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The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe L metre long. The length of the open pipe will be
- a)L
- b)2L
- c)1/L
- d)4L
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The second overtone of an open organ pipe has the same frequency as t...
Explanation:
Open and closed organ pipes have different modes of vibration, which result in different overtones.
Given:
- Second overtone of an open pipe = frequency 2f
- First overtone of a closed pipe = frequency f
- Length of the closed pipe = L
Relation between frequency and length:
- For an open pipe: f = v/2L where v is the speed of sound
- For a closed pipe: f = v/4L
Given:
- 2f = v/2L (for open pipe)
- f = v/4L (for closed pipe)
Equating the frequencies:
2f = v/2L
f = v/4L
Substitute the values:
v/4L = v/4L
2L = L
Therefore,
The length of the open pipe will be 2L.
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The second overtone of an open organ pipe has the same frequency as t...
Second overtone of an open organ pipe
=Third harmonic = 3 × υ′0 = 3 × v/2L′
First overtone of a closed organ pipe
= Third harmonic = 3 × υ0 = 3 × v/4L
According to question,
3υ′0 = 3υ0 ⇒3 × v/2L′ = 3 × v/4L
⇒ L′ = 2L
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The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe L metre long. The length of the open pipe will bea)Lb)2Lc)1/Ld)4LCorrect answer is option 'B'. Can you explain this answer?
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