Experiment 9: Concave and Convex Mirrors

9/25/2012

The purpose of this experiment is discovering the image formed by both a convex and concave mirror.

For this experiment, we need a convex mirror, concave mirror, object(marker), ruler and worksheets.

First, we measure the height of the marker which is 11.95+/-0.05cm.

Then we place an object in front of a convex mirror. 

The image appears smaller than the object. The image is upright. The image is in front of object and seem further in the mirror. When we move the object closer to the mirror. The image is changing larger till it is as same size as the object.

When we move the object further from the mirror than it was in step 1, we find that the image is changing smaller.

 Then we measure the distance between object and mirror which is 50.00+/-0.1cm, and the height of image is 3.9+/-0.1cm. Then we can calculate the magnification is hi/h0=0.326+/-0.01, then due to the relationship between distance and height, we can find the distance between image and mirror is 16.32+/-0.52 cm.

In part B, we place the marker in front of a concave mirror.

The image appears bigger than the size of object. The image is upright. The image is in front of the object and it is closer in mirror. When move the object until it is close to the mirror, the image is changing smaller till it is as same as the size of the object. And it is upright. When we move the object much further from the mirror than it was in step1, we find that the image is changing bigger first then become smaller and smaller and from upright to inverted.

We measure the distance between object and mirror is 89.05+/-0.05cm. And the height of image is 24+/-0.1cm. Then we can calculate the magnification is 2+/-0.02cm. Then we also can calculate the distance between image and mirror is 178.85+/-1.6cm.

Expriment 7: Introduction to Reflection and Refraction

9/22/2012

The purpose of the experiment is measure the incident angle and the refractive angle and find the relationship between them.

Equipment: Light box, semicircular plastic or glass prism, circular protractor, pasco optical kit or hardtl disk.

The angle of incidence for the light ray at the flat surface is theta1, the angle of refraction at the flat surface is theta2. When light ray leaves the plastic piece at the curved edge and goes in to the air, it has no refraction between the cured edge and air; just a straight light ray passing through it. This experiment is from lower density to higher density.

Set up the equipment shown as above and begin measure it. Let make theta1 begin from 5 degree to 70 degree.

Then we can collect the measurement and make a graph which is linear. We found that the slope is 0.6676. n1*sin(theta1)=n2*sin(theta2) We know that n1 is the index of air which is 1. so the 1/n2=sin(theta2)/sin(theta1)=0.667 then we can calculate the n2 which is index of glass is 1.49.

Then we change the the glass direction. And set up the equipment shown below.

 When the light ray through the first curved surface of the semicircular prism, the light ray doesn't have any changes. Because the angle of incidence is ever zero. When it strikes the flat surface, there is refractive angle. This experiment is from greater density to one of lower density.
Then we begin measure the angle of refraction and make a graph.

From the graph, we know we can complete all 10 trails, because when the incident angle is over 45degree. There has no refraction.

The slope of the graph is 1.46. n1*sin(theta1)=n2*sin(theta2) n2 is the index of air which is 1. So n1=sin(theta2)/sin(theta1) n1 is the index of glass which is 1.46.
Summary: Ok, now we have two slope of the graph which one of them is 0.667 and other is 1.46. Is it incorrect??? No for sure. Because they are different cases, one is from lower density to higher density; other is opposite. Although we used the same equation n1*sin(theta1)=n2*sin(theta2), but because the situation is different, so the n1, n2 will be changed. n2 is the index of glass from part one; n1 is the index of glass from part two. So the result we got 0.667 is closed to 1/1.46. Of course, we have some errors when we measure the refractive angle because the light is so wide not just like a small line.

Experiment 6: Speed of Sound

9/13/2012

The purpose of this experiment is measuring the speed of sound waves which are reflected back from the closed end of the tube.We measure the time for the waves to go down to the end of the tube and comeback again.

Apparatus: Logger Pro software, microphone, LabPro, computer, long hollow tube closed at one end, two-meter meterstick.

