Group3_6_ch11

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**Group 3 Period 2: Lerna, Katie, Brianna**

= **Mass on a Spring** = May 1, 2012

Katie: B Brianna: A  Lerna: C  Katie: D


 * Objectives:**
 * To directly determine the spring constant k of a spring by measuring the elongation of the spring for specific applied forces.
 * To indirectly determine the spring constant k from measurements of the variation of the period T of oscillation for different values of mass on the end of the spring.
 * **To compare the two values of spring constant k.**

Hypothesis: The greater the mass, the longer the period of oscillation will be. This is due to the equation for period of a mass on a spring.

Methods and Materials: The purpose of this lab was to find the spring constant. We were able to find this by first measuring the extension of the spring, which was hanging from a support attached to a rod on a base. There was a ruler on the rod which allowed us to measure how far the spring stretched. Then, we took a mass holder and attached it to the spring. We added different weights to the holder and recorded the change in distance as the force (weight) was increased. This data was put into a data table, as shown below, and that data was then graphed, and the slope of the line was equal to the spring constant. Next, to find the spring constant by looking at variations in the period, we let the holder become still at equilibrium. We pulled down the holder, released it, and recorded the time the holder took to oscillate ten times. Then, we would divide this time by 10 to get the time for one oscillation. We then added more mass to the holder and repeated the experiment. Then we made a period v. mass graph of the data.

Picture and Video:

media type="file" key="Movie on 2012-05-01 at 13.29.mov" width="300" height="300"

__Data__ Part I:

Part II:

Sample Calculations:

Finding the value of k constant for different masses:

Finding percent error:

Discussion Questions:

1. Do the data for the displacement of the spring versus the applied force indicate that the data for the spring constant is indeed constant for this range of forces?

The data does show that the data for the spring constant is constant for two reasons. One, the slope is positive meaning that it goes up by the same positive interval every time. If the slope had been negative, it would have meant that the different masses brought down the value of k. Two, the R2 value is 99% which means that the points practically form a line that goes through each one. This means that the points are going by the same interval.

2. Why is the time for more than one period measured?

The time for more than one period was measured due to the difficulty of observing the total oscillation for one period. Because of this, the time was measured in this lab for 10 periods because it was easier to spot each oscillation that way.

3. Discuss the agreement between the k values derived from the two graphs. Which is more accurate?

The k values that were achieved in this lab were very close and provided little percent error. However, the more accurate of the two k's would definitely be the k from the Force vs. Distance graph which had a value of 10. This is because unlike the other experiment where someone had to observe the oscillations closely, this experiment only required attaching more mass and measuring the x distance. This is more accurate because attaching more masses on a spring provides evident data that can be used for interpretation.

4. Generate the equations and the corresponding graphs for Position with respect to time Velocity with respect to time

Acceleration with respect to time

5. A spring constant k = 8.75 N/m. If the spring is displaced -0.150 m from its equilibrium position, what is the force that the spring exerts?



6. A massless spring has a spring constant of k = 7.85 N/m. A mass m = 0.425 kg is placed on the spring, and it is allowed to oscillate. What is the period T of oscillation? 7. We neglected to take into account the mass of the spring itself. Are your results any better when using the more accurate relationship (where //m// is the hanging mass and //ms// is the mass of the spring)? Redo graph #2 using, and explain these results.

The goal of this lab was to find the relationship between the period of oscillation and mass of an object. Our hypothesis that as the mass increases, the period of oscillation increases proved to be true.The first way that we tested our hypothesis was by using the law of conservation of energy by measuring the change in force and the change in distance from the springs equilibrium spot. The second way we tested the hypothesis was by using harmonic motion. For this, we needed to find the period and the mass. Once we were able to find these values, we compared them. In our results, we found that the spring force constant, //k//, was similar for the trials, which makes sense, considering that it is a constant and should not change. The theoretical was 10.3, while the actual was 9.95. While those are not exact, they only gave a percent error of 3.5% which is great. One source of error is human error. It was difficult to read the displacement of the spring sometimes, which could lead to an inaccurate reading, which would in turn throw off the results of the experiment, as well as the calculations. This could be fixed by reading the displacement using a ruler placed next to the spring instead of relying on the one attached to the stand. Additionally, two or three people could double-check it to make sure the value is right. Another possible source of error could come from timing the period. It was difficult to count ten periods (for which we divided the time by ten to get the time for a single period), and some people have better reaction time than others. It is possible that the time was thrown off, which would again affect the data and calculations. We could have used a motion detector to make it more exact. This can be applied to real-life as well. Consider a bungee-jumper. When he jumps off the platform, he will accelerate downwards, and then because of the springy properties of bungees, he will begin to oscillate. The calculations above could be applied to this situation to find the spring force constant of the bungee, or even to find the maximum weight that the bungee can hold.
 * Conclusion**

