Group2_6_ch11

=Lab: Speed of Sound-Resonance Tube=


 * 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.

-We can use closed and open tubes to find the lengths at which resonance occurs at a certain frequency (500 Hz). We think that if the length increases, the resonance will increase.
 * Hypothesis:**

First, attach the frequency generator to a speaker and set the frequency to 500 Hz. Then set the amplitude to a comfortable setting. Make sure to close off one end of the tube with a cap and then find it’s loudest point by pulling the tube out. Check the measurement given on the tap attached to the tube. Do this multiple times until the tube runs out of length. Then repeat this cycle on the tube but without the cap on so that both ends are open. Make sure that the thermometer is used to check the temperature for future calculations.
 * Methods and Materials:**

Closed Tube:
 * Data:**

Open Tube:


 * Graph:**


 * Picture:**

Open tube^ Closed tube^
 * Sample Calculations:**


 * Analysis:**

Open tube: For this kind of tube the slope is equal to one half of the wavelength. L is being graphed on the y axis, while n (harmonic number) is being graphed on the x axis. The equation is L=n(1/2)*wavelength and the equation for the line is y=mx. Through these equations we are able to see that the slope of the line is equal to half the wavelength. Closed tube: For this kind of tube the slop is equation to one fourth of the wavelength. We are able to see this by looking at the equations. Both the length of the string and the harmonic number is being graphed on the line which just leaves (1/4) wavelength, which is equal to the slope. λ The length of the tube is always smaller than expected because it is hard to hear when it is at the exact amplitude/ highest volume. Also how we calculated our values were not valid in real life therefore some of our values were less than they should have been. is directly related to the velocity. If the temperature increases than the velocity increases. Since the velocity directly affets the wavelength then the wavelength would increase. The temperature of the room was 27 degrees celsius. We see that this is true through the equation that they are directly proportional. <><>< This shows that the left is closed, while the right side is open. Each arrow is a fourth of a wave and 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.
 * Discussion Questions:**
 * 1) What is the meaning of the slope of the graph for the open tube? For the closed tube?
 * 1) Why was the length of the tube always smaller than expected?
 * 1) 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?
 * 1) 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 shows openings at two ends. 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. Playing a instrument and it for it to make sound has to do with all of these concepts. Musicians are able to change the length of the string, on a guitar, in order to change the sound. By changing this the wavelength would change which would there for make a different sound due to different frequencies. These variations allow for music to be made.
 * 1) 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.
 * 1) What does this have to do with making music?

For this lab, we found two different percent errors. The first is the percent error of the length of the open tube. This percent error was 5.6 percent, which is modest, and not problematic. The next percent error is for the length of the closed tube, which is 4.48 percent. This amount is well under a high percent.
 * Conclusion:**

This lab had several sources of error. The first source of error is that each person heard the tube differently, based on location or sense of hearing. This mean that while one person thought the noise was loudest at one point, others could have disagreed, meaning that we didn't necessarily get the correct lengths for the actual most intense sound. Also, the tube was moved several times during the experiment, which would change the lengths that we recorded, thus giving inconsistent results. To fix these sources of error, we would have to have 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, they heard different loudnesses for the tube. Also, the tube should be fixed to the table so that it can't be moved during testing.

This lab has many practical, real life roles. One specific example is the role of resonance in music, for a variety of instruments. In the case of a wind instrument, the player blows into a mouthpiece. The vibrations created from the mouthpiece push the air into the body of the instrument, and when a specific valve is closed or opened, changes the pitch of the sound. For an instrument with a reed, blowing on the mouthpiece causes the reed to vibrate, and in the case of an instrument with a metal mouthpiece, the player vibrates their lips in a specific way to cause vibrations/sound. The natural frequency of the reed or metal mouthpiece is essential in the tone of the instrument. Also, string instruments rely on the body (be it wood or metal) to amplify the vibration of the string, which allows for a wide range of pitches. Strings are held tightly onto the body of the instrument, thus changing the pitch of each string. Also, strings can be thicker or thinner, which would change their natural frequency. The vibrations are brought through the body of the instrument, and are amplified through the body or loudly amplified through sound holes (ex: acoustic guitar).

