[LANG] HIGH FREQUENCY VIBRATIONS, ETC. 167 



tube were used. These results give the velocity of air waves at 

 moderate frequencies in a smooth brass tube of 1.4 cms. diameter 

 as 325.6 meters per second at 0°C. 



Correcting this velocity in the tube for the temperature of the 

 room as given in the table the velocity of the wave in the steel bar 

 was found to be 5090 meters per second at 18.2°C. Using Newton's 

 equation for velocity we obtain the value E = 2. 15X10^- dynes per 

 square cm. for Youngj's modulus for the steel. 



The possible error in this result cannot be stated definitely 

 since the error in Blaikley's results is not known; but aside from this, 

 which is not vital in any case, it is clear that the error in the length 

 of the bar need not exceed 0.1% and in the density 0.1%. In esti- 

 mating the error in the distance between two successive nodes in the 

 dust figures it may be stated that this may be made very small by 

 measuring a large number of the vibrating segments. It was found 

 practicable to employ a tube 150 cms. long and measurements were 

 taken over 30 vibrating segments. Estimating the error, then, in 

 this distance as say 0.15% gives the possible error in E as approx- 

 imately 0.7% or the modulus is given to the third significant figure. 



It might be questioned whether the velocity obtained for the 

 waves in the steel bar is really that corresponding to the equation 



V= /— when E is simply Young's modulus, or whether the lateral 



V p 



contraction operates to alter this velocity by introducing a factor 

 corresponding to rigidity. Rayleigh^ has investigated this point and 

 finds that the lateral inertia operates to increase the natural period, 

 i.e. to decrease the natural frequency in the ratio: 



1 



1 + 



i' 0-^ TT' r^ 



4/2 



where a is Poisson's ratio, r is radius of bar, / is its length and i is 

 integral and corresponds to the modes of vibration. 



If we take r equal 1 inch and / equal 10 inches, and i equal 1, 

 and a equal to 0.31, we find that the ratio obtained is 1:1.0000435. 

 Therefore, in the present case, the lateral effect is insignificant and 

 need not be considered. 



The question as to whether the air waves are affected by the 



yielding of the walls of the glass tube was also investigated. The 



dy 

 potential energy corresponding to a given strain -t~ of the fluid in 



'Rayleigh, "Theory of Sound, Vol. 1, pages 251-3. 