= Standing Waves Lab = May 8, 2012

Objective: What is the relationship between Frequency and tension of the transverse waves traveling in a stretched string? What is the relationship between frequency and harmonic number? What is the relationship between frequency and wavelength? *this is inversely related

Hypothesis: -As tension increases, the frequency will decrease. -As the frequency increases in multiples of its natural resonant frequency, the number of antinodes will increase at a rate of 1 less than that multiple. This means that if natural resonant frequency is multiplied by 5, there will be 4 antinodes. -Because velocity is increasing and the wavelength is constant (v=wavelength x frequency) the frequency will increase. As the frequency increases the wavelength would get smaller because their would be more interference creating more nodes.

First, we attached the string to a generator. This generator is clamped to the table, and the string is stretched across the table and through the pulley. To keep the string taught, we attached a set mass to the end of the string. We turned on the generator and adjusted it until it was at its maximum amplitude. Next we moved the dials until the string was vibrating at its maximum amplitude for that specific amount of antinodes. Each time, we increased the number of antinodes, we had to adjust the dials until we found the maximum amplitude. We repeated step three in order to find the frequency for a different amount of antinodes.This process was then repeated until enough data was collected to form a conclusion.
 * Methods and Materials:**

Data:

Sample Calcs:

Calculating Tension: Calculating Velocity:

Discussion Questions: 1. Calculate the tension T that would be required to produce the n = 1 standing wave for the red braided string.



2. What would be the effect if the string stretched significantly as the tension increased? How would that have affected the data?

If the string stretched significantly as the the tension increased, it would have raised the frequency just as significantly. As the data shows, an increase in tension causes the frequency to increase because it is harder to reach the same number of nodes as before. If this had happened, it would have made the slope on the Frequency vs. Tension graph much steeper.

3. What is the effect of the type of string on the amount of hanging mass needed to create a set number of nodes? Explain this.

4. What is the effect of changing frequency on the number of nodes?

The effect of changing frequency on the number of nodes makes the amplitude on each node bigger. This makes it easier to see, which allows for a more accurate reading of each frequency vs number of nodes. In addition, by increasing frequency but keeping the mass the same, the number of nodes also increases.

5. What factors affect the number of nodes in a standing wave?

The mass and frequency affect the number of nodes. If the mass stays the same, but frequency is increased, the number of nodes will also increase. If the mass increases, the frequency will have to increase but the number of nodes will stay the same.

= Speed of Sound = May 15, 2012

Lerna: B Katie: A Lerna: C Katie: D

Objectives:


 * 1) Determine several effective lengths of the closed tube at which resonance occurs for a frequency.
 * 2) Determine several effective lengths of the open tube at which resonance occurs for a frequency.
 * 3) Determine the speed of sound from the measured wavelengths and known frequency of the sound.

Hypothesis:
 * 1) For a closed tube, the lengths must be shorter in intervals.
 * 2) For an open tube, the lengths must be larger in intervals.
 * 3) The speed of sound would be close to 343.2 metres per second because this is the norm for when there is dry air at 20 degrees.

Methods and Procedure: First, gather all necessary materials and circle around the table to work with class. The setup includes attaching a speaker to the frequency adjuster and putting the closed end of a tube near the speaker. Next, pull out the inner tube and listen for when the pitch of the frequency at 500 Hz is loudest. Measure this length. When completed getting the lengths for the closed end, flip the tube so that the open end is near the speaker. Repeat.