=Lab: Transverse Standing Waves on a String= toc Remzi, Bennet, Rachel, Lindsay

-What is the relationship between Frequency and the tension of transverse waves traveling in a stretched string? -What is the relationship between frequency and harmonic number? -What is the relationship between frequency and wavelength?
 * Objectives:**

-As tension increases, frequency will decrease. -Relationship between frequency and harmonic number (n) - 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. For example, if the natural resonant frequency is multiplied by 3, there will be 2 antinodes. -Because velocity is increasing and the wavelength is constant (v=wavelength x f) the frequency will increase. As the frequency increases the wavelength would get smaller because their would be more interference creating more nodes.
 * Hypothesis:**

We attached the string to a generator that is clamped to the table and sent the string through the pulley and attached a set mass to the end of the string. We turned on the generator and made it at its maximum amplitude. Next we moved the dials until the string was vibrating at its maximum amplitude for that amount of antinodes. We Repeat step three but find the frequency for a different amount of antinodes. We repeated the previous step until we got enough data to make a conclusion.
 * Methods and Materials:**


 * Data:**


 * Picture:**

Scalc:


 * Percent error:**

__Frequency vs. Tension__ 1. wavelength 2. exponent

__Frequency vs. Harmonic number__ 1. Fundamental frequency

__Frequency vs. Wavelength__ 1.exponent: 2. Wavespeed

Discussion Questions:
 * 1) Calculate the tension T that would be required to produce the n = 1 standing wave for the red braided string.
 * 2) [[image:discus1.png]]
 * 3) What would be the effect if the string stretched significantly as the tension increased? How would that have affected the data?
 * 4) If the string stretched as the tension increased then due to this we would see an increase in the velocity of the waves. Since the velocity would have increase so would the harmonic number. This is because we see that they are directly related in their equation, which is velocity = frequency * wavelength. Due to this our results would have been different for the lab as the frequency would have been less to get a certain harmonic number.
 * 5) 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.
 * 6) Each string will have a different set of characteristics than any other string. This means that if a string is thicker or thinner than another string, the frequency that causes each string to resonate will be different from one another. Also, a string will resonate at different at a different frequency depending on how much mass is added on it, which will increase the tension. A string with a higher tension will resonate at a different frequency than a string with little to no tension.
 * 7) What is the effect of changing frequency on the number of nodes?
 * 8) When the frequency is increased, the number of nodes also increases. This is because frequency and wavelength are indirectly related, as one goes up the other goes down. Therefore as frequency increase, and the size of the string remained the same, the wavelength decrease, which means that there were more waves on the string, meaning that there were more nodes.
 * 9) What factors affect the number of nodes in a standing wave?
 * 10) Factors that affect the number of nodes in a standing wave are the tension in the string, the frequency the string is vibrating at, and the properties of the string.
 * Conclusion:**

In this lab we were trying to find the relationship between three different things. We were trying to see the relationship between the frequency of a wave and its harmonic number, wavelength and tension. We thought that frequency and tension would have an inverse relationship and as one increase the other would decrease. After our experiment we found these results to be wrong. In actuality they have a power relationship with each other. Our hypothesis about frequency and harmonic number we predicted that as the frequency increases so would the harmonic number. This proved to be correct as we found that they had a positive linear fit. The last hypothesis that we made was for frequency and wavelength. We thought that they would have an indirect relationship and as frequency would increase the wavelength would decrease. After running our experiment we can conclude that our hypothesis was correct in the sense that they had a negative relationship, but wrong because we thought they had a linear relationship when in fact they have a power fit.

