An open and closed organ pipe have the same length. The ratio of pth mode of frequency of vibration of air in two pipes is

Question

An open and closed organ pipe have the same length. The ratio of pth mode of frequency of vibration of air in two pipes is (A) p(2p + 1) (B) (2p/2p-1) (C) p (D) 1

Tardigrade Admin · Accepted Answer

The frequency of note produced in the p th mode of vibration in open pipe is v text open =(p v/2 L) The frequency of note produced in the pth mode of vibration in closed organ pipe is v text closed =((2 p-1) v/4 L) ∴ Ratio of pth mode of frequency of vibration of air in two pipes is (v text open /v text closed )=(p v / 2 L/(2 p-1) v / 4 L)=(2 p/2 p-1)

Q. An open and closed organ pipe have the same length. The ratio of $p^{t h}$ mode of frequency of vibration of air in two pipes is

$p (2 p + 1)$

$\frac{2 p}{2 p - 1}$

$p$

$1$

Q. An open and closed organ pipe have the same length. The ratio of pth mode of frequency of vibration of air in two pipes is

p(2p+1)

2p−12p​

p

1

Q. An open and closed organ pipe have the same length. The ratio of $p^{t h}$ mode of frequency of vibration of air in two pipes is

$p (2 p + 1)$

$\frac{2 p}{2 p - 1}$

$p$

$1$