An open and a closed pipe have same length. The ratio of frequency of their nth overtone is

Question

An open and a closed pipe have same length. The ratio of frequency of their nth overtone is (A) (n+1/2 n+1) (B) (2(n+1)/2 n+1) (C) (n/2 n+1) (D) (n+1/2 n)

Tardigrade Admin · Accepted Answer

Let l be the length of the pipes and v the speed of sound Then frequency of open organ pipe of nth overtone is f1=(n+1) (v/2 l) and frequency of closed organ pipe of nth overtone f2=(2 n+1) (v/4 l) Therefore, the desired ratio is (f1/f2)=(2(n+1)/(2 n+1))

Q. An open and a closed pipe have same length. The ratio of frequency of their $n$ th overtone is

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

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

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

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

Q. An open and a closed pipe have same length. The ratio of frequency of their nth overtone is

2n+1n+1​

2n+12(n+1)​

2n+1n​

2nn+1​

Let l be the length of the pipes and v the speed of sound Then frequency of open organ pipe of nth overtone is f1​=(n+1)2lv​ and frequency of closed organ pipe of nth overtone f2​=(2n+1)4lv​ Therefore, the desired ratio is f2​f1​​=(2n+1)2(n+1)​

Q. An open and a closed pipe have same length. The ratio of frequency of their $n$ th overtone is

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

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

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

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