Question

A pipe closed at one end vibrating in fifth overtone is in unison with open pipe vibrating in its fifth overtone. The ratio of l_c : l_o is [l_c = vibrating length of closed pipe, l_o = vibrating length of open pipe]:

Options

• 12 : 11

• 1 : 1

• 11 : 12

• 5 : 1

Answer 1

11 : 12

Explanation:

For a pipe open at both ends, the fifth overtone is given by:

n = `6 (V/(2 l_o)`

= `(3 V)/l_o`

For a pipe closed at one end, the fifth overtone is given by:

n' = `11 (V/(4 l_c)`

n = n'

∴ `(3 V)/l_o = 11 (V/(4 l_c)`

∴ `l_c/l_o = 11/12`