The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe L metre long. The length of the open pipe will be

Question

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

Tardigrade Admin · Accepted Answer

(3v/2ℓ0) = (3v/4L) 2ℓ0 = 4L ℓ0 = 2L

Q. The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe $L$ metre long. The length of the open pipe will be

$L$

$2 L$

$\frac{L}{2}$

$4 L$

$\frac{3 v}{2 ℓ _{0}} = \frac{3 v}{4 L}$
$2 ℓ_{0} = 4 L$
$ℓ_{0} = 2 L$

Q. The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe L metre long. The length of the open pipe will be

L

2L

2L​

4L

2ℓ0​3v​=4L3v​ 2ℓ0​=4L ℓ0​=2L

Q. The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe $L$ metre long. The length of the open pipe will be

$L$

$2 L$

$\frac{L}{2}$

$4 L$

$\frac{3 v}{2 ℓ _{0}} = \frac{3 v}{4 L}$
$2 ℓ_{0} = 4 L$
$ℓ_{0} = 2 L$