe.

Conclusion
In conclusion, the end correction in an open organ pipe can be calculated using the formula i = 0.6r, where i is the end correction and r is the radius of the pipe. The effective length of the pipe is given by L' = L + i, where L is the actual length of the pipe. The end correction is proportional to the radius of the pipe.

Is the answer 6cm?