An open organ pipe of length 1m contains a gas whose density is twice the density of the atmosphere at STP. Find the difference between its fundamental and second harmonic frequencies if the speed of sound in atmosphere is 300m/s.

Options

A. 150.75Hz
B. 106.08Hz
C. 105.75 Hz
D. 212.16 Hz

Answer

B

Explanation

Velocity of sound in gas, `v= sqrt((B)/(rho))`
`:. (v_("pipe"))/(v_("air")) = (sqrt((B)/(2 rho)))/(sqrt((B)/(rho)))= (1)/(sqrt2) = v_("pipe") = (v_("air"))/(sqrt2)`
`f_(n) = ((n+1))/(2l) v_("pipe")`
`:. F_(1)= (2v_("pipe"))/(2l) and f_(0) = (v_("pipe"))/(2l)`
`:. f_(1) - f_(0) = (2v_("pipe"))/(2l) - (v_("pipe"))/(2l)= (v_("pipe"))/(2l)`
`= (v_("pipe"))/(sqrt2 xx 2l) = (300)/( sqrt2 xx 2 xx 1)`
`=(300)/(2 sqrt2)`
`=(300)/(2 xx 1.414) = 106.08Hz`