The fourth overtone of an open organ pipe has the same frequency as the second overtone of a close pipe of length L. The length of open pipe will be.

Question

The fourth overtone of an open organ pipe has the same frequency as the second overtone of a close pipe of length L. The length of open pipe will be. (A) L (B) 2 L (C) 4 L (D) (L/2)

Tardigrade Admin · Accepted Answer

Fourth overtone of open is its fifth harmonic. f=5 × (v/2 L0) f'=5 × (v/4 L) (second over tone of close is its fifth harmonic) given f'=f (5 V/2 L0)=(5 V/4 L) ∴ 2 L0=4 L L0=2 L

Q. The fourth overtone of an open organ pipe has the same frequency as the second overtone of a close pipe of length $L$ . The length of open pipe will be.

$L$

$2 L$

$4 L$

$\frac{L}{2}$

Fourth overtone of open is its fifth harmonic.
$f = 5 \times \frac{v}{2 L _{0}}$
$f^{'} = 5 \times \frac{v}{4 L}$
(second over tone of close is its fifth harmonic)
given $f^{'} = f$
$\frac{5 V}{2 L _{0}} = \frac{5 V}{4 L}$
$∴ 2 L_{0} = 4 L$
$L_{0} = 2 L$

Q. The fourth overtone of an open organ pipe has the same frequency as the second overtone of a close pipe of length L. The length of open pipe will be.

L

2L

4L

2L​

Fourth overtone of open is its fifth harmonic. f=5×2L0​v​ f′=5×4Lv​ (second over tone of close is its fifth harmonic) given f′=f 2L0​5V​=4L5V​ ∴2L0​=4L L0​=2L

Q. The fourth overtone of an open organ pipe has the same frequency as the second overtone of a close pipe of length $L$ . The length of open pipe will be.

$L$

$2 L$

$4 L$

$\frac{L}{2}$

Fourth overtone of open is its fifth harmonic.
$f = 5 \times \frac{v}{2 L _{0}}$
$f^{'} = 5 \times \frac{v}{4 L}$
(second over tone of close is its fifth harmonic)
given $f^{'} = f$
$\frac{5 V}{2 L _{0}} = \frac{5 V}{4 L}$
$∴ 2 L_{0} = 4 L$
$L_{0} = 2 L$