The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20cm, the lenght of the open organ pipe is
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Fundamental frequency open organ pipe , n₁ = v/2L₁
Here v is the speed of sound wave and L₁ is length of open organ pipe .
Third harmonic of closed organ pipe , n₂ = 5v/4L₂
Here, L₂ is the length of closed organ pipe .
A/C to question,
n₁ = n₂
v/2L₁ = 5v/4L₂
1/2L₁ = 5/4L₂
4L₂ = 10L₁
Given, length of closed organ pipe is 20cm e.g., L₂ = 20cm
so, L₁ = 2/5 × L₂ = 2/5 × 20 = 8 cm
Hence, length of open organ pipe is 8cm
Here v is the speed of sound wave and L₁ is length of open organ pipe .
Third harmonic of closed organ pipe , n₂ = 5v/4L₂
Here, L₂ is the length of closed organ pipe .
A/C to question,
n₁ = n₂
v/2L₁ = 5v/4L₂
1/2L₁ = 5/4L₂
4L₂ = 10L₁
Given, length of closed organ pipe is 20cm e.g., L₂ = 20cm
so, L₁ = 2/5 × L₂ = 2/5 × 20 = 8 cm
Hence, length of open organ pipe is 8cm
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3
Answer:8 cm
Explanation:
n1 = n2
V/2L1 = 5V/ 4L2
L2/L1 = 5/2
20×2/5 = L1
L1= 8 cm
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