Question

An open organ pipe produces its fundamental frequency f. When the pipe is dipped in water so that `2/5` of its length is under water, then its 5 fundamental frequency becomes ____________.

Options

• `12/5"f"`

• `6/5"f"`

• `8/7"f"`

• `5/6"f"`

Answer 1

An open organ pipe produces its fundamental frequency f. When the pipe is dipped in water so that `2/5` of its length is under water, then its 5 fundamental frequency becomes `5/6"f"`.

Explanation:

Let `l` be the length of the pipe.

`"f" = "v"/(2l)`

When `2/5l` is inside water,length of te air column, `l_1 = l - (2l)/5 = (3l)/5`

`therefore "f'" = "v"/(4l_1) = v/(4 xx (3l)/5)`

` = (5"v")/(12l) = 5/6("v"/(2l))`

` = 5/6"f"`