The value of end correction for an open organ pipe of radius r is _________ .

Options

A. `0.8` r
B. `0.6`r
C. `0.9`r
D. `1.2`r

Explanation

To find the value of the end correction for an open organ pipe of radius \( r \), we can follow these steps:

### Step 1: Understand the concept of end correction
End correction is a phenomenon that occurs in open organ pipes where the actual wavelength of the sound wave is slightly longer than what is predicted based on the physical length of the pipe. This is because the sound waves do not start exactly at the open ends of the pipe but slightly before them.

### Step 2: Determine the formula for end correction
For an open organ pipe, the end correction \( e \) for one open end is given by the formula:
\[ e = 0.3 \times D \]
where \( D \) is the diameter of the pipe.

### Step 3: Calculate the diameter of the pipe
The diameter \( D \) of the pipe can be expressed in terms of the radius \( r \):
\[ D = 2r \]

### Step 4: Substitute the diameter into the end correction formula
Now, substituting \( D = 2r \) into the end correction formula:
\[ e = 0.3 \times (2r) = 0.6r \]

### Step 5: Calculate the total end correction for both ends
Since the organ pipe is open at both ends, the total end correction \( E \) is:
\[ E = e_1 + e_2 = 0.6r + 0.6r = 1.2r \]

### Final Answer
Thus, the value of the end correction for an open organ pipe of radius \( r \) is:
\[ \text{End Correction} = 1.2r \]

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