Lab 4 - Air Columns

SPH3U1 Names: Date: Air Columns Mark /35 An air column that is closed at one end and open at the other is called a closed air column. When a vibrating tuning fork is held over the open end of such a column and the length of the column is increased, the loudness increases sharply at very specific lengths. If a different tuning fork is used, the same phenomenon is observed except the maxima occur at different lengths. Purpose In this lab, you will determine the speed of sound in air by finding the lengths of closed air columns that resonate with given frequencies. Materials copper pipe large, graduated cylinder water tuning forks of different frequencies (512 Hz, 1024 Hz, 2048 Hz) meter stick Procedure 1. Students are going to work in groups of four for this lab. 2. Place the copper pipe in the graduated cylinder, as shown in the figure shown. Fill the graduated cylinder with water as close to the top as possible. 3. Sound the tuning fork and hold it over the mouth of the copper pipe. Have your partner move the pipe slowly out of the water and listen for the first resonant point. At points of resonance, the intensity of the sound originating from the tuning fork will increase dramatically. Ignore points of slightly increased intensity that are not of the same frequency as the tuning fork. 4. Use the metre stick to measure the length of the air column for the first resonant point. Record your measurements in a chart similar to Table 1. Table 1a: Observations and Measurements (3 marks, T) Trial Frequenc y (Hz) Length 1 (m) Length 2 (m) 1 512 0.160 0.500 2 1024 0.236 0.395 3 2048 0.146 0.295 5. Continue to raise the pipe, finding and measuring other resonant points. 6. Repeat steps 3 through 5 with a tuning fork of a higher frequency.

Theory 1. State the three fundamental equations required for the analysis of this lab. Define the variables for each equation and indicate the unit for each quantity, if any. State any assumptions made when using the equations. (7 marks, C) 1) v = fλ 2) v = 331.4 + 0.606 T 3) L n = ( 2 n − 1 ) 4 λ Some assumptions that were made when using the equations are that the temperature stayed at a constant value, making the velocity consistent as well. The third equation is assumed that the tube is a fixed-end pipe with one end open and the other closed. The first equation assumes that the wave is travelling through a medium at a constant velocity. First equation, the units are m/s for velocity, Hz for frequency, and m for wavelength. Second equation, the units m/s for velocity and ℃ for temperature. Third equation, the units are m for wavelength. 2. Using your fundamental equations, show that the distance between any two subsequent resonant lengths, Δ ? in ? , is related to the wavelength of sound, ? in ? , by equation 1: (2 marks, T) ∆ L = 1 2 λ [1] ∆ L = L = 1 2 λ λ = 2 L v = f λ λ = v f 2 L = v f → v f = λ 2 L = λ 3. Include labeled diagrams of the experimental setup you used in this experiment. Make sure to clearly label key quantities that were measured during the lab. (2 marks, C) Water Container: