Question

The closed and open organ pipes have same length. When they are vibrating simultaneously in first overtone, produce three beats. The length of open pipe is made `1/3` rd and closed pipe is made three times the original, the number of beats produced will be ______.

Options

• 8

• 14

• 17

• 20

Answer 1

The closed and open organ pipes have same length. When they are vibrating simultaneously in first overtone, produce three beats. The length of open pipe is made `1/3` rd and closed pipe is made three times the original, the number of beats produced will be 17.

Explanation:

For open pipe first overtone, v₁ = `"v"/"L"`

For closed pipe first overtone, v₁ = `(3"v")/(4"L")`

∴ v₁ - v₁ = `"V"/"L"-(3"V")/(4"L")=3`

or, `"V"/(4"L")` = 3

∴ `"V"/"L"` = 12

When length of open pipe is made `"L"/3`,

Fundamental frequency v = `"V"/(2("L"/3))=(3"V")/(2"L")`

When length of closed pipe is made 3 times,

Fundamental frequency v' = `"V"/(4(3"L"))="V"/(12"L")`

Beats produced = v - v'

`(3"V")/(2"L")-"V"/(12"L")=17/12,"V"/"L"         [∵ "V"/"L"=12]`   

= `17/12xx12`

= 17