9/7/2012
The purpose of the experiment is to gin know ledge and understanding of standing waves driven by an external force. Resonant conditions for standing waves on a sting will be investigated.
In the lab, we need: a Pasco Variable Frequency Wave Driver with string, a Pasco Student Function Generator, 50g weight hanger and slotted weight set, short rod, pendulum clamp, pulley, and meter stick.
First, we measure the mass and legth of the string and record these values into an excel spreadsheet. And we can calculate the μ.
Then we assemble all equipment like shown below.
For case 1, we measure at least 10 harmonics, recording oscillation frequency, the number of nodes, and the total length of the string that participates in the oscillation. Determine the distance between the nodes, and the wavelength of the oscillation.
We can calculate the slope of the line which should be equal to the wave speed. So wave speed we determined from slope is 41.915m/s.
Compare to wave speed obtained using equation show as below
It is so closed. But it still exists some errors.
Repeat steps for case 2.
Wave speed we got from slope is 21.672m/s. Using equation, we got 20.338m/s. They are still closed.
I found that wavelength is equal to 2L/(n-1), n is the number of nodes from each runs.
The ratio of wave speeds for case 1 compared to 2 is almost equal to the ratio of the predicted wave speeds.
From the form we got for case 1, we found that fn=nf1. (n=the number of harmonic)
The ratio of the frequency of the second harmonic for case1 compared to case2 is equal to third harmonic and fourth fifth. There is a pattern here show below.
The slope we got from graph is 1.9112 which is closed to 2.0.
Summary: We cant make the actual data and theoretical data as the same because there exists some errors when we measured the length of the wire. And in our process to make the harmonics, it is so hard to make a big amplitude.It is approximate number. And in case 2, the T is smaller. So when we turn up the frequency of generator, the node above the wave driver keeps moving. It is so hard to find the actual position. But anyway, we only got a small error from this experiment which is smaller than 5%. That is great. Besides, we find that the λn=2L/n (n is the number of harmonic, also equal to the number of nodes minus one) is true.And the velocity we measure is equal to that we calculate from equation which show as above from the picture.
For case 1, we measure at least 10 harmonics, recording oscillation frequency, the number of nodes, and the total length of the string that participates in the oscillation. Determine the distance between the nodes, and the wavelength of the oscillation.
Then we make a graphic. X-1/λ;Y-f
Compare to wave speed obtained using equation show as below
Repeat steps for case 2.
I found that wavelength is equal to 2L/(n-1), n is the number of nodes from each runs.
From the form we got for case 1, we found that fn=nf1. (n=the number of harmonic)
The slope we got from graph is 1.9112 which is closed to 2.0.
Summary: We cant make the actual data and theoretical data as the same because there exists some errors when we measured the length of the wire. And in our process to make the harmonics, it is so hard to make a big amplitude.It is approximate number. And in case 2, the T is smaller. So when we turn up the frequency of generator, the node above the wave driver keeps moving. It is so hard to find the actual position. But anyway, we only got a small error from this experiment which is smaller than 5%. That is great. Besides, we find that the λn=2L/n (n is the number of harmonic, also equal to the number of nodes minus one) is true.And the velocity we measure is equal to that we calculate from equation which show as above from the picture.
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