Resonance Tube Lab Essay Sample free essay sample

Resonance 1 Williams Lab 1: Tube Staci Williams Kevin Schesing. Nicole Harty. Caitlin Kubota Section 015 2 Performed February 2. 2010 Due February 13. 2010 3 Theory: 2. 1 Air As A Spring Williams Gas is a bouncy stuff. and when placed in a cylinder with Pistons on each side it can be compressed as Pistons push in. raising the force per unit area indoors. There will be a net force from the force per unit area to force the Piston back out. Since gas has mass it can back up oscillations and moving ridges. 2. 2 Traveling Sound Waves in Air When a cone of a talker moves out. it compresses air following to is and imparts an outward speed to the air molecules around it. in add-on to the random thermic speeds of air molecules. The molecules nearest to the talker will clash with those near them and leave those molecules into gesture. propagating off from the talker bring forthing sound. Similar statements use to when the cone is moved in every bit good. If talker cone vibrates sinusoidally. a going moving ridge will be emitted form the talker and the moving ridge relation degree Fahrenheit = V lt ; = wavelength. f = frequence of moving ridge. V = speed of moving ridge gt ; is satisfied. AS the gesture of the moving ridge molecules move along the way of the extension of the moving ridge are called longitudinal moving ridges. which is contrasting to transverse moving ridges which are on strings. The moving ridges as the elements of the twine move transverse to the way in which the moving ridges travel. In going moving ridges the supplanting of air satisfies the wave equation. V = ( P/ ) lt ; v = speed of moving ridge. = specific heats at changeless pressure/ † changeless volume = Cp/Cv. P = air force per unit area. = air mass denseness gt ; . With the ideal gas jurisprudence it can be written as V = ( RT/M ) lt ; R = grinder gas invariable. T = absolute temperature. M = Molar mass gt ; . For a given gas the velocity will be relative to the square root of the temperature giving the equation vrms = ( 3RT/M ) lt ; vrms ~ thermic velocity of the gas molecules gt ; . The velocity of sound in gas is close to the thermic velocity of molecules in gas. so the speed of extension is basically the thermic velocities of the molecules giving this equation V = 331. 5 + . 606T m/s. 2. 3 Traveling Sound Waves in a Tube Sound moving ridges are able to go in a tubing of a changeless cross subdivision much similar to how they travel in unfastened air. The tubing is assumed to hold stiff walls that will non flex under force per unit area fluctuations. every bit good as be smooth so that there is non much fading of the moving ridge. leting the velocity of the moving ridges to be about the same as in unfastened air. 2. 4 Standing Sound Waves in a Finite Tube Traveling sound moving ridges in a finite closed tubing will reflect at the terminals. leting for resonance to happen at certain conditions called resonating frequences ( normal manners ) . Resonance will happen when the reflected moving ridges at both terminals reinforce one another. The â€Å"pressure† of the air in the moving ridge is the alteration of force per unit area from the mean value. with the â€Å"displacement† of air to be its supplanting from the equilibrium place. with both force per unit area and supplanting changing sinusoidally in infinite and clip. Points where force per unit area is maximal are called force per unit area antinodes. and zero are called force per unit area nodes. Likewise. points where supplanting is maximal are called displacement antinodes and zero supplanting are called displacement nodes. In standing sound moving ridges force per unit area nodes occur at supplanting antinodes and force per unit area antinodes occur at supplanting nodes. An unfastened terminal of a finite tubing will be a force per unit area node because of the normal air force per unit area outside of the tubing. doing the point same a displacement antinode. while the terminal of a closed tubing must be a displacement node and a force per unit area antinode. Frequencies can be calculated for tubing with both terminals closed. one terminal closed and one terminal 4 opened. and both terminals open. Resonance wavelengths can be calculated y suiting standard moving ridges into the tubing so that boundary conditions are settled. The lowest resonance frequence is called the cardinal frequence or the 1st harmonic. The n-th harmonic is n multiplied by the cardinal frequence. and non all harmonics must be present. Data and Calculations: 4 Measuring Wavelength ( m ) . 708. 412. 582. 759. 350. 268. 384. 501. 618. 736. 233 D3 ( m ) D4 ( m ) D5 ( m ) D6 ( m ) D7 ( m ) Frequency ( Hz ) 500 1000 1500 D1 ( m ) . 159. 059. 038 D2 ( m ) . 513. 248. 152 Velocity ( m/s ) 343 343 343 Theoretical ( m ) . 686. 343. 229 Percent Error ( % ) 3. 21 2. 04 1. 75 Sample Calculations 1500 Hz: . 513m – . 159m = . 354m. 354m * 2 = . 708m ( . 708m – . 686m ) / . 686m * 100 % = 3. 21 % Since wavelength observed. multiply by 2 5 Pulsed Experiments 5. 1 Speed of Sound X = . 55m ( Distance from Piston to talker ) T = . 0015 sec. ( pulse clip ) V = X / T = . 55/ . 0015 = 366 m/s ( speed of sound ) 366 -343/343 * 100 % = 5. 83 % 5. 2 Boundary Conditions. 2 centimeter needed to alter reflected pulse Error Analysis: There was really small mistake nowadays during the experiment when we calculated the wavelength. all of which had a per centum of mistake 3. 21 per centum or less. The little mistake that was encountered could be 5 William s attributed to human mistake. in such a instance that the distance was falsely read. or that the graph was non zoomed in adequate to see precisely where the maximal strength occurred. The per centum mistake decreased as the sum of informations points we were able to take went up. proposing that if more informations points were available. the per centum mistake would be less. In the experiment where we found the velocity of sound a possible mistake may hold arisen due to the microphone non being to the full vertical towards the other side of the tubing. potentially making false resonance/pulse. Another factor that may hold caused mistake is that the terminal of the tubing was non wholly sealed. which means sound moving ridges could stream out or in. diminishing or increasing the frequence. Decision: Measuring Wavelengths For a frequence of 500 Hz the talker is about a one-fourth of a wavelength off from a lower limit or upper limit. Comparison to the twine experiment†¦ The wavelengths change with frequence in the manner I expect that as the frequence additions. the wavelength decreases leting for more informations points to be detected in the tubing. This expe riment adequately demonstrated how to cipher the wavelength utilizing points of maximal strength of the SWS package. Speed of Sound The reflected pulsation in this experiment was inverted. While traveling the Piston easy toward the microphone with the range running it is seen that the reflected pulsation had a lower amplitude than that of the original pulsation. This experiment allowed for the computation of the velocity of sound. This information figured is off of the expected value. but it is close to the expected value. demoing that if a better point would hold been chosen. the consequence would hold been better than the consequences that were attained. Boundary Condition The tubing must be cracked. 2cm to alter the reflected pulsation. It allows sufficiency of the pulsation to get away leting for a alteration in the amplitude. Questions: 1. open/open FN = NV/2L —— F 1 = V/2L open/closed FN = NV/4L —— F 1 = V/4L 2. V = F = V/F F = V/2L = V*2L/V = 2L = 2L PV = NRT. P = NRT/V = M/V V = ( NRTV/VM ) V = ( RT/M ) 3. V = ( P/ ) 6