Lab 5: Cylindrical Air Columns

Transcription

1 Lab 5: Cylindrical Air Columns Objectives By the end of this lab you should be able to: Calculate the normal mode frequencies of an air column. correspond to a pressure antinode - the middle of a hump. The open end has a pressure node near it, but there is an end correction. We do not know what the end correction is. We will use tuning forks to drive the air column as was done with the Florence flask in class. What to do: Take notes on what you do. You will turn in a lab report the following Monday. A template is on the web site. Materials needed: Air column with water reservoir Tuning forks Rubber mallets Water Vernier calipers Speaker driver Lab stand Lab clamp, and arm PVC tube Function generator Tape measure Ruler Activity 1: Air column in a tube with one end open and one end closed In this experiment, frequency is fixed and the length of an air column is varied. This will produce resonances in the air column that you will be able to hear. The apparatus consists of a long glass tube that is connected to a movable reservoir by means of a rubber siphon. The water level in the tube and, thus, the length of the air column is controlled by the position of the reservoir. The water surface acts as a closed end and will Glass tube Water reservoir Choose a tuning fork with frequency above 300 Hz. This experiment works best if one person holds the tuning fork, one person marks the water positions, and one person adjusts the water levels. The first person should hold the vibrating tuning fork above the opening of the tube, and listen with one ear close to the opening of the top of the tube. Another person should have a piece of tape ready, and observe the water level. Another person will raise and lower the water reservoir to change the water level. Start with the water level high, for example 5-10 cm below the top of the tube. With the tuning fork vibrating, lower the reservoir about a

2 meter, causing the water level to drop. The person with the tuning fork should listen for the increase in loudness of the sound. At the maximum loudness, mark the water level with a piece of tape on the glass tube. Mark a few positions where resonance occurs, and record the measurements below. Water level in tube at which resonance occurs (m) Determine the wavelength of the wave. Wavelength is twice the hump length. Wave length (m) Now that the hump length is known we can easily find the end correction. For mode one it is simply ½ the hump length minus the actual length of the air column. Determine this below. Measured end correction (m) Mode one has about ½ hump and mode two has about 1½ humps. The end correction for the two is the same because the frequency is the same. The difference between the water levels must therefore be one hump length, so we can get a good value for the hump length even though the end correction is not known. Determine the hump length. Hump length (m) The author claims the end correction for one open end should be End correction = 0.61R..(1) where R is the radius of the air column. Measure the inner radius of the air column, and calculate the end correction below. Is the claim true? Calculated end correction (m)

3 The speed of a wave is given by v = fλ where v= wave speed, f=frequency, and λ=wavelength. Determine the speed of sound in the tube, based on your previous measurements. Speed of sound (m/s) Table 1: Predicted resonance frequencies Speed of sound in air at 20 C Inner radius of tube (m) 343 m/s End correction for two open ends (m) Activity 2: Resonances in a tube with both ends open In class we made the claim that the fundamental frequency of an air column of length L in a tube with both ends open is f 1 = v 2L..(2) where v is the speed of sound, which equals 343 m/s at temperature 20 C. We also claimed that the normal mode frequencies formed a harmonic series. Use Equations 1 and 2 to predict the normal mode frequencies of the tube (shown in Activity 3) with both ends open. Fill in Table 1. Length of tube (m) Length of air column L (meters) f 1 (fundamental frequency) f 2 (second harmonic) f 3 (third harmonic) f 4 (fourth harmonic) f 5 (fifth harmonic) This includes the end correction

4 Activity 3: Excite the normal modes Set up the experiment shown. A PVC tube with both ends open is clamped and held above a speaker, which is connected to a function generator that is set to produce sine waves. normal mode frequencies. One way to do this is to calculate the percent difference between the two. Table 2. Measured values f 1 (fundamental frequency) f 2 (second harmonic) Tube Function generator set to sine wave f 3 (third harmonic) f 4 (fourth harmonic) f 5 (fifth harmonic) Speaker Turn the function generator on. Be sure it is set for sine waves. Put your ear near the top of the tube, and listen carefully as you start at low frequency and slowly increase the frequency until you find the fundamental mode. Record the frequency indicated on the function generator in Table 2. Repeat this for the first several modes. Enter your results in Table 2. In your report, address whether the normal mode frequencies form a harmonics series. Also address whether equations 1 and 2 correctly predict the

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