Question

A pipe P_c closed at one end and point P_o open at both ends are vibrating in the second overtone. They are in resonance with a given tuning fork. The ratio of the length of pipe P_c to that of pipe, P_o is ______.

(Neglect end correction).

Options

• `5/6`

• `4/5`

• `2/3`

• `3/5`

Answer 1

A pipe P_c closed at one end and point P_o open at both ends are vibrating in the second overtone. They are in resonance with a given tuning fork. The ratio of the length of pipe P_c to that of pipe, P_o is `underlinebb(5/6)`.

Explanation:

Here, `f_c = ((2n - 1)"v")/(4l_c)` and `f_o = (n"v")/(2l_o)`

Also, `f_c = f_o ⇒ ((2n - 1))/(4l_c) = n/(2l_o)`

`l_c/l_o = ((2n - 1))/(2n)`

= `([2(3) - 1])/(2(3))` (∵ for second overtone, n = 3)

= `5/6`