Although our hypothesis was wrong about the relationship between frequency vs. tension we were able to obtain data that was very accurate and helped us prove our hypothesis wrong. We were able to find an experimental wavelength by plugging the slope into and equation above. After finding this value we were abel to compare the wavelength that we measured to the experimental number. For this we got 9.14% error, which is very low. This shows that our data results were good because our measurements and calculations were not far off from the real thing. We also knew that the exponent for our line should have been 0.5 so we were able to compare the exponent we got of 0.49 to what it was supposed to be. When doing this we got 0.8% error, which is another reason to show that our results were good.

Our hypothesis about frequency vs. harmonic number held up during our experiment. We were able to use our results to conclude that what we thought was in fact true. We were able to do this because we compared the calculated theoretical fundamental frequency to the one on the graph that was found through our data collection. When doing this we found that we only had a 5.5% error. This error is very small and so it allows us to conclude that the data we found was good and that our hypothesis from the begining was correct.

For frequency vs. wavelength our hypothesis was wrong, but we knew that they had a negative relationship. We were still able to gather data to prove why we were wrong. We found the percent error between the average wave speed that we calculated and the one that was on the graph (The slope of the graph was equal to wave speed). When doing this we found only 5.5% error. Due to this we figured that our collection of data was accurate and allowed us to conclude that our finding in this experiment were correct. We also proved this by finding the error in the exponent of the line on the graph. This is because we knew that it was supposed to be -1 and so we were able to see the error compared to what we got. After calculating it we found that the error was only 2.5% which also proves that our data collection was successful and accurate.

There wasn't a lot of place for error in this experiment. One issue that we had was when we put the frequency up to certain numbers the string began to rotate around instead of just staying in place. This may have been where some of our error came from. In order to fix this we would have to make sure that the string was staying in place and not collect bad data. Another source of error was when trying to get the greatest frequency for a certain number of wavelengths we may have chose a frequency too low. This is because there are many frequency's where there are a certain number of standing waves, but you want to choose the one with the greatest amplitude and we may not have done that. In order to fix this we would have to try to test all the frequencies until we see the greatest amplitude. By doing this some of our percent error would decrease. Also we may have measured the wavelengths wrong because it was hard to see where one full wave was and get that correct measurement. We could have used another ruler to go up and down to pinpoint the exact end of the wave so that it would be easier to read it length. Also we could have taped the ruler down to the table so that it wouldn't move and our readings would be more accurate.

The concept of waves affects everything around us. Sound has waves that we cannot see and so what we did in this lab is very important and deals with sound waves. It would be able to tell us the relationship between the loudness or frequency of a sound to other things, like its wavelength and harmonic number.

=Lab: What is the relationship between the mass on a spring and its period of oscillation?= Rachel, Bennett, Remzi, Lindsay

- 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.
 * Objectives:**

We hypothesize that the spring constant, k, will be very similar between the two experiments, as k is a constant. Any change would be because the data is experimental, and not fully accurate.
 * Hypothesis:**


 * Methods and materials:**
 * To find the spring constant by measuring the extension of the spring, we took a support, which was a rod on a base, which had a ruler on the rod. Then, we took a mass holder and attached it to the spring, which was attached to the rod. We would add weight to the holder and record the change in distance as the force (weight) was increased. This data was 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 would once again let the holder become still at equilibrium. We would then pull down the holder, release it, and record the time the holder would take to oscillate ten times. Then, we would divide this time by 10 to get the time for one oscillation. We would add more mass to the holder and repeat the experiment, then we would graph the data on a period v. mass graph. The slope of this line would be the spring constant.

