Explore Download 0CommentLinkEmbedof 6Readcast0 inShare Xavier Bourret-Sicotte Physics18/09/2007 Measuring the speed of sound In this experiment, we will measure the speed of sound. The apparatus consisted of a plastic tube filled with water linked to a water container. Thiscontainer could be displaced vertically in order to change the water level. We would thenmake a tuning fork vibrate above the pipe and change the water level until the resonance wasat maximum intensity. Hypothesis: The velocity of sound is 330 ms -1 , the relationship between velocity, frequencyand wavelength is represented by the formula v= ? , 1) Raw data presented Table 1 Table 1 shows the frequency of the different tuning forks and the length of air needed for maximum resonance. The error on the length was estimated to 0. 1 cm as we repeated eachexperiment several times. Note the error on the forks’ frequencies is a mere estimation as theyare accurately calibrated during manufacture. Frequency /HzLength /m 512. 00. 157480. 00. 169456. 10. 178426. 60. 192406. 40. 202384. 00. 215362. 00. 226341. 30. 243320. 00. 260304. 40. 270288. 00. 288271. 20. 308256. 00. 323Error +/- 0. 1error +/- 0. 001 2) Data analysis and interpretation

During the experiment, we have created a fundamental standing wave between the surface of the water and the opening of the pipe. The distance measured represents ? of the completestanding wave therefore ? = measured length * 4-From the general formula v= ?? , we find that velocity of sound in ms -1 for the first tuningfork experimented is v = 512 ? 0. 157 ? 4 = 321. 536-Calculating the error for velocity: ? v = ( ?? / ? + ?? / ? ) ? vFor the first tuning fork: ? v = (0. 001 / 0. 157+0. 1/512) ? 321. 536 ? v = 2. 1108 ms -1 ? v ? 2 ms -1 ? v ? 322 +/- 2 ms -1 To find the mean velocity we add all values of v and divide the sum by the number of values. A similar process was completed for the mean ? v. Results of all processed data are shown in table 2 Table 2 Frequency Hz -1 Length m -1 Velocity ms -1 ? velocity +/- ms -1 512. 00. 1573222480. 00. 1693242456. 10. 1783252426. 60. 1923282406. 40. 2023282384. 00. 2153302362. 00. 2263271341. 30. 2433321320. 00. 2603331304. 40. 2703291288. 00. 2883321271. 20. 3083341256. 00. 3233311error +/- 0. 1error +/- 0. 001 Mean velocity = (322+324+325+328…) / 13 ? 329Mean ? v = (2+2+2+2+2+2+1+1+1…)/13 ? +/- 2 ms -1 As v = ?? , and ? = v / ? , let be constant of 330 ms -1 then ? ? 1/ ? By plotting the graph of Frequency over 1/ ? we obtain a straight line. The gradient of thisline represents the constant v and the y-intercept a systematic error. The situation is illustrated by graph 1 Graph 1 y = 313. 24x + 16. 736200. 0250. 0300. 0350. 0400. 0450. 0500. 0550. 00. 55 0. 75 0. 95 1. 15 1. 35 1. 55 1. 75 1/wavelength m-1 Note that if we add the y-intercept to the gradient we obtain the value of 329. 976 ms -1 for thespeed of sound. Moreover, the second best fit line (in red) illustrates the most extreme interpretation of the Speed of Sound IB Physics HL Lab report