Speed+of+Sound+Lab

Lab Title: Speed of Sound Lab

Primary Author: Alex Abstract: The goal of this lab was to explore a multitude of ways in which to find the speed of sound. Through three methods, two experimental and one theoretical, a good understanding of a few ways to calculate the speed of sound was created. The first experiment used a speaker with an open tube, while the second experiment used a tube filled with water, creating a closed end. In the end, a percent error calculation was performed comparing the two experiments with the theoretical solution, and a decision on which method is better was made.

Introduction: We translate waves into sound everyday. Unfortunately, most people have a very minimal understanding of these sound waves. While listening to music, many do not understand that singers are hitting harmonics. The same can be said for a multitude of other situations. The speed of sound is actually an interesting topic. In this lab report, a few methods to derive the speed of sound are expanded upon.

When discussing the speed of sound, it is important to understand the equation speed of sound= 331.3(1+(degrees C/273))^(sqrt root), which dictates the theoretical speed through air. It is also important to understand that sound waves are longitudinal mechanical waves. They can travel through a variety of objects, and their speed, as all other waves, depends on the object they're traveling through. In this lab, only the speed of sound through air is examined.

Data:

Part 1:

The first experiment gave me a speaker with adjustable frequency and an open tube.

1. The length of the tube was measured. 2. The sheet described the standing wave as extending past the tube by an "amount equal to 40% of the diameter on each side" so that was accounted for. 3. The fact that the first harmonic produced 1/2 of the wavelength inside the tube was noted, and was acted upon to find the wavelength. 4. After finding the wavelength, the frequency was searched for. This was a long process, but can be lessened in the future if the theoretical frequency is found first. 5. Settling with a frequency of 401 Hz, the equation v = frequency x wavelength was employed, and the speed of sound was determined.


 * Name of Quantity || Magnitude ||
 * = Length of Tube ||= 40.5 cm ||
 * = 40 % of diameter ||= 1.2 cm ||
 * = 1st harmonic ||= 1/2 of wavelength ||
 * = Wavelength ||= .258 cm ||
 * = Frequency ||= 401 Hz ||
 * = Speed of Sound ||= 344.058 m/s ||

Part 2:

The second experiment gave me an open tube, a large graduated cylinder filled with water, and two tuning forks.

1. The length and diameter were measured, and the 40% addition was noted for the first harmonic. 2. The frequency of the tuning forks were documented. 3. After striking the tuning forks agains a rubber object, the fork was held just above the unsubmerged and open side of the tube. At the same time, the tube was moved up and down in an attempt to find a point where the note of the tuning fork is loudly audible. 4. The points where the notes were loudest were found, and the distance between the top of the open tube and the water at those points were noted. 5. The wavelength was found by taking the previous measurement, multiplying by two, and adding 40% of the diameter. The reason for this calculation was the fact that, as stated earlier, the first harmonic is where half of the standing wave is located in the tube. Multiplying the tube by two, and account for the added 40% the lab discussed, led to the wavelength. 6. Finally, the equation Velocity = frequency x wavelength was used again. The speed of sound was calculated using the wavelength and frequencies found using both tuning forks


 * Named of Quantity || Magnitude || Magnitude ||
 * Diameter of Tube || 3 cm || 3 cm ||
 * Frequency || 324 || 349.2 ||
 * Total Length of Tube || 40.5 cm || 40.5 cm ||
 * Water to top for First Harmonic || 23.2 cm || 25.7 cm ||
 * Harmonic || 1 || 1 ||
 * Wavelength || .932 m || 1.028 m ||
 * Speed of Sound || 357.888 m/s || 358.928 m/s ||

Part 3:

This part was completely theoretical. I used the equation for the speed of sound in air as dictated by temperature in my introduction.


 * Name of Quantity || Magnitude ||
 * Temperature || 23 degrees Celsius ||
 * Speed of Sound || 344.661 m/s ||

Results:

Through this three part lab, a multitude of values for the speed of sound were found. These values were all different but at the same time very near to each other. This tells us that the results were fairly accurate. To test this accuracy, % error calculations were employed. An extremely small .2% error was found for the first one, and very minimal 3.3 and 4.1 % errors followed in the second experiment. Finally, the most reliable method for finding the speed of sound was chosen. This method is seen in experiment one. By using a large open pipe with a speaker giving off a frequency, there is not much room left for error. The same cannot be said for the method seen in experiment two where the tube must be moved up and down by hand. While the open tube is easily measurable, the closed tube must be held entirely still in it's position to measure correctly, which is not easy. When it comes to the most reliable method, the lack of a lot of room for error in the first method makes it a much more reliable option.

Conclusion:

There are a handful of ways to find the speed of sound while traveling through air. A clear understanding of a few of these methods was achieved, and the most reliable method was chosen to be the one from part 1.