ANALYSIS The uncertainty in the Lengths L1 and L2 can be found by using the maximum and minimum values found experimentally for each. We have: Ll max: Ll + 6L1 L1 min = L1 - 5L1 Adding these two expressions: L1 max + L1 min = L] + 5L1+ L1 - EL]: 2 L1 L L . CIT Ll = lmax : [mm (5) Similarly, by subtracting them: L1 max - L1 min = L1 + 5L1- L] + dL1= 2 5L1. or L . 6L = lmax Innn 6 1 2 1) The same. Applies to L2: L +1.. L _ L2: 2max2 2mm and 61:2: 2Inax2 2mm The uncertainty in the speed of sound using the resonance tube apparatus is ' 6L 15L 5 :u 3+ii4, (n Lip LXI] f L2 _ Ll where V is found from (2). The uncertainty using the temperature expressions (3) is MW. 2 H67"). {8) where k is 0.6 for air. Calculate separately for each tuning fork the speed of sound in air and the corresponding uncertainties from (2) and (7). Also calculate the expected values of the speeds of sound and uncertainties for each temperature reading from (3), and (8}. Report these values in a table of results. V exp = fx (1) or V exp = 2 fL (2) The speed at which sound travels is also dependent upon the temperature of the gas. For air it is approximately theory = 331.4+0.67 (3) where T is the temperature of air in degrees Celsius and the velocity is in meters per second