If the various sources of uncertainty were independent, then the s would combine according to the rule. While this formula is useful qualitatively, we observe deviations from it in the range of 30% - 50%, indicating significant correlation among the different contributions to the uncertainty.

Lab Report for Experiment 14 Standing Waves Shivam Agarwal Lab Partner: Anton Draayer TA: Kunpeng Mu May 18, 2016 Introduction:The experiment had two investigations and the main goals of the experiment were to studystanding waves of a string, to examine the relationship between string tension and wave velocity,to study standing waves in an air column and to measure the sound velocity. Both theinvestigations were very different to each other and to conduct the experiment, we had a 120Hzvibrator, 2 stands with 2 rods, 3 rod clamps, 1 pulley, a short rod with a string clamp, a meterstick, a sound wave apparatus, 3 tuning forks with different frequencies and brass weights. In thefirst investigation, we created standing waves on a string and also measured the mass of theweights we were adding to the bucket to get the different number of nodes on the string.

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We alsomeasured the distance between the nodes which helped us calculate various values of the stringincluding the wavelength, tension, density and the speed of the wave. These values helped usmake a graphical analysis of the standing waves using the tension of the string and the square ofvelocity. In the second investigation, we used three different tuning forks with differentfrequencies to create standing longitudinal waves in an air column. As we struck the fork overthe column, we measured the position where the sound from the column was the loudest. Usingthe position and the frequency of the fork, we calculated the wavelength, speed and the period.Using all these values we did a graphical analysis of these values by plotting a graph using thewavelength and the period of the waves. All the calculations and the graphs were drawn usingMicrosoft Excel and all these values are shown under the data analysis parts of the twoinvestigations.

Investigation 1:Setup and procedure:In this investigation, we had to create standing waves on a string. So we first set two rods about ameter apart from each other and then attached the two rods by a string. On one end of a string,we attached a bucket and the other end of the string was on the other rod on which we clampedthe electromagnetic vibrator and the string holder. The other rod had a pulley through which thestring passed and the bucket was hanging. As the investigation was set up, we then switched thevibrator on due to which the string started to vibrate and we were able to see different number ofnodes on the string. To get different number of nodes, we started adding brass weights to thebucket and so we recorded the distance between nodes for 3, 4, 5, 6, 7 and 8 number of nodes.Using these values, we also calculated the average distance, the wavelength, the velocity and thetension in the string. After calculating these values, we made a graph using the velocity squaredand the tension force of the string to find out the mass per unit length of the string.Data and analysis:0 1 2 3 4 5 025000f(x) = 3440.03 x + 1813.R² = 1 v^2 vs fv^2 vs f Linear (v^2 vs f) Linear (v^2 vs f)Tension forceV^measured these values which helped us find the period, wavelength of the wave and the speed ofthe sound.

We also made a graph using the period and the wavelength.Data and analysis:0 0 0 0 0 0 0 0 000.0.0.0.1f(x) = 341.62 xR² = 1 Wavelength vs PeriodWavelength vs Period Linear (Wavelength vs Period)PeriodWavelengthAverage speed of sound: 341.This was calculated by adding all the speeds of sound and then dividing by three. Conclusion:Investigation 1 –Calculated String Density: 0.Theoretical String Density: 0.The error in the calculated and the theoretical value can be caused due to the parallax error as itis very difficult to count the number of nodes as the number increases. It is also very difficult tosee where the node starts and ends which causes the distance between the nodes to be uncertain.The uncertainties in all the other errors also cause the values to be a little different.Investigation 2 –Calculated speed of sound: 341.62 m/sTheoretical value: 343 m/sThe calculated value is very close to the theoretical value and the error that could have caused inthis to happen would be the way the measurement was handled as it was not easy to accuratelymeasure the position where the loudest sound was produced. Questions:1) Speed = wavelength. frequency= (0.65 m. 2).

248 Hz= 322 m/s2) Tension = (v^2. μ)= (322^2. 0.0005)= 52 N3) 0.5. λ = 0.48 m  λ = 0.96 mF = v/ λ  343/0.96 = 357 Hz4) Resonance occurs at 0.25 λ = (1000/512)  λ = 0.ANDResonance occurs at ¾ λ = (1000/512)  λ = 1.Hence the separation between maxima = 1.46 – 0.4883 = 0.97m Acknowledgement:I would like to thank my T.A. Kunpeng Mu and my lab partner Anton Draayer who helpedme in the lab. References:O.Batishchev and A. Hyde, Introductory Physics Laboratory, Hayden-McNeil, 2016.