It is desired to increase the fundamental resonance frequency in a tube which is closed at one end. This can be achieved by

Options

A. Increasing the length of the tube
B. Decreasing the length of the tube
C. Replacing the air in the tube by hydrogen gas
D. Opening the closed end of the tube

Answer

A

Explanation

(1) For a tube, closed at one end, the fundamental frequency ` n = v/(4l)`
` :' n propto 1/l `,
` :. ` n can be increased by decreasing (l). Thus (b) is correct . But if l is increased then n will decrease.
(2) Similarly , `n_("open") = 2n_("closed") `. Thus by opening the tube n can be increased . Hence (d) is correct .
(3) Similarly , `v = sqrt((gammaRT)/M) :. v propto 1/sqrtM`
`M_(H_(2)) = M_("air") :. v_(H_(2)) gt v_("air") " and " n_(H_(2)) gt n_("air") `
` :. " With " H_(2)`, the frequency will increase.
Thus n cannot be increased, by increasing the length of the tube (a) is the correct choice.