A closed organ pipe and an open organ pipe of same length produce `4` beats when they are set into vibrations simultaneously. If the length of each of them were twice their initial lengths, the number of beats produced will be

Answer

2

Explanation

`v_("open") = V/(2L)`
`V_("closed") = V/(4L)`
`rArr V/(2L)- V/(4L) = 4`
`rArr V = 16 L`
Now in 2nd case:-
`V_("open")^(.) = V/(4L)`
`V_("closed")^(.) = V/(8L)`
`therefore V_("open")^(.) - V_("closed")^(.) = V/(8L) - V/(4L) = V/(8L)`
`rArr = (16L)/(8L) = 2`