diameter. Place the microphone near the middle of the pipe (but not exactly at the middle, since some of the modes have nodes there). Make a table of resonance frequencies ƒ, like you did for the modes in the Strings lab, measuring the frequencies of the first 5 modes. Attention: You may have missed the fundamental. From your table, you will be able to guess where it is. The table should have the following columns: # Mode Measured f n x measured deviation diagram fundamental Are all of the overtones multiples of the fundamental frequency? Figure out what multiple of the fundamental frequency each consecutive mode’s frequency is, and write it down in the third column. (Note: For the fundamental mode itself, use the measured value.) Now, locate the nodes and antinodes of the standing waves, by moving the microphone back and forth in the pipe for the first and fifth resonance frequency. Are the ends of the pipe nodes or antinodes? 2. Effect of Length and Diameter of the Pipe Compare the fundamental frequency you measured with the frequency given by the pipe formula f = v/2L, where v is the velocity of sound in the air (344.7 m/sec at 70°F, increasing or decreasing by 0.3 m/sec for each 1°F increase or decrease in temperature respectively) and L is the pipe length, in this particular case, 60 cm. Does the fundamental frequency you just calculated agree with the fundamental frequency you measured (and wrote in your table)? If not, for what value of would the calculated fundamental frequency be L identical to the measured one? In order to answer this question, you need to express in terms of and that is, you need to rewrite the L v f, formula given above as = and then use the measured value for the L v/2f, fundamental frequency f. The value of L you obtained through the procedure outlined above is
diameter. Place the microphone near the middle of the pipe (but not exactly at the middle, since some of the modes have nodes there). Make a table of resonance frequencies ƒ, like you did for the modes in the Strings lab, measuring the frequencies of the first 5 modes. Attention: You may have missed the fundamental. From your table, you will be able to guess where it is. The table should have the following columns: # Mode Measured f n x measured fundamental deviation diagram Are all of the overtones multiples of the fundamental frequency? Figure out what multiple of the fundamental frequency each consecutive mode’s frequency is, and write it down in the third column. (Note: For the fundamental mode itself, use the measured value.) Now, locate the nodes and antinodes of the standing waves, by moving the microphone back and forth in the pipe for the first and fifth resonance frequency. Are the ends of the pipe nodes or antinodes? 2. Effect of Length and Diameter of the Pipe Compare the fundamental frequency you measured with the frequency given by the pipe formula f = v/2L, where v is the velocity of sound in the air (344.7 m/sec at 70°F, increasing or decreasing by 0.3 m/sec for each 1°F increase or decrease in temperature respectively) and L is the pipe length, in this particular case, 60 cm. Does the fundamental frequency you just calculated agree with the fundamental frequency you measured (and wrote in your table)? If not, for what value of L would the calculated fundamental frequency be identical to the measured one? In order to answer this question, you need to express L in terms of v and f, that is, you need to rewrite the formula given above as L = v/2f, and then use the measured value for the fundamental frequency f. The value of L you obtained through the procedure outlined above is
Fall2017P109LabManual.docx