Question

The fundamental frequency of an open organ pipe is 300 Hz. The first overtone of this pipe has same frequency as first overtone of a closed organ pipe. If speed of sound is 330 m/s, then the length of closed organ pipe is:

Options

• 41 cm

• 37 cm

• 31 cm

• 80 cm

Answer 1

41 cm

Explanation:

For open pipe, n = `"v"/(2ℓ)`, where n₀ is the fundamental frequency of open pipe.

∴ ℓ = `"v"/(2"n") = 330/(2 xx 300) = 11/20`

As freq. of 1st overtone of open pipe = freq. of 1st overtone of closed pipe

∴ `2"v"/(2ℓ) = 3"v"/(4ℓ"'")`

⇒ ℓ' = `(3ℓ)/4`

= `3/4 xx 11/20`

= 41.25 cm