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The first overtone of an o0pen organ pipe beats with the first overtone of a closed organ pipe with a beat frequency of 2.2 Hz. The fundamental frequency of the closed organ pipe is 110 Hz. Find the lengths of the pipes.

The first overtone of an o0pen organ pipe beats with the first overtone of a closed organ pipe with a beat frequency of 2.2 Hz. The fundamental frequency of the closed organ pipe is 110 Hz. Find the lengths of the pipes.

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
8 years ago
Hello Student,
Please find the answer to your question
236-1387_6.png
First overtone frequency
ℓ 0 = ℷ
⇒ (v1)0 = v/ℷ’ = v/ ℓ0 = 330/ ℓ0
Fundamental frequency
236-277_6.png
ℓc = ℷ1/4 ⇒ ℷ1 = 4 ℓc
⇒ (v1)c = v 4 ℓc = 10 Hz (given)
But beat frequency is 2.2
Case 1 : (v1)0 > (v1)c
(v1)0 - (v1)c = 2.2
⇒ 330/ℓ0 – 330 = 2.2 ⇒ ℓ0 = 0.9933 m
236-2109_6.png
Case 2 : (v1)0 < (v1)c
(v1)0 - (v1)c = 2.2
330 – 330/ℓ0 = 2.2 ⇒ ℓ0 = 1.006 m

Thanks
Aditi Chauhan
askIITians Faculty

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