Question

A pipe open at both ends and a pipe closed at one end have same length. The ratio of frequencies of their p^th overtone is ______.

Options

• `("p + 1")/"2p"`

• `("p + 1")/"2p + 1"`

• `(2("p + 1"))/"2p + 1"`

• `("p")/"2p + 1"`

Answer 1

A pipe open at both ends and a pipe closed at one end have same length. The ratio of frequencies of their p^th overtone is `underline((2("p + 1"))/"2p + 1")`.

Explanation:

Frequency of p th overtone of open organ pipe

`= ("p" - 1) "v"/"2L"`    ...(i)

where, L = length of organ pipe

and that of closed organ pipe is

`= ("2p" + 1)"v"/"4L"`    ....(ii)

So, the ratio of p th overtone of open to closed

`= (("p" + 1)"v"/"2L")/(("2p" + 1) "v"/"4L")`   [using Eqs. (i) and (ii)]

`= (2("p + 1"))/"2p + 1"`