First, we measure the inside length of the tube which is 1.30+/-0.01m, then assemble the equipment. Put the microphone close to the end of the open tube. Before we make a snap by two fingers, we click collect on computer. In process, we did it three times. So we got three different graph for this sound and reflected sound.

Then take the average of them, which t=7.68*10^3+/-1.49*10^-4 s.

Use the formula v=s/t, which s=2L.

The speed of sound we measure is 338.5+/-9.4m/s

Then we use the speed of sound in air at room temperature T can be calculated from v=331+0.6T. As the result, we got v=331+0.6*18=341.8m/s The error between my measured value and the actual value is (341.8-338.5)/341.8=0.97%. The error is small. It is important for the sound we use to be as brief as possible because it is easy to find the time from begin to reflect and it can easy to reduce the error. For inaccuracies, i think we can't make sure the microphone standing on the same place of the edge of the tube. Secondly, i think it is not quiet in the classroom. But anyway, compare to snap, noisy cant have too much influences when we measure.Third, it is a little bit hard to find the accurate time from the graph.

Experiment 5: Introduction to Sound

9/11/2012

The purpose of this lab is compare different sound waves(number of waves, wavelength, frequency, amplitude)

  In this experiment, we need a microphone and LabPro, and connect to a computer. Set up the sensor through the Experiment tab. Like shown as below.

   First, say "AAA...."smoothly in to the microphone and hit Collect. Once we get a graph that we think is quality, label it #1.

   Then have someone else in my group say "AAA..." in to the microphone. Then compare to each other.Label it #2

The 1st student voice is louder, so frequency and amplitude are not same.

Then collect data for a tuning fork by striking it on a soft object. Label it #3; and also use the same tuning fork to collect data for a sound that is not as loud, label it #4.Compare to the human voice and them each other.

As we can see, they have different frequency and wavelength. Compare to human voice. The frequency is bigger than human voice, but the amplitude is smaller than human voice. Hitting loud by fork from #3, the frequency is bigger than the lower sound, but the amplitude is smaller than the lower sound. 

Experiment 4: Standing Waves

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.

Then we make a graphic. X-1/λ;Y-f

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.

Experiment 2: Fluid Dynamics

9/6/2012

The purpose of the experiment is finding the time to empty a given volume by measurement and calculation from equation.

In this lab, we need a bucket with a small hole drilled in the bottom,bottle with volume marks,ruler, and stop watch.

Fill water into bucket to height h, and use a ruler to measure the height.

h=15cm(In case, to stop water flowing out, we use a piece of tape)

Then we set up the equipment like shown as below.

Second step is that remove the stopper and start the stopwatch. When volume in the small bottle reaches 100ml, stop the stopwatch. Record the time elapsed. Repeat for a total of six tests.

The data is t1=5.83s; t2=6.35s; t3=6.43s; t4=6.23s; t5=6.04s; t6=6.30s

So we take the average of these data which is 6.2s

Follow step is measure the diameter of the hole so that we can figure out the area of drain hole.

We measured the diameter as 5.8mm so the area of drain hole is 0.26cm^2 (A=pi*r^2)

Then we plug in all the data we measured into the equation t show as below

Then t=2.2s(we got this t from theoretical equation)

The theoretical time and actual time are totally different. For the theoretical time, we still used the data we measured like r,v,h. So there must be existing errors. 

Assume the diameter we measured isn't accurate. Then we rearrange the time to drain equation to solve for the diameter of the hole. Then we got the calculated diameter is 3.5mm. 

The given diameter and calculated diameter still need our measurement, so when we calculate the error we only can use the equation show as below.

We plug in x1=5.8; x2=3.5, then we got the error=49.5%

Summary: Theoretically, if we have no error when we measure the data of it h, v, d, we should get the theoretical time as same as the actual time. But error cant be ignored because when we calculated time of empty, we got some trouble from catching the water by the beaker. And when it reaches 100ml, we stop cant stop the stopwatch at time for sure.