Experiment 6: Length of the pipe

Objective: The purpose of this lab is to find out the length of the hollow pipe without using ruler. The concept of sound wave will be used. Students will spin the pipe and record the sound pressure respect to time using logger pro. This procedure will be repeated second time with a faster spinning speed and a greater frequency.

                                Figure 1: Procedure, data, and calculations

Data

Data table 1: calculated wavelength and frequency

Spinning Speed	ω(rad/s)	ƒ(Hz)	λ(m)
slow	3859 ± 0.4736	614.18 ± 0.07538	0.558 ± 0.0000002
Fast	5068 ± 1.016	806.60 ± 0.1617	0.425 ± 0.000000249

V= ƒ*λ

(V=343m/s)

Data Table 2: length of the pipe

Spinning Speed	Value of n	Exp. length(m)	Actual length(m)	% Error(%)
slow	3	0.837 ± 0.000102	0.80 ± 0.05	4.6
Fast	4	0.850 ± 0.000169		6.3

% Error= (experimental length-actual length)/actual length*100%

Conclusion:

The purpose of this experiment was to find out the length of an opened hollow pipe using sound waves. The pipe was first spinned in a slower speed, and then in a faster speed. If the harmonics of the slower speed was n, that of the faster speed should be n+1. This relationship was used in calculating the length of the pipe by using f_n=(nv)/(2L). n for the slower speed trial is calculated to be 3, so that for the faster speed trial should be 4. The length was calculated to be 0.837m and 0.850m respectively for the slow and fast speed. The percentage errors for these two trials were acceptable. Sources of error could be the stretching pipe. Both of the experimental lengths had larger results than the actual length. This could be caused by the pipe stretched during spinning.