Group18_6_ch11

=Lab: Resonance Tube= Maddy, Jessica, Dani, Gabby

Task A: Jess Smith Task B: Gabby Leibowitz Task C: Dani Rubenstein Task D: Maddy Weinfeld

Objectives:
 * 1) Determine several effective lengths of the closed tube at which resonance occurs for a frequency.
 * 2) Determine several effective lengths of the open tube at which resonance occurs for a frequency.
 * 3) Determine the speed of sound from the measured wavelengths and known frequency of the sound.

Hypothesis: Our group hypothesizes that, in the closed tube, resonance will occur at even intervals. In addition, in the open tube, resonance will also occur at even intervals. Finally, the speed of sound measured during this lab will be the same value as the speed of sound in air.

Methods and Materials: A resonance tube, with a sliding inner tube, is used to find the length at which resonance occurs at a certain frequency. The first part of this experiment involves a closed tube. The closed tube is covered with a cap in order to measure the length of how much of the tube is pulled out. After these measurements are recorded, an open tubed is used. For the open tube, the length of the actual tube IN ADDITION TO how much length was increased needs to be accounted for. Measurements for the open tube are then, recorded. This process is used to find all the locations at which the pitch is the highest, in other words, the resonance points.

Data:

Calculations:

Wave Speed Theoretical Length First Length to Hear Resonance in Open Tube First Length to Hear Resonance in Closed Tube Average L Experimental
 * We did not have an average for most as we only did one trial due to time restraints

Open Tube with End Correction

Conclusion: This lab was extremely relevant to everything that we have been discussing in class and was very helpful in reenforcing the concepts and equations we are working with. We collected data as a large group and all worked together to gather our different data points. Our hypothesis was that as frequency increased, resonance would increase as well, with a linear relationship. We also thought that the smaller tube would have a smaller slope than the open tube. Our data showed a positive correlation between the frequency and resonance, as we had expected. PERCENT ERROR. When we first did the calculations, we did not account for the diameter of the tube, so there was a large percent error. However, when we redid our calculations with an equation to take care of ___, the percent error was significantly lower. Also, there is a good chance that we misheard the loudest sounds because we were working as such a large group. To fix this, we could have had more people verifying that the sound was the loudest and ran more trials. This lab was extremely useful and has many real world applications because frequency and resonance are so important to music. If any of us decide to play an instrument, or even just listen to somebody else play, we will be able to understand and more fully appreciate the different sounds that we hear. = = =Lab: Transverse Standing Waves On a String= Sammy Caspert, John Chiavelli, and Gabby Leibowitz

Task A: John Chiavelli Task B: Gabby Leibowitz Task C: John Chiavelli Task D: Sammy Caspert

Objectives: What is the relationship between frequency and the tension of transverse waves traveling in a stretched string? What is the relationship between frequency and harmonic number? What is the relationship between frequency and wavelength?

Hypothesis: The relationship between frequency and the tension of transverse waves traveling in a stretched string will reflect a power fit. The relationship between frequency and harmonic number will be linear. The relationship between frequency and wavelength will also take the shape of a power fit.

Materials and Methods In this laboratory, we used an electrically-driven oscillator to generate standing waves of varying frequencies on a string. We attached the other end of the string to a pulley and table clamp, which held a hanging mass. The electronic balance was used to determine the mass of varying masses. In the first section of the lab, we measured frequency v. tension by changing the hanging mass, yet keeping the harmonic number constant. The second component of the lab entailed changing the harmonic number through frequency controls, which enabled us to analyze frequency v. harmonic number and wavelength.

Videos

Pictures

Sample Calculations

Percent Difference:

Velocities

Wavelengths

Fundamental Frequency

Percent Error:

Exponent of Frequency v Wavelength

Exponent of Frequency v Tension

Data

Analysis Discussion Questions:


 * 1) ** Calculate the tension T that would be required to produce the n=1 standing wave for the red braided string. **

If the string stretched significantly as the tension increased, the tension would increase drastically which would cause the wave speed to increase, as well, as a result of the direction relationship between in the two present in the equation. The wavelength would increase, as well, since the velocity is increasing and the frequency is neither increasing nor decreasing. Therefore, the harmonic number would ultimately change.
 * 1) ** What would be the effect if the string stretched significantly as the tension increased? How would that have affected the data? **

Every different type of string as a different kg/m ratio. As a result, it demonstrates different properties. A different string could require more tension or less tension/ more mass or less mass to produce a given number of nodes. If the string produces a different number of nodes than in the first place, the wavelength will be altered, ultimately, altering the accuracy and consistency of the experiment.
 * 1) ** What is the effect of the type of string on the amount of hanging mass needed to create a set number of nodes? Explain this. **

Changing the frequency, and only the frequency, will directly effect how many nodes will exist. As expressed in a graph, the frequency and the number of nodes have a linear, or direct, relationship. Therefore, increasing the frequency will increase the number of nodes. Decreasing the frequency will decrease the number of nodes.
 * 1) ** What is the effect of changing frequency on the number of nodes? **

Frequency directly affects the number of nodes in a standing wave, as these two elements have a linear relationship. Therefore, as frequency increases, the number of nodes increases, and vice versa. Therefore, velocity also affects the number of nodes since the velocity affects the frequency in the equation v=λf. In addition, the wavelength also directly affects the number of nodes when the velocity changes. However, this can only occur if frequency is constant. Assuming the length of the string will remain the same, harmonic number impacts the number of nodes as a result of the equation L=n*(1/2)(λ). If the harmonic number increases, the wavelength will decrease and the number of nodes will decrease. On the other hand, if the harmonic number decreases, the wavelength will increase and the number of nodes will increase. Essentially, you can say there is an indirect relationship between the harmonic number and number of nodes. However, if the length of the string does //not// stay the same, it will have an impact, as well. There is an indirect relationship between the number of nodes and the length of the string. A longer string will give you a longer wavelength and fewer nodes.
 * 1) ** What factors affect the number of nodes in a standing wave? **

**Conclusion** By doing this lab, we were able to prove our hypothesis that there is a power relationship between frequency and the tension of transverse. By plugging in our data, the graph fit the y=Ax^.5 fit. Our exponent was very similar at 0.5168 which is only a 3.36% percent error. We also hypothesized that the relationpship between frequency and harmonic number will be linear was correct with an equation of y=Ax. Lastly, our hypothesis that frequency and wavelength would have a power fit was wrong. Instead they are inversely releated with an equation of y=Ax^-1. Our lab had very little error as it should have. There was only a 2.58% percent error between the theoretical and experimental wavelengths. And there was a small 1.26% percent error for our velocities. The only major error in this lab was a 14.6% percent error in the fundamental frequency. While it is easier to see harmonics with more nodes from the human eye, we must have had a tough time looking at and determining the actual fundamental frequency. Considering we compared these two, this is where the mistake comes from. In general however, there were very few errors in this lab. It is not too hard to look at the string and find the the second, third, fourth, etc. harmonics in this lab. A potential error source could have come from friction in the string as it goes through the hook at the end of the table because it was not taken into account in the lab. Another is just human error in looking to find the perfect nodes. One way to solve this source of error would be to replace the white string with a a colored string or keep the white string and put a black background behind it. This would help out the eyes greatly.