Relationship between wavelength and frequency

Relationship between wavelength and frequency:

Introduction:
The purpose of this experiment is to determine the relationship between frequency and wavelength by measuring the number of waves to pass through a spring. In this experiment, we will use a long spring with a length of 1.2m. We will wiggling the sping to creave 10 waves to and record the time.

 

Conclusion:

There is an inversely proportional relationship between wavelength and frequency. When frequency is decreasing; wavelength has increased. The source of error contributed in this experiment can be the inaccurate measurement of the length of spring, and the time needed for 10 waves to pass through the point.

Experiment 11: Measuring a huaman hair

Experiment 11: Measuring a  huaman hair
Introduction:
The purpose of this experiment is to accurately measure the thickness of a human hair by using laser or light interference. First, we taped a human hair on to a 3x5 card with hold, than we pointed a laser through the hole. Finally, we used the image to be projected on to the white board, and measure the distance between the board, and the distance between the middle of the zero overtone and third.  We used equation d=λL/y to get the theoretical value in order to compare with the experimental value by using a micrometer.

Experimental Method: (micrometer)
d= 89.2 μm

Theoretical Method:
d=λL/y
  =(632.8nm) (0.935m)/(0.075m)
  = 77 μm

Conclusion:
By compare the experimental and theoretical value, the percent of error is pretty samll and these values were within the uncertainties range. By we still could find a lot of mistakes that can be made during the processes of the experiment. Such as measuring the distance between the two first order minima due to the lack of precision in equipment.

 

 

 

Experiment 9: Concave and Convex Mirrors

Experiment 9: Concave and Convex Mirrors


Introduction:
In this experiment, we are to show the different effects of a convex mirror and a concave mirror. For a convex mirror, the image appears to be smaller than the object itself, it does however stays upright, and is located about the same position inside and outside the mirror. Also, when the object is moved closer to the mirror the image becomes bigger, and when it is moved further away the image gets smaller.

Part II

For concave mirrors, the image that appears in the mirror is larger, but it is inverted, and relative to the position of the mirror the object well seem closer. When moving the object closer to the mirror makes the image smaller, and upright and as for moving further away the image grows to infinite

Conclusion:

In this experiment we can clearly see how convex and concave mirrors would work on an object being placed in front of them. We also identified how we can see the image in the mirror by drawing lines to where the focal point, the lens of the mirror and the center of the sphere.  

Marshmallows Lab Quiz

Marshmallows Lab Quiz

Introduction:

The purpose of this experiment is to study the electromagnetic waves by microwave marshmallows and water. We microwaved some marshmallows for approximately 11s. The standing wave on the marshmallows is about 12cm±1cm long from antinode to antinode. Then we microwaved a cup of 100g of water at temperature of 20oC for 10s.  The temperature of the cup of water increases from 20 oC to 57 oC. The measurment of the microwave is 35cm x 35cm x 23cm. Based on these information, we have to determine the frequency, the dimensions of the waves, the total energy content of the cavity, the number of photons per second oscillating in the microwave, and the pressure these photons exert on the side of the microwave.

 

 

Questions:

1.  f = v/λ

       = (3*10^8) /0.12

       = 2.5 *10 ^9 HZ

2. The smallest dimensions of the microwave must be 24 cm x 24 cm x 12 cm. This is assuming that the wave travels along the diagonal of the microwave where the diagonal is 12 cm.

3.  Q = mc (⊿T)

         = (0.1) (4.184)* (57 ^oC - 20 ^oC )

         = 15481 J 

4. E = (hc)/λ

       = (6.626*10^-34)(3*10^8)/ 0.24

       = 8.28 *10^25 J/photons

    Photons/Time = Q/E

                            = 15481 / (8.28*10^-25)

                            = 6.23 * 10^26 photons/s

5. P = Q/T

       = 15481J/ 30s

       = 515.5 W

    

    p = P/Ac

       = 515.5/((0.35*0.35)*(3*10^8))

       = 2.13 *10^-5 N/m

Experiment 5: Introduction of Sound

Experiment 5: Introduction to Sound

Introudction:
The purpose of this experiment is to learn the properties of sound waves by using LabPro and microphone to make recordings of "AAAA" sound. We will obtain sound wave graphs and analyze the graphs to understand the properties of sound waves.

