Experiment 6: Length of the Pipe

Introduction

The purpose of this experiment is to determine the length of an open pipe by using sound waves. The experiment was conducted using an open pipe, a microphone, Logger Pro, a guitar, and two tuning forks. In part 1, an open pipe with unknown length was spun with a speed till a clear tone was heard. The microphone was put near the spinning pipe, and the sound wave was recorded by using Logger Pro. This process was repeated with a greater spinning speed that gave the next level of tone.

Data and Analysis

Table 1: Data recorded from spinning the open pipe

Spinning Speed	ω(rad/s)	ƒ(Hz)	λ(m)
Low	3859 ± 0.4736	614.2 ± 0.07538	0.558 ± 0.0000679
Fast	5068 ± 1.016	806.6 ± 0.1617	0.425 ± 0.0000845

Table 2: Comparison of the length of the open pipe obtained from 2 data sets

Spinning Speed	Lexp(m)	Lact(m)	% Error(%)
Low	0.837 ± 0.000102	0.80 ± 0.05	4.6
Fast	0.850 ± 0.000169		6.3

Figure 1: Calculation of the length of the open pipe

Conclusion

                In this experiment, the length of the pipe was computed by using the concept of the fundamental frequency and its harmonics. Since it was an open pipe, it had the wavelength that was twice of the length of the pipe. Since the second frequency produced the next tone after the first, the second frequency had a half wavelength longer than the wavelength of the first frequency. By using this relationship, as shown in figure 1, n value was calculated, and the length of the pipe was found. As shown in table-1, the lengths of the open pipe obtained from two sets of data were 0.837m and 0.850m. This resulted in a percent error of 4.6% and 6.3%. Even though the experimental results were not within the uncertainties of each other, these values were within the uncertainty of the actual length of the pipe. Table 1 showed that the experimental lengths were greater than that of the actual length. This was possibly due to the fact that the pipe stretched when it was spun. Since the pipe had tension, the pipe could stretch approximately 4cm longer.