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The fundamental frequency of an open organ pipe is 300 Hz. The first overtone of this pipe has same  frequency as first overtone of a closed organ pipe. If speed of sound is 330 m/s, then the length of closed organ pipe is
  • a)
    41 cm
  • b)
    37 cm
  • c)
    31 cm
  • d)
    80 cm
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The fundamental frequency of an open organ pipe is 300 Hz. The first o...
For open pipe, n = V2l, where n0 is the fundamental frequency of open pipe.

As freq. of 1st overtone of open pipe = freq. of 1st overtone of closed pipe.

= 41.25 cm
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Most Upvoted Answer
The fundamental frequency of an open organ pipe is 300 Hz. The first o...
Given:
- Fundamental frequency of an open organ pipe (f1) = 300 Hz
- Speed of sound (v) = 330 m/s

To find:
- Length of a closed organ pipe

Explanation:

The fundamental frequency of an open organ pipe is given by the formula:

f1 = v / (2L)

where L is the length of the pipe.

The first overtone of an open organ pipe is the second harmonic, which has a frequency of 2f1. Therefore, the first overtone of the open organ pipe is 600 Hz.

To find the first overtone of a closed organ pipe, we use the formula:

f2 = v / (4L)

where L is the length of the pipe.

Since the first overtone of the closed organ pipe is the same as the first overtone of the open organ pipe, we can set up the following equation:

2f1 = f2

Substituting the values, we get:

2(300 Hz) = v / (4L)

Simplifying the equation, we have:

600 Hz = 330 m/s / (4L)

Solving for L, we get:

L = 330 m/s / (4 * 600 Hz)

L = 330 m/s / 2400 Hz

L ≈ 0.1375 m

Converting the length to centimeters, we have:

L ≈ 0.1375 m * 100 cm/m

L ≈ 13.75 cm

Therefore, the length of the closed organ pipe is approximately 13.75 cm, which corresponds to option A.
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The fundamental frequency of an open organ pipe is 300 Hz. The first overtone of this pipe has same frequency as first overtone of a closed organ pipe. If speed of sound is 330 m/s, then the length of closed organ pipe isa)41 cmb)37 cmc)31 cmd)80 cmCorrect answer is option 'A'. Can you explain this answer?
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