I then found the actual speed of sound by using the equation V speed of sound = 331. 4 + 0. 6Tc m/s. The experimental speed of sound was 344. 064 m/s and the actual speed of sound was 345. 8 m/s. By knowing these values I could then find the percent error. My calculations are above in the calculations section. The calculations show that the percent error was 0. 502 %. I found this percent error to be acceptable and due to random error. The independent variables in this experiment would be temperature and composition of the air. The dependent variable would be the speed of sound.
Depending on the composition of the medium through which the sound wave is travelling through, which in this case is air (78% nitrogen, 21% oxygen, and 1% other gases), the speed of sound would vary. The more elastic a medium, the faster sound travels. The less elastic a medium, the slower sound travels. Because sound is traveling through air (gases) in this case, the altitude affects the speed of sound because of the air pressure. At lower altitudes sound travels faster because of higher air pressure. At higher temperatures sound travels faster because as explained by the equipartition theorem of thermodynamics.
This means that each molecule has 1/2kT of energy per degree of freedom, and this is related to its kinetic energy through the usual 1/2mv 2 rule (Stony Brook University Staff, 2010). As stated earlier, the experimental results were very close to the actual values. The reason for the . 0502% error was due to both problems with an idealized equation and random error. The best way to decrease uncertainty would be to repeat the experiment many times over. The results could then be averaged. Standard deviation could then also be determined. The biggest drawback to the experimental procedure was the measurement of the first harmonic.
If there were a measurement of distance integrated into the actual tube, it would have been easier to get a more precise measurement. Interpretation of Results: The results of the experiment show that I was able to calculate the speed of sound at which sound travelled through the air very accurately. I know this because the percent error was very small. I believe I did an adequate job of keeping uncertainty to a minimum in this experiment. I think if I had conducted this experiment at a controlled temperature, elevation, and with more precise instruments I would have found more accurate values for the speed of sound.
The theory behind this exercise was that the velocity of sound was equal to the frequency multiplied by the wavelength. My results agree with this theory because I found the experimental value of the speed of sound using the process described in the results section and it was extremely close to the accepted actual value that was calculated in the calculations section. My experimental results show that the speed of sound was 344. 064 m/s and the actual speed of sound was 345. 8 m/s. This is a percent difference of 0. 502%.
I was surprised that I could accurately calculate the speed of sound so easily and the results forced me to change this preconceived notion. I also had originally thought that sound travelled faster in objects that were more dense. I was forced to change this belief, not based on my results, but by researching the topic. I found that this was not true. Elasticity, the composition of the air, temperature, and pressure are factors that determine how fast sound travels. I always thought that sound travelled in water at a faster speed than through air because of the density. I guess this was not true.
I also thought sound would travel faster at colder temperatures, due to the density of the air, and I found that this was also not true (to an extent). I was surprised to learn that sound travelled faster at higher temperatures in air. All in all, I am confident with my results and glad that I researched the topic and found additional information that corrected my preconceived notions. Error Sources and Why: Errors were caused by random error in this laboratory. It was difficult to get a good measurement of the first harmonic. As stated earlier, this could be corrected by introgration of a measurement device onto the outside of the tube.
I also think that the equation used to find the actual speed of sound was idealized and could contribute to a small and varying amount of error at different temperatures. Additionally, I believe that my altitude and the amount of humidity in the air contributed to the error. I had no way of knowing my altitude. I also had no way of knowing what the humidity was. If I had instruments to measure these factors, it would have helped. Then, sources of error could be eliminated by knowing what the altitude and humidity values were when the equation used to find the actual speed of sound was made.
I could then construct a new equation and find a more precise actual value for the speed of sound travelling through air by using the values I measured.
References: Stony Brook University Staff. 12 February 2010. Lecture 36: First Law of Thermodynamics. Stony Brook Physics 141/142. Web. Retrieved 29 April 2011. http://www. ic. sunysb. edu/Class/phy141md/doku. php? id=phy141:lectures:36 Mathpages Staff, n. d. The Speed of Sound. Mathpages. com. Web. Retrieved 29 April 2011. http://www. mathpages. com/home/kmath109/kmath109. htm Jeschofnig, Peter, Ph. D. 2009. Determining the Speed of Sound. LabPaq Manual PK-S. pp. 115-117.