Picture:

Data tables:

Graph:

Sample Calcs:

Speed of Sound:

Length for an open tube:

Length for a closed tube:

Calculating wavelength:

Percent Error for open tube:

Percent error for closed tube:

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Discussion Questions:

<span style="font-family: 'Times New Roman',Times,serif; font-size: 14px; line-height: 21px;">1. What is the meaning of the slope of the graph for the open tube? For the closed tube?

The slope for both graphs is a positive 1 which means that all of the points lined up perfectly. The positive number tells us that for as the harmonic number increased so did the length. It also means that the intervals were almost exactly the same when calculating the lengths for the tube when pulled out. This tells us that we did a good job in measuring the lengths and listening to highest pitch.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 14px; line-height: 21px;">2. Why was the length of the tube always smaller than expected?

There are certain areas that could have caused differences in our theoretical and experimental values. One source could have been from not picking the exact length at which the pitch was highest.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 14px; line-height: 21px;"> 3. Suppose that the temperature had been 10 ˚C higher than the value measured for the room temperature. How much would that have changed the measured value of L?

For the closed tube, the value at 27˚C for L had been .174. If the temperature had been 37˚C the value of L would have increased due to the equation: L = n1/4λ. This is also true for an open tube due to the equation: L=n1/2λ.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 14px; line-height: 21px;"> 4. Draw a figure showing the fifth resonance in a tube closed at one end. Show also how the length of the tube L5,is related to the wavelength, λ.

<><>< This drawing shows that the left side is closed, while the right side is open. Each "arrow" represents one fourth of a wavelength. Due to the equation, we are able to know to draw it like this. Since it is the fifth harmonic number we know to draw (5/4) of a wavelength and since each piece is one fourth we know that this is the correct drawing.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 14px; line-height: 21px;"> 5. Draw a figure showing the fifth resonance in a tube open at one end. Show also how the length of the tube L5,is related to the wavelength, λ.

><><><><>< This shows openings at both ends, which means the tube is open. From the equation we are able to see that each piece is 1/2 of a wavelength. Since we are drawing the 5 harmonic number we know to have 5/2 wavelengths.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 14px; line-height: 21px;"> 6. What does this have to do with making music?

This concept is extremely relevant to music. Musicians are able to change the length of the string, on a guitar, or a piano in order to change the sound. By changing this, the wavelength would also change, which would make a different sound due to different frequencies. This is the reason that there are different notes that can be played, and these different variations allow for music to be made.

To evaluate our results for this lab, we had to find two different percent errors. The first percent error is for the length of the open tube. This percent error was 53.59% which is a significant amount and signifies that something went wrong. The next percent error is for the length of the closed tube, which is 18% which is not amazing, but at the same time, it is not awful either. This lab had multiple possible sources of error. The first possible source of error is that each person heard the tube differently, based on proximity to the tube or a person's sense of hearing. Because of this one person could think that the noise was loudest at one point, while others could have disagreed, meaning that we didn't necessarily get the correct lengths for the actual most intense sound- it was all based on perception. In addition, the tube was moved several times during the experiment, which would change the lengths that we recorded, thus giving inconsistent results, which would effect the calculations. In order to fix these sources of error, we could have used a sound meter to hear the actual volume of the tube. Also, this meter would have to be placed at the same spot during each test, because one complication was that based on the positioning of people in the room, as they heard different loudnesses for the tube. This would have kept the results more consistent. Also, we could have made sure that the tube was fixed to the table so that we avoided changing the length inadvertantly, which also effected our results. This lab has many practical, real life applications. One of the most relevant examples is the role that resonance plays in music. This can be applied to a variety of instruments. For example,in a reed instrument, blowing on the mouthpiece causes the reed to vibrate, creating a sound. With wind instruments, the musician blows into a mouthpiece, and the vibrations created from this push the air into the instrument's body, then when a specific valve is closed or opened, the pitch of the sound changes.String instruments rely on the body of the instrument to amplify the string's vibration, allowing for a wide variety in the range of pitches created by the instrument. The strings can be tightened to change the pitch. Also, the thickness of the string can alter the natural frequency, which changes the sound produced. The vibrations can be amplified by an air hole in the instrument, like in an acoustic guitar.
 * Conclusion:**