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

Answer

`106`

Explanation

`V=sqrt(B/(rho))`
`(V_("pipe"))/(V_("air"))=(sqrt(B/(2rho)))/(sqrt(B/(rho)))=1/(sqrt(2))`
`V_("pipe")=(V_("air"))/(sqrt(2))`
`f_(n)+((n+1)V_("pipe"))/(2l)`
`f_(1)-f_(0)=(V_("pipe"))/(2l)=300/(2sqrt(2))`
`=105.75Hz` (if `sqrt(2)=1.41`)
`=106.05Hz` (if `sqrt(2)=1.414`)