Question

An open pipe is in resonance in its 2nd harmonic with tuning fork of frequency f₁. Now, it is closed at one end. If the frequency of the tuning fork is increased slowly from f₁, then again a resonance is obtained with a frequency f₂. If in this case the pipe vibrates nth harmonic, then ______.

Options

• n = 3, f₁ = `3/4`f₂

• n = 3, f₂ = `5/4`f₁

• n = 5, f₂ = `5/4`f₁

• n = 5, f₂ = `3/4`f₁

Answer 1

An open pipe is in resonance in its 2nd harmonic with tuning fork of frequency f₁. Now, it is closed at one end. If the frequency of the tuning fork is increased slowly from f₁, then again a resonance is obtained with a frequency f₂. If in this case the pipe vibrates nth harmonic, then `underlinebb("n" = 5, "f"_2 = 5/4"f"_1`.

Explanation:

Open pipe resonance frequency f₁ = `(2"v")/(2"L")`

Closed pipe resonance frequency f₂ = `"nv"/(4"L")`

f₂ = `"n"/4`f₁(where n is odd and f₂ > f₁)  

∴ n = 5