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SPEED OF SOUND Objective To determine the speed of sound in air by means of a resonating air column at room temperature

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SPEED OF SOUND Objective To determine the speed of sound in air by means of a resonating air column at room temperature. Equipment Tube, clamps, flexible tubing, water, a thermometer, water jug, meter stick and two tuning forks Procedure 1. Measure and record the temperature of the room. Measure and record the radius of the tube. 2. With the column full of water, strike the tuning fork on the heel of your hand. DO NOT HIT THE TUNING FORK AGAINST A HARD SURFACE, this can permanently damage the tuning fork and produce harmonics of the fundamental frequency (stamped on the tuning fork) which will confuse the interpretation of your data. Touch the tuning fork near the base to damp out the harmonics. 3. Hold the tuning fork approximately two centimeters from the open end of the tube, with the tines of the fork perpendicular to the axis of the tube. Listen near the edge of the tube for a sudden increase of sound intensity as the water level in the tube is lowered. This will occur when the length of the air column in the tube is one of the resonant lengths. Mark this point with a rubber band and measure the distance from the top of the tube. 4. Continue to lower the water level until you find the next increase in sound intensity. Again, mark this point with a rubber band and measure the distance from the top of the tube. 5. Try to find at least one more resonance length. 6. Repeat using the other tuning fork. Graphs and Diagrams 1. Plot the frequency versus 1/wavelength (calculation 1). Questions and Calculations 1. Knowing what fraction of a wavelength that fits inside the air column, the wavelength can be computed for each of your measurements. To find the correct wavelength from your measurements you will need to make a small adjustment because the center of the anti-node is not exactly at the end of the tube but slightly beyond it. A good approximation to use is to add six-tenths of the radius of the tube to your measurements. compute the corrected wavelength for each measurement. 2. From the graph, find the speed of sound. The speed of sound in dry air at 0C is 331.5 m/s and increases 0.6 m/s for each C rise in temperature, thus v(T)=(331.5+0.6T)m/s. Compare your value of the speed of sound and the value calculated using this formula. 3. If the room temperature were lowered how would this effect the experiment? How would your measurements change? 4. If you were underwater and had a trapped column of air, you could repeat this experiment. Except, this time the sound waves would be traveling through water and not air. How would the results be affected, if at all? Explain. 5. Suppose you performed this experiment on the Moon. How would your results differ? Free Fall Lab Report PHYS 201L – J11 Summer 2021 Saif Almahrezi May 16th, 2021 Abstract: We investigated the relationship between drop height of a solid ball and the free fall time of the ball. We dropped the ball from multiple different heights and recorded the amount of time in seconds it took for the ball to hit the ground. Within uncertainties of our measurements, a linear correlation between the height at which the ball is dropped and the time it takes for the ball to hit the ground was observed. From this correlation we were able to calculate the rate at which the ball was dropped, which was found to be the acceleration due to gravity. We determined that the acceleration due to gravity on earth is approximately 9.81 m/s2. 1 Introduction: This lab deals with using methods of measuring to find the acceleration due to gravity (g). A free fall apparatus with pad is a simple device for determining the rate of acceleration due to gravity. The free fall apparatus with pad calculates the amount of time it takes for the ball to fall from the free fall apparatus and hit the pad. From the time and the measured height, X (m), the acceleration for earth’s gravity (9.81 ms-2) can be found. Equipment: • 2-long and 1-short lab post. • 3-clamps. • Timer. • Free fall apparatus with pad. • Two different sized metal balls. • Meter stick Procedures: the electronic timer measures the time it takes for the metal ball to reach the gray pad once the ball has been released from the apparatus. In this experiment we used two different metal balls with differing masses. We tested the apparatus to make sure that the ball hit the gray pad after being released before we took formal calculations of the time. In this lab, we used the electronic timer to release the balls at five different heights. At each of the different heights the ball is dropped seven times. The times were recorded in table form as the balls were tested with the electronic timer. Once