Velocity of Sound in Tubes at Audible and Ultrasonic Frequencies

The velocity of sound in air contained in glass tubes ranging in diameter from 0.1 cm to 3.0 cm was measured at ultrasonic frequencies over a frequency range from 30 to 200 kilocycles per second by using quartz crystals as sound oscillators, and the Kundt's dust tube method. The results do not agree with those calculated by use of Helmholtz-Kirchhoff equation $V^1=V_0(1-\frac{C}{2R{\left(2\mathrm{}\pi N\right)}^{\frac{1}{2}}}).\mathrm{}$ An equation of the form $V^1=V_0(1-\frac{C}{D^2}-\frac{K}{D{\mathrm{}\left(N\right)\mathrm{}}^{\frac{1}{2}}})$ is fairly satisfactory for both audible and ultrasonic frequencies. In this equation $V_0=331.77\mathrm{}$ m/sec., $C=0.001512\mathrm{}$, $K=0.174\mathrm{}$, $N=\mathrm{frequency}$ and $D=\mathrm{diameter}\mathrm{of}\mathrm{the}\mathrm{tube}$. The agreement between experimental and calculated values is better for the larger tubes than for the smaller.