A pipe open at both ends and a pipe closed at one end have same length. The ratio of frequencies of their Pth overtone is

Question

A pipe open at both ends and a pipe closed at one end have same length. The ratio of frequencies of their Pth overtone is (A) (p+1/2p) (B) (p+1/2p+1) (C) (2(p+1)/2p+1) (D) (p/2p+1)

Tardigrade Admin · Accepted Answer

Frequency of p th overtone of open organ pipe =(p+1) (v/2 L)...(i) where, L= length of organ pipe and that of closed organ pipe is =(2 p+1) (V/4 L)...(ii) So, the ratio of p th overtone of open to closed =((p+1) (v/2 L)/(2 p+1) (v)4 L) (using Eqs. (i) and (ii) =(2(p+1)/(2 p+1))

Q. A pipe open at both ends and a pipe closed at one end have same length. The ratio of frequencies of their $P^{t h}$ overtone is

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

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

$\frac{2 ( p + 1 )}{2 p + 1}$

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

Q. A pipe open at both ends and a pipe closed at one end have same length. The ratio of frequencies of their Pth overtone is

2pp+1​

2p+1p+1​

2p+12(p+1)​

2p+1p​

Frequency of p th overtone of open organ pipe =(p+1)2Lv​...(i) where, L= length of organ pipe and that of closed organ pipe is =(2p+1)4LV​...(ii) So, the ratio of p th overtone of open to closed =(2p+1)4Lv​(p+1)2Lv​​ (using Eqs. (i) and (ii) =(2p+1)2(p+1)​

Q. A pipe open at both ends and a pipe closed at one end have same length. The ratio of frequencies of their $P^{t h}$ overtone is

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

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

$\frac{2 ( p + 1 )}{2 p + 1}$

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