The first overtone of an o0pen organ pipe beats wi

Question

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.

Aditi Chauhan · Accepted 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
askIITians Faculty

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