How would you find the linear mass density of a string?
Our Procedure
Task - Find the linear mass density of a string
How we did it...
1. Make a written plan for what we were going to do.
2. Set up the string, oscillator, weight, and meter stick.
3. Hang a weight from the string and assume the force of gravity equals the force of tension.
4. Find the frequency by setting the oscillator to the second harmonic and looking at the frequency.
5. Measure the length of the string and since it is in second harmonic we know length equals the wavelength.
6. We calculated the velocity based on the frequency times the wavelength.
7. We used the velocity and the tension to find the linear mass density.
8. Then retests the experiment using a different frequency to confirm results.
How we did it...
1. Make a written plan for what we were going to do.
2. Set up the string, oscillator, weight, and meter stick.
3. Hang a weight from the string and assume the force of gravity equals the force of tension.
4. Find the frequency by setting the oscillator to the second harmonic and looking at the frequency.
5. Measure the length of the string and since it is in second harmonic we know length equals the wavelength.
6. We calculated the velocity based on the frequency times the wavelength.
7. We used the velocity and the tension to find the linear mass density.
8. Then retests the experiment using a different frequency to confirm results.
Our Equations
Our Lab Setup
How we found linear mass density?
First we found that the force of tension is equal to the force of gravity. Then we found out for the string to be in the second harmonic the frequency would have to be 27 Hz. Then we used the meter stick to measure the length of the string to 130 cm or 1.3 meters which knowing it is in the second harmonic is equal to the wavelength. After we multiplied the frequency by the wavelength to find the wave's velocity which was 35.1 m/s. Knowing the velocity and the tension the only missing variable was the linear mass density of the string so we used the velocity and the tension to find the linear mass density of the string is 0.002449 kg/m. Then we checked our results in the third harmonic with a different frequency and they matched.
Conclusion and evaluating procedures
Our conclusion was that the linear mass density of the string is 0.002449 kg/m. I have a high confidence in this result since when we checked our finding by doing another trial it came out the same. If you're smart enough to be reading a physics website you probably know a string is very small and thin so it does make sense that the linear mass density is also very small. The only uncertainty I have is with the measuring of the string and the harmonic. There could have been and error in measuring the string with having a couple of cm off and this would change the number we got at the end. Also I am not 100% sure the string was in the second harmonic, it did look that way and did have nodes and anti-nodes, but with the equipment we have we cannot be 100% certain. Overall I have a high confidence with our experiment because even though there was some room for error it was small.