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In open organ pipe, first overtone produ...

In open organ pipe, first overtone produced is of such frequency that length of the pipe is equal to

A

`lamda//4`

B

`lamda//3`

C

`lamda//2`

D

`lamda`

Text Solution

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The correct Answer is:
To solve the problem regarding the length of an open organ pipe producing its first overtone, we can follow these steps: ### Step 1: Understand the concept of harmonics in an open organ pipe In an open organ pipe, both ends are open, which means that there are antinodes at both ends. The harmonics in an open pipe can be described as follows: - The fundamental frequency (first harmonic) has a wavelength \( \lambda_1 = 2L \) (where \( L \) is the length of the pipe). - The first overtone (second harmonic) has a wavelength \( \lambda_2 = L \). ### Step 2: Relate the wavelength to the length of the pipe For the first overtone, we know: - The first overtone corresponds to the second harmonic, which has a wavelength \( \lambda \) equal to the length of the pipe \( L \). Thus, we can write: \[ \lambda = L \] ### Step 3: Conclusion From the relationship established, we conclude that for the first overtone in an open organ pipe, the length of the pipe is equal to the wavelength of the sound wave produced: \[ \text{Length of the pipe} = \lambda \] ### Final Answer The length of the pipe for the first overtone is equal to \( \lambda \). ---
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