the times were recorded, we took the average time of the trials and squared the average time. The average is found by taking the sum of the five values and dividing it by five. To get the time squared when simply square the average number that was calculated. The table below gives the data corresponding with the smaller sized ball: Trail Distance(m) 1.029 1.095 1.168 1.315 1.54 1.807 1.915 1 Time(s) 0.4667 0.4752 0.4836 0.5319 0.5644 0.6051 0.6233 2 0.4616 0.4773 0.4834 0.5117 0.5677 0.6124 0.6243 3 0.4569 0.4721 0.4873 0.5161 0.5804 0.6014 0.6282 4 0.4579 0.4738 0.489 0.5108 0.5535 0.6035 0.6212 5 0.4653 0.4713 0.489 0.5224 0.5636 0.5977 0.6181 6 0.4578 0.4745 0.4904 0.5129 0.5605 0.6012 0.6145 7 0.4484 0.4663 0.4902 0.5187 0.5609 0.6209 0.6159 Average 0.4592 s 0.4729 s 0.48755 0.5178 s 0.5644 s 0.6060 s 0.6207 s Time s [Average 0.2109 0.2237 0.2377 0.2681 0.3186 0.3673 0.3854 Time]2 ?? ?? ?? ?? ?? ?? ?? Once the results were recorded, we used the computer software to generate a graph of the results. The graph below shows the data for the small ball with the distance (in meters) on the vertical axis and the [average time]2 (in seconds2) on the horizontal axis. 2 Distance(m) Vs.[Average Time]2 2.5 y = 4.9943x - 0.0258 R² = 0.9987 Distance(m) 2 1.5 1 0.5 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 [Average Time]2 Figure 1: This is the graph of height versus [average time]2 for the smaller ball. The height is measured in meters and the [average time]2 is measured in seconds2. The slope that was found (4.9943) gives approximately half of the acceleration based on the equation: d= ½ gt2. 1 The graph has a fairly good linear fit. Based on the equation: ? = 2 ?? 2 , the slope of the graph is ½ g, when g is the acceleration due to gravity. Therefore, if we multiply the slope of the graph by 2, we get the acceleration of the experiment. Slope (4.9943) x 2 = 9.99 m/s2 Therefore, the acceleration due to gravity for this experiment was 9.99 m/s2 with a percent error of 1.835 %. We repeated the same procedure for the large ball and got the following results: 3 Trail Distance(m) 0.582 0.598 0.76 0.878 1.182 1.462 1.984 1 Time(s) 0.3424 0.35 0.3909 0.4228 0.4928 0.5499 0.6345 2 0.3448 0.3493 0.3874 0.4219 0.5016 0.5435 0.6321 3 0.3468 0.3476 0.3906 0.4245 0.4886 0.5426 0.625 4 0.3444 0.343 0.3964 0.4223 0.4909 0.546 0.6264 5 0.3461 0.349 0.3951 0.4238 0.4961 0.5574 0.636 6 0.3452 0.3523 0.397 0.4194 0.5016 0.5388 0.6327 7 0.3487 0.3545 0.3923 0.4231 0.494 0.549 0.6278 0.3455 s 0.3494 s 0.3928 s 0.4225 s 0.4951 s 0.5467 s 0.6306 s Average Time [Average Time]2 0.1193?? 0.1221?? 0.1543?? 0.1785?? 0.2451?? 0.2989?? 0.3977?? Once we graphed the results from the table, we generated the following graph: 4 Distance(m) Vs.[Average Time]2 2.5 y = 4.9869x - 0.0163 R² = 0.9993 Distance(m) 2 1.5 1 0.5 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 [Average Time]2 Figure 2: This is the graph of height versus [average time]2 for the larger ball. The height is measured in meters and the [average time]2 is measured in seconds2. The slope that was found (4.9869) gives half of the acceleration based on the equation: d= ½ gt2. The graph of the results for the larger sized ball resulted in a more linear fit than the graph for the smaller ball. The slope of the graph of the larger sized ball was 4.9869. Once we doubled this number, we got 9.97 m/s2 for the acceleration and a percent error of 1.67%. Questions: Q1. What is your measured result for the acceleration due to gravity on Earth g for each ball? A1. 28g ball: 9.97 m/s2 16g ball: 9.99 m/? 2 Q2. How well do your measurements compare with the standard value of 9.81 m/s2 for the gravitational acceleration? 5 A2. the gravitational acceleration are fairly accurate based on the percent error calculations (1.67 % and 1.835%). Q3. What factors contribute to any differences between what you have found and what you expected? A3. There are aspects of the experiment that can result in error. For example, the electronic timer is very sensitive, and we had to continuously reset the stopwatch for the same trial to try to get the most accurate reading. Conclusion: This lab required the use of two different methods to find values that corresponded with gravitational acceleration (g=9.81 m/s2). The method used is the electronic timer. When using the electronic timer, we used two different balls with slight differing mass to find the gravitational acceleration value. Using the graph of distance, the ball dropped (in meters) versus the [average time]2 (in seconds2), we found the acceleration due to gravity for the small ball to be 9.99 m/s2 and the acceleration due to gravity for the large ball to be 9.97 m/s2. 6 frequency (Hz) 256 384 512 resonance lengths in units of lambda (m) 1/4 3/4 5/4 0.33 1.00 1.67 0.21 0.66 1.10 0.16 0.49 0.83 cylinder radius: 0.01384 m air temperature: 23 C