III. Procedure: Longitudinal Waves in Air

Standing waves in air, quite analogous to the standing waves on a string, can be produced in the air column inside a cylindrical tube. An aluminum plug may be moved along the tube and the presence of the standing wave detected by listening for nodes and anti-nodes in the standing wave pattern. In this case, the excitation is provided by a small speaker driven by a function generator. The arrangement is sketched below. 

 

 

 

 

Set the frequency of the function generator to 1000 Hz.  Starting with the movable piston near the speaker, move the piston away from the end until the sound reaches a minimum.  Record the position of this minimum intensity, which is found when the end of the tube is at a node.  Continue to move the piston along the tube, recording all the rest of the points along the tube where the sound is weakest.  Average the distances between these successive nodes, find the corresponding wavelength which is twice the average distance, and use Eq.(1) to calculate the speed of sound in air. Obtain a 90% confidence interval for this measurement by propagating the uncertainty in node separation.

The velocity of sound in air is known to vary with temperature as:

(3)                         

where               R = gas constant = 8.314 joules/mole K,
M = molecular weight = .0288 kg/mole for air,
T = absolute temperature,
and                   g = ratio of specific heats = 1.40 for air.

Compare your value of v measured for the standing wave with the one found from Eq.(3).  For this comparison, you can assume that the uncertainty in the value from Eq.(3) is zero.