Question

The sequence of harmonics of a pipe open at one end and closed at the other end is 250 Hz and 350 Hz, The resonating length of the air column in its fundamental mode will be ______ 

(velocity of sound in air = 340 m/s) 

Options

• 0.25 m

• 0.85 m

• 1.7 m

• 1.35 m

Answer 1

The sequence of harmonics of a pipe open at one end and closed at the other end is 250 Hz and 350 Hz, The resonating length of the air column in its fundamental mode will be 1.7 m.

 (velocity of sound in air = 340 m/s) 

Explanation:

For a pipe closed at one end only odd harmonics are produced.

If n is the fundamental frequency, then the frequencies produced are n, 3n, 5n, etc.

The difference of successive harmonics is 2n.

∴ 350 - 250 = 100 Hz = 2n

∴ n = 50 Hz

∴ `lambda = "v"/"n" = 340/50 m = 6.8 m`

Resonating length of the air column in its fundamental mode is equal to `lambda/4`.

∴ ℓ = `6.8/4 = 1.7` m