Experiment Image:


 * Data:**


 * Graph:**
 * Sample Calculations:**


 * 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?** Yes it is constant. After finding both k values we found that the spring constant for displacement was 3.493 while the spring constant for the applied force was 4.25. Though it may seem far off it is not much different. We found only a 19% error which helps us conclude that the range on forces between the two different ways is constant.
 * 2) **Why is the time for more than one period measured?** In order to get more accurate results and reduce human error we timed 10 periods and then divided the answer by 10 to get a single period. We also did 5 trials of this to ensure our timings were correct.
 * 3) **Discuss the agreement between the k values derived from the two graphs. Which is more accurate?** On Both graphs we are able to solve for the k value, which are close to one another. On the Force vs. Distance graph the slope of the line is the k value, but on the period vs. mass graph one must insert the slope into an equation ([[image:http://honorsphysicsrocks.wikispaces.com/site/embedthumbnail/placeholder?w=NaN&h=NaN]]) to find the k value. This is a reason to why the Force vs. Distance graph may be more accurate. That graph also doesn't involve calculations so it leaves less room for error.
 * 4) **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?** In order to find the force that the spring exerts we would need to use Hooke's law. We can use this since we know that the spring is at equilibrium.

. 2. velocity with respect to time . 3. acceleration with respect to time .
 * 1) position with respect to time


 * 5. 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?**


 * 6. We neglected to take into account the mass of the spring itself. Are your results any better when using the more accurate relationship m+(1/3)m (where //m// is the hanging mass and //ms// is the mass of the spring)? Redo graph #2 using [[image:http://honorsphysicsrocks.wikispaces.com/site/embedthumbnail/placeholder?w=NaN&h=NaN]] and explain these results. **

To find the k value we needed to use the slope from this graph and plug it into the equation above. Our k value from this graph was 5.75n/m, which was higher than the other k values that we calculated. The percent error that we calculated was high at 39.2% error. Since the intervals between our masses were so close together our results seem to be very wrong. By graphing it this way instead of the first way the masses are even closer together which caused the slope to be steeper than if we made the masses of each trial much more different. Other than this slight issue our results and data were good.

In this lab we were trying to find the spring force constant to different ways and compare them to see if the results turned out to be the same.The first way was by using the law of energy conservation by measuring the change in force and the change in distance from the springs equilibrium spot. The second way we did this was by using harmonic motion. We needed to find the period and the mass. After finding these two different values we compared them. In our hypothesis we predicted that k would be very similar since k is a constant. With our results we found that the two k's were close but not as similar as we thought. For the first way using law of conservation of energy we got a k of 3.493, but for the second way when using harmonic motion k was 4.25. For the first way we did it the slope of the graph (Force vs. distance) was the k value. For the second way we needed to use the slope of the line and plug it into the equation to find the k value. After finding these two values we were able to compare them to see if our results were good or not. After taking an average of the two k's we got a percent error of 19.5%, which may seem a little high, but our data seemed to be precise and accurate. Since our percent error seemed a little high we looked to see where we could have made some errors. Human error may be a large part of the reason why the k's aren't that similar. This is because when trying to read the displacement of the spring, the spring kept swinging and it though we used two ruler to try and get an accurate reading, but this may be a reason that our data is off. (This source of error was for the first part of the experiment - when we did law of conservation of energy) This may be fixed by ensuring that the spring is not moving when the displacement is measured and to use a flat straight ruler so that it is easier to read. A source of error for the other part of the experiment (when we used harmonic motion) was when we released the spring itself it did not go straight up and down. We could fix this by only using trials where it went up and down and also using less weight so that it wouldn't pull on the spring as much to ensure for a straighter bounce. Another source of error was when we were timing the period. Even though we did 5 trials for each different weight, getting exact times for the period is hard and that may lead to some of our data being off. Another place for error that came from this timing was allowing the spring to bounce for 10 periods and then divide the time by ten. This is because as the spring goes through more and more periods it looses energy along the way, which may be why some of our data is off.This could be fixed by using a motion detector because it would have been more exact. If all of this was fixed then our percent error would decrease.
 * Conclusion:**

This can be applied to many real life situations. It can relate to a person that is going bungee jumping. This is because the bungee oscillates just like the spring each period loosing more and more energy. The company that makes the bungee would need to test it to find the k value to be able to know the maximum weight it can hold.