Task: Find the linear mass density of the string
Our plan: In order to find μ, we need to find the tension and velocity. To get the velocity, we can measure the wavelength and the frequency. To find the tension, we will hang a mass on the string and when the weight is still, the forces are balanced and the tension is equal to the force of gravity.
Steps
Our plan: In order to find μ, we need to find the tension and velocity. To get the velocity, we can measure the wavelength and the frequency. To find the tension, we will hang a mass on the string and when the weight is still, the forces are balanced and the tension is equal to the force of gravity.
Steps
- Find the tension of the string. We found this by hanging a mass on the pulley and assuming that the force of gravity was equal to the force of tension (when the mass is still, the forces are balanced)
- In order to find the velocity, we have to find the wavelength and the frequency
- Next, we adjusted the oscillator to find the second harmonic
- Then we know the frequency based on the oscillator, and the wavelength is the length of the string because it is the second harmonic.
- We measured the length of the string to find the wavelength
- We used this to calculate the velocity of the string based on the equation v = λf
- With this value along with the tension force, we can solve for the linear mass density.
To the right are my calculations for this lab. First, I found the tension force. I wrote down the frequency that we found the second harmonic at, and then the length of the string / the wavelength. After finding the velocity, I showed how to solve for μ based on the velocity equation, and then I plugged in the values. I repeated this for a different mass value, and found a similar linear mass density. Finally, I did some math with units to determine the final units, and I used the conversion 1 N = 1 kg m/s^2. I determined that the units are kg/m, and I averaged the two values of μ that we found to come up with a more exact answer. |
Conclusion- Based on our data, we can be confident that we found the linear mass density or a pretty accurate value for it. Solely looking at the number value, it makes sense to me that it is a very small number because a string weighs very little but can have a lot of length. Since we repeated our method for two different masses and still found similar answers, an average of these to answers for μ is probably accurate.
Evaluating Procedures- One source of uncertainty is whether or not we were truly at the second harmonic. It looked like there were clearly defined nodes and antinodes on the standing wave, but we could have been off by a couple of Hz, which would have impacted our calculation for the velocity of the wave. Another source of uncertainty is that we didn't take into account the friction on the pulley, which would make the tension force a little bit less than the force of gravity.
Improving the Investigation- If there had been time in class, we should have tested our linear mass density value with more masses. I also think we could have changed the harmonic to make sure that the linear mass density stayed the same with this as well.
Evaluating Procedures- One source of uncertainty is whether or not we were truly at the second harmonic. It looked like there were clearly defined nodes and antinodes on the standing wave, but we could have been off by a couple of Hz, which would have impacted our calculation for the velocity of the wave. Another source of uncertainty is that we didn't take into account the friction on the pulley, which would make the tension force a little bit less than the force of gravity.
Improving the Investigation- If there had been time in class, we should have tested our linear mass density value with more masses. I also think we could have changed the harmonic to make sure that the linear mass density stayed the same with this as well.