up-dated 5/10/16 closed organs, flute clarinet , obie . - pipes hon. Last Name, First: Ken displacement y=Ausx C 4= +A PV=nRT open A .p=0 disp = mak high pressure no displacement Student ID: Physics 170A - Final Exam, May 09, 2016 - 6 Problems L Problem 1: 25 Points, You must show all your work - no sound - sound wave 1 x (radians) > disturbance 2 ? 4TT pressure The diagram shows a column of undisturbed air (open-circles and a column of air (dark circles) with a sinusoidal sound wave propagating in the x-direction, both at the instant of time t = 0. The arrows point to the molecules that in both sound and no - sound instances have been left undisturbed. The horizontal arrows indicate the direction of the molecules disturbance from its equilibrium position. 7 1 p=m =2 Mmol V = " Manrol (a) On the graph, carefully sketch the sine curve y = Asin(x) as a func- tion of x which best describes the gas molecules displacement y from their equilibrium position at z. (b) Now writing pV = nRT in terms of molar - mass M and density p find an expression relating pressure p to density p. Using this relation, carefully sketch the pressure as a function of position r along the column. Comment on the phase difference between the displacement curve and the pressure curve. How does this suggest that pressure and displacement are related. (c) Both the displacement curve (a) and pressure curve (b) are static, that is, a picture of curves moving to the right towards +r taken at time t = 0. Explain how letting the waves phase increase as ax - bt, or taking p(x, t) = Posin(ax - bt) will cause the wave to move to the right. With what velocity v will it move? pr ModORT 0 P= PRT Mmol Note 8 at x=it when t=0. white x> =21 (? -* ) O= constant at = d =0>dx-d/=0 d=v2=> == > P = p.six (d) Knowing that a is measured in radians and t in seconds derive appropriate expressions for a and b in part (c)in terms of the wavelength A, and frequency . f of the wave y=Acon (ax-bt) ?Aces Sar(?) -?} = Aco (kx-wt) - 1. a ==== K 7 b=2 =2xf=w=
VA=VB A 3 PB Paz 50? 10 Problem 2: 25 points 5 We have two equal-size boxes, A and B. Each box contains an Ideal gas. We measure the gas temperature in each box and find that box A is at 50C while box B is at 10C. This is all we know about the gas. Which of the statements must be true? Which could be true? 18.33 know * V=nRT = ART NA = Mit RT M (a) The pressure in A is higher than the pressure in B p = ner, we don't know n , so either pressure could be greater, PAR Ys - YA= VB TAYTB (b) There