Goal of Lab - Find the linear density of the string
Plan
To find the linear density (μ), we need to know the force of tension acting upon the string, the wavelength, and the frequency. The formulas v=√(Force of tension/linear density) and v=wavelength * frequency can be manipulated into μ=Ft/(λ*ƒ)^2. The force of tension will be the masses weight in kg * 9.8 and the frequency will be given by the oscillator. This means that wavelength is the only thing that needs to be calculated. Wavelength can be calculated by measuring the length of the string in the part that will be oscillating and then dividing by the amount of that is one wave. In our lab we had our string oscillating with the third harmonic as its fundamental frequency. This means that one wave was 2 thirds of the length from our oscillator to pulley.
How we Calculated it
In order to do find the linear density, we needed to first measure the length of the string from the oscillator to the pulley which was 1.16 m. Then, we put the oscillator to a known frequency of 31 Hz in order to create a wave with a node at the pulley. Then using the measurement of the string and position of nodes, we found the wavelength of the string to be 0.773 m. Using the wavelength and the frequency, we found that the wave speed was 24.0 m/s. Using these values as well as the 1.96 N tension force on the string from the hanging mass, I found the linear density to be 0.00341 kg/m.
Conclusion
Based on our data, I am confident that the linear density that we found is at least very close to the real linear density of the string. We only did it for one mass, but it still most likely is very close to the real value. It makes sense that the linear density is very low because the string weighs very little and is very long.
Evaluating Procedures
One source of uncertainty is that we only did one trial and with one mass. This makes our calculations more uncertain, but I still believe our value is close to the correct value. Another possible source of uncertainty is the fact that it may not have been exactly the third harmonic which would have messed up our value for wavelength. Overall, I am somewhat confidant in our results, but we could have done more to ensure the accuracy of them.