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.

Question

Aditi Chauhan · Answer

Hello Student,

Please find the answer to your question

First overtone frequency

ℓ ₀ = ℷ

⇒ (v₁)₀ = v/ℷ’ = v/ ℓ₀ = 330/ ℓ₀

Fundamental frequency

ℓ_c = ℷ₁/4 ⇒ ℷ₁ = 4 ℓ_c

⇒ (v₁)c = v 4 ℓ_c = 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

Case 2 : (v₁)₀ < (v₁)_c

(v₁)₀ - (v₁)_c = 2.2

330 – 330/ℓ₀ = 2.2 ⇒ ℓ₀ = 1.006 m

Thanks
Aditi Chauhan
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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.

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