132 Davis — Anemometer for Stationary Sound Waves. 



the linear velocity of the cups and the average velocity of the 

 vibrating air. The 'No. 5 anemometer rotates with a some- 

 what less velocity in all parts of the wave. This may arise 

 from the fact that, owing to the small size of the cups, the 

 forces acting are very small, and hence the friction of the 

 pivot may have an appreciable effect, as this friction factor is 

 proportionately much larger than in the case of the other 

 anemometers. 



If we could measure either the average velocity of the maxi- 

 mum velocity of the vibrating air at the middle of the loop, 

 one could easily calculate the amplitude of vibration. Since 

 the air is executing a harmonic motion, the velocity of the 

 cups will not bear a simple relation to the average velocity of 

 the air, as the motion of the air, near the instant of reversal, 

 will be slower than that of the cups and have a retarding effect 

 even though it be in the same direction. The greater part of 

 the impulse will be delivered to the anemometer at the time 

 when the air is at the middle of its swing and the velocity is a 

 maximum. For the purpose of approximate measurement I 

 have assumed a ratio of 1 to 2*7 between the linear velocity of 

 the crips and the maximum velocity of the air. This ratio is 

 approximately that applied to the ordinary anemometer in 

 measuring wind velocities. 



The linear velocity of the anemometer cups at the middle of 

 the loop was about llT'-i " 1 per second, hence the maximum 

 velocity of the air was 317 cm per second. In order to obtain 

 the amplitude it is convenient to know the average velocity Y. 



/ A sin ptdt 



7 



dt 



where A is the maximum velocity. Hence Y = 202 cm per 

 second. 



The frequency of the pipe was 338 vibrations per second, 

 hence the amplitude was 2'99 mm . The term amplitude is here 

 used to denote the total excursion of an air particle during a 

 half period. 



This value for the amplitude is somewhat greater than a 

 corresponding value obtained by means of a new effect which 

 was soon afterwards applied by the writer to the same prob- 

 lem.* 



The experiments above described were performed at the 

 Physical Laboratories of Columbia University two years ago, 

 but the pressure of other affairs has delayed their publication 

 to the present time. 



GottiDgen, Oct. 5, 1901. 



*This Journal, September, 1900, also Physical Review, July, 1901. 



