2 SOUND WAVES 



1.2. Sound Waves. — Sound is an alteration in pressure, particle dis- 

 placement or particle velocity propagated in an elastic material or the 

 superposition of such propagated alterations. 



Sound is also the sensation produced through the ear by the alterations 

 described above. 



Sound is produced when air is set into vibration by any means whatso- 

 ever, but sound is usually produced by some vibrating object which is in 

 contact with the air. If a string, such as used in a banjo or similar in- 

 strument, is stretched between two solid supports and plucked, sound is 

 produced which dies down in a fairly short time. When the string is 

 plucked it tends to spring back into its rest position, but due to its weight 

 (mass) and speed (velocity) it goes beyond its normal position of rest. 

 Then, in returning it again goes beyond its normal position of rest. The 

 excursions become smaller and smaller and finally the string comes to rest. 

 As the string moves forward it pushes air before it and compresses it, while 

 air rushes in to fill the space left behind the moving string. In this way 

 air is set in motion. Since air is an elastic medium, the disturbed portion 

 transmits its motion to the surrounding air so that the disturbance is propa- 

 gated in all directions from the source of disturbance. 



If the string is connected in some way to a diaphragm such as a stretched 

 drumhead of a banjo, the motion is transmitted to the drum. The drum, 

 having a large area exposed to the air, sets a greater volume of air in 

 motion and a much louder sound is produced. 



If a light piston several inches in diameter, surrounded by a suitable 

 baffle board several feet across, is set in rapid oscillating motion (vibration) 

 by some external means sound is produced (Fig. 1.1). The air in front of 

 the piston is compressed when it is driven forward, and the surrounding air 

 expands to fill up the space left by the retreating piston when it is drawn 

 back. Thus we have a series of compressions and rarefactions (expan- 

 sions) of the air as the piston is driven back and forth. Due to the elas- 

 ticity of air these areas of compression and rarefaction do not remain sta- 

 tionary but move outward in all directions. If a pressure gauge were set 

 up at a fixed point and the variation in pressure noted, it would be found 

 that the pressure varies in regular intervals and in equal amounts above 

 and below the average atmospheric pressure. Of course, the actual varia- 

 tions could not be seen because of the high rate at which they occur. Now, 

 suppose that the instantaneous pressure, along a line in the direction of 

 sound propagation, is measured and plotted with the ordinates representing 

 the pressure; the result would be a wavy line as shown in Fig. 1.1. The 

 points above the straight line represent positive pressures (compressions, 



