Lab Report #2 Standing Waves lab

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Northeastern University *

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Physics

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Jan 9, 2024

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Report for Experiment # 14 Standing Waves Vaughn Montoya Lab Partner: Ricardo Macrron TA: Ji Tae 2/3/2022 Abstract In this experiment standing waves of a string were looked at along with wave velocity and string tension along with standing waves in an air column and measuring the sound velocity. In the first Investigation, nodes 3-8 were found using a string that was at a frequency of 120 Hz and measured using a ruler stick to find the average distance between each node. A graph of string tension ࠵? ! vs. ࠵? " string was made to look at the slope which was found to be 0.000314 kg/m ± 0.0000382 kg/m which did fall within the excepted value of μ, 0.00032 kg/m. In Investigation 2, a premade apparatus was used in which a reservoir of water was connected on the side and tuning forks were hit over the top at different frequencies. The first sound maximum, L #/% was found and second maximum L &/% was also found. A graph of λ vs 1/f was made and the slope was 348.0 m/s ± 4.20 m/s which did not fall within the expected speed of sound, 343m/s.

Introduction Everybody knows waves, the kind that form when a rock drops into a body of water or the oceans waves. There are multiple other waves, matter waves, light waves, and sound waves. Recognizing waves is critical in transporting energy form one place to another. Waves such as the ones listed above contain consecutive peaks and valleys that can move in a definite position. For example, a sound wave in air it will have higher pressure next to regions of lower pressure traveling in a certain direction which is known as a longitudinal wave. Another instance, a wave moving through a string stretched out horizontally causes one part of the string to move upwards, an adjacent part moves downwards. This is known as transverse waves. The speed of a wave can be found by dividing the distance traveled after a particular time. The time for a complete up, down, and back motion is known as the period T. The opposite of this is known as frequency, f, which is the total number of oscillations in one second. The velocity of wave can be using the equation below: ࠵? = ࠵?࠵? ࠵?ℎ࠵?࠵?࠵? ࠵? = ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?, ࠵? = ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?ℎ The velocity of a wave along a string rests on the tension force of the string and the mass per unit length μ of the string. This can be highlighted below in the equation: ࠵? !’()*+ = 8 ࠵? ! ࠵? However, the velocity of sound in air rests on the atmospheric pressure p, the density of air p, and a constant y= 7/5. The speed of sound is generally 343 m/s at room temperature, sea level pressure. The goal of this lab was to study standing waves of a string, to examine the relationship between string and tension and wave velocity, to study waves in an air column and to measure sound velocity. In Investigation 1 the number of nodes was found all the way up to 8 which was done by adding weight to a bucket. The average distance was found, and the wavelength was calculated for each respective node along with the velocity of the string. A graph of ࠵? ! in the string vs. ࠵? " string was made to check the measure value of μ found to highlight the association between wave velocity and string tension. In Investigation 2, a tuning fork was used to measure the L #/% , maximum sound intensity and the second loudest sound intensity, L &/% . A graph of λ vs. 1/f was made to find the slope and see if it agreed with the velocity of sound in the air. Investigation 1 The setup for Investigation 1 consisted of setting up the apparatus like figure 14.6 in the IPL lab manual. First two rods were needed and screwed into the table, along with multiple clamps which were attached to the rods. An electric vibrator was attached at one end while the other had a pully. A piece of string was used which stretched between the rods and over the pully which was used to hang the bucket. The distance between the pully and the clamp was approximately five feet. The vibrator was turned on to create standing waves and a meter stick was used to measure the node lengths. Weight was added to the bucket as well as washers and the mass of the bucket was weighted after each node was found. For three nodes around 1.11 kg of mass was added with an error of 0.0005 kg, this included the weight of the bucket. For four nodes roughly 0.53 kg of weight was needed with an error of 0.0005 kg. The fifth node

was found at 0.30 kg of mass and error of 0.0005 kg. The sixth node was at 0.19 kg of weight and an error of 0.0005 kg. The seventh node was found at 0.13 kg and an error of 0.0005 kg. The eighth and final node was found at 0.10 kg and an error of 0.0005 kg. The error was found by dividing half the smallest increment and which resulted in a 0.0005 kg error. The distance between nodes was measured using a ruler stick and can be seen in the table below along with the average and error in the average. Table 1: Data from Investigation 1 Nodes: L # (m) L " (m) L & (m) L % (m) L , (m) L - (m) L . (m) L /0+ (m) δL /0+ (m) n=3 0.775 0.775 x x x x x 0.775 0.00354 n=4 0.530 0.532 0.532 x x x x 0.531 0.00289 n=5 0.405 0.406 0.407 0.403 x x x 0.405 0.00250 n=6 0.324 0.325 0.323 0.328 0.325 x x 0.325 0.00224 n=7 0.265 0.265 0.268 0.273 0.272 0.272 x 0.269 0.00204 n=8 0.229 0.26 0.227 0.223 0.231 0.231 0.23 0.233 0.00189 The lengths between the nodes were measured using a ruler stick. The average distance between adjacent nodes was calculated by adding the lengths and dividing by how many nodes there were and dividing by that number. The error of L /0+ was calculated by using the following formula: ࠵?L /0+ = √3 3 ࠵?࠵? The wavelength and error in wavelength were obtained as well as the tension force and the error were found by adding washers until the wave vanished. The wave velocity, wave velocity squared, and their respective errors were also found which can be seen in the table below. Table 2: Lambda, Tension, Velocity, and Velocity Squared along with the associated errors n λ (m) δλ (m) Fs (N) δFs (N) ࠵? 1’()*+ (m/s) δ ࠵? 1’()*+ (m/s) ( ࠵? 1’()*+ )^2 (m/s) (δ ࠵? 1’()*+ )^2 (m/s) 3 1.55 0.00707 10.84 1.56 186.0 0.849 34596.0 316.0 4 1.06 0.00577 5.15 0.920 128.0 0.693 16261.4 177.0

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