An air column in a pipe, which is closed at one end will be in resonace with a vibrating tuning fork of frequency 264 Hz for various lengths. Which one of the following lengths is not possible ? [v = 330 m/s]

Options

A. `93.75` cm
B. `156.25` cm
C. `62.50` cm
D. `31.25` cm

Answer

C

Explanation

For a pipe closed at one end,
`f = n (V/(4l)) " where " n = 1,3,5, ...`
` :. l = (nV)/(4f) `
For ` n = 1, l_(1) V/(4f) = (1 xx 330)/(4 xx 264) xx 100 = 31.25` cm
For ` n = 3, l_(3) = 3l_(1) = 3 xx 31.25 = 93.75` cm
For ` n = 5, l_(5) = 5l_(1) = 5 xx 31.25 = 156.25` cm
For ` n = 7, l_(7) = 7 xx l_(1) = 7 xx 31.25 = 218.75` cm
Thus the length `62.50` cm is not possible.