PH263 Resonance in Air Columns Lab # Name Lab Partner(s) I. EQUIPMENT LIST · Horizontal Resonance tube w/plunger · Oscilloscope · Function Generator Date · BNC - Dbl Banana cable · Microphone assembly · 1 meter brass rod II. BACKGROUND INFORMATION The air enclosed in a tube or pipe is elastic and can be set into vibration by placing a source of sound near one end of the tube. When the frequency of the sound source matches the natural or resonant frequency of the air column the amplitude of vibration will be much larger. This is due to an increase in the efficiency of energy transfer from the source to the column. The speed of sound of the medium in a tube can be calculated by finding the lengths that are resonant for a known frequency. A standing wave pattern is formed in the tube by the resonant frequency. The frequency of the standing wave pattern is determined by the length of the column and whether the ends are open or closed. The sound vibrations travel down the tube and reflect from the end (in the lab the end will be the surface of the plunger. If the length of the tube is an odd multiple of a quarter-wavelength [(2n+1)(\/4)] (n= integer) of the sound wave, then the reflected waves will reinforce the incoming waves and the sound will increase in loudness. (This can be noted by listening or by using an oscilloscope). The L plunger end of the air column will have a node V and the open (air) end of the tube will have an 41 = 1/4 antinode. (See figures to the right.) L2 For the open end of the tube, the antinode is just outside the open end of the tube, and this is called the end effect. The acoustical length of the tube is slightly longer than the physical length. This difference can be negated by taking the difference L2 = 34/4V between two consecutive resonance points. The lengths would be for example L1= A/4 and L2 = 3A/4 so L2 - L1= \/2. Solve for the speed of sound using the wave equation, v = Af, where f is the frequency, A is the wavelength and v is the speed of sound in the medium. The speed of sound in air is dependent on the temperature of the air and can be computed from v = v. + 0.6T where v. is the speed of sound in air at 0? (331.3 m/s) and T is the temperature in Celsius.
III. EXPERIMENTAL PROCEDURE Speaker Microphone A. The resonance tube apparatus consists of a clear tube, a plunger, a brass rod, a small microphone, and two end supports. All connections are made at the end where the speaker is located (left). DO NOT TOUCH THE SPEAKER SURFACE B. Set the resonance tube assembly on the table. C. Locate the small hole just below the speaker. Insert the microphone into the hole and tighten the thumb screw.