A closed organ pipe and an open organ pipe of same length produce 2beats when they are set into viberations simultaneously in their fundamental mode. The length of open organ pipe is now halved and of closed organ pipe is doubled, the nunber of beats produced wil be

Options

A. 7
B. 4
C. 8
D. 2

Answer

C

Explanation

The fundamental frequency of an open organ pipe of length L is `upsilon_(o)=(v)/(2L)`
The fundamental frequency of an closed organ pipe of same length L is `upsilon_(c)=(v)/(4L)`
As `upsilon_(o)-upsilon_(c)=2 therefore (v)/(2L)-(v)/(4L)=2 or(v)/(4L)=2or(v)/(L)=8" "...(i)`
Now, `upsilon_(o).=(v)/(2((L)/(2)))=(v)/(L)upsilon._(c)=(v)/(4(2L))=(v)/(8L)`
Number of beats per second
`=upsilon._(o)-upsilon._(c)=(v)/(L)-(v)/(8L)=(7)/(8)(v)/(L)=(7)/(8)xx8=7` (Using (i))