1 "AAA" Sound
a. Yes, this is a periodic wave. From the graph, we can see the wave has repeating pattern.

b. About 2 waves are shown in the sample. One complete wave is from one high peak to the second high peak. In the graph there are three peaks, so there are two waves.

c. The probe collected data as fast as the frames separated on TV.

d. The period of these waves should be 0.01s/wave.

e. The frequency should be 1/T=1/0.01=100Hz

f. lambda=v/f=360/100=3.6m. This can be the length of a table in the classroom.

g. w=2pi*f=2*3.14*100=628rad/s
     A=v/w=360/628=0.571m

h. The number of waves would change and be increased. The time it takes to collect the data will increase too. Period, frequency, wavelength, and amplitude wont  change.

 2. The period is much shorter than the previous more.

Experiment 4: Standing Waves

Experiment 4: Standing Waves

Introduction:
The purpose of this experiment is determine a relationship between wavelength and frequency in order to understanding the standing waves driven by an external force.
We are going to measure and compare different wavelength of waves on a single string by changing the frequency of the wave.The weight and length of the string to be 3.08 g and 140 cm; also the hanging mass is 199.8g. We had two cases for this lab, by changing the amount of tension we give to the string we should be able to change the wavelength and thus the frequency of the string.  We repeated this measurement multiple times to get an idea of the uncertainties involved.

Calculations & Graphs:

Case 1
Osciallation Frequency (Hz)	16.5	32.5	45.6	56.7	74.6	87.4
Nodes	2	3	4	5	6	7
Wave Length (m)	1.4	0.67	0.45	0.37	0.26	0.21
1/λ	0.71	1.49	2.22	2.70	3.85	4.76
Case 2
Osciallation Frequency	21.8	29.5
Nodes	4	5
Wave Length	0.46	28

Both cases' frequencies followed the patter of f = vn/2L where v is the wave velocity, n is the number of antinode, and L is the length of the string. As we expected, when the wave lengths are the same, the lower velocity requires lover frequency inorder to reach certain resonance frequency. On the other hand, the higher the velocity requires higher frequency to reach the resonance frequency.

By looking at the graph, it is clear that there is a linear relationship between frequency and wavelength. As the wavelength is increased, the frequency correspondingly decreases. The ratio of velocities between case 1 is about 1.48, which is close to radical 2 as we expected. However, we cannot get enough data for case 2 since the tension on the string is too small.

Conclusion:

The uncertainties relating to the wavelength is due to our ability to correctly measure the spring using a large 2-meter stick, and to correctly hold that measured length during that phase of the experiment.  Finally, the uncertainty related to the frequency is naturally derived from the uncertainties related to the time.

Experiment 2: Fluid Dynamics

Experiment 2: Fluid Dynamics

Introduction:
The purpose of this experiment is to apply Bernoulli equation to determine the diameter of the hole on the bottom of the bucket.

First, we began the experiment by filling a large bucket with water and then allowed water to flow out of a small hole drilled near the bottom of the bucket. We took 6 trials and record the time took for a 16 ounces of water to exit from the bottom of the bucket. All measurements are in seconds and have an uncertainty of +/- 0.1s.

	1st run	2nd run	3rd run	4th run	5th run	6th run
Time to empty(tactual)	29.1 +/- 0.1s	28.9 +/- 0.1s	28.8 +/- 0.1s	29.2 +/- 0.1s	29.3 +/- 0.1s	28.9 +/- 0.1s
Volume of water before (inch)	3 1/6	3 1/8	3  1/16	3	3	3
Volume fo water after (inch)	2 1/2	2 1/2	2  7/16	2  7/16	2  7/16	2  7/16
Volume emptied (V): 16 ounces = 1.67 × 102 ft3
Area of drain hole (A): πr2 = 4.144 × 10 -4 ft 2
Acceleration due to gravity (g) : 32 ft/s2
Height of water (h): 3 inches = 0.25 ft
ttheoretical: V / A√2gh = (1.601 ×10-2)/ (4.144 × 10 -4)(√2(32)(5.58)) = 25.5 s
% error	1st run	2nd run	3rd run	4th run	5th run	6th run
	14.90%	13.30%	12.94%	14.51%	14.90%	13.33%
taverage : 29.03 s
A theoretical: V / t√2gh = (1.601 ×10-2)/ (29.03)(√2(32)(5.58)) = 0.000292 ft2
Calculated Diameter: 0.588 cm
Given Diameter: 0.700 cm
% error: 16 %

Conclusion:
Compare the experimental value and the theoretical value, we have 16 % error. The 16 % error are due to several uncertainties and unaccounted human errors. First one is during the experiment, when we use stopwatch to catch the time until the beaker reach 16 ounces, there have some time delay. Second, the hole was made with a drill and never properly finished, this would create variations in stream diameter due to roughness around the hole.