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midterm_solution - Name: M lZC/va ME 51300 Exam 1 — Fall...

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Unformatted text preview: Name: M lZC/va ME 51300 Exam 1 — Fall 2010 --- 11/10/2010 Note: To help you complete this exam, you may refer to your class notes, your homework, solutions provided to you and other material distributed as part of the course, but you may not refer to the text (Kinsler, Frey, Coppens and Sanders) or to any other acoustics text 0 Probleml: /20 0 Problem 2: ' /20 0 Problem 3: /20 Problem 1. (i) (ii) (iii) (iv) (V) (vi) What is sound? it MAWM sew/m For free oscillations to occur, a physical system must have both mm s 5 and The motion of the mass in a SDOF system is governed by a second order, ordinary different'al equ ion. As a result, the solution features a % sizd 4&5 that must be determined by application of boundary conditi us. The time phasor e‘ja’t can be represented in the complex plane by a vector that rotates in the ' direction. For an undamped SDOF system, the restoring force equation relates the t o quantities: MC 2 and What physical property of a SDOF system controls its forced response at frequencies well below the resonance frequency? alfva (Vii) The wave numbe can a so be referred to as (viii) The restoring force acting on a segment of a tensioned string is not proportional to the slope of the seaent: instead, it is proportional to (ix) In the calculation of sound pressure levels, Why was the reference root mean square sound pressure chosen to be 2 X 10'5 Pa? M w W W W W a a 7% 04,944,111, W A2 44 (X) Why is a spherically-symmetric wave expanding into free space referred to as a one-dimensional wave? 044 MM» L It. in 3 Problem 2. Two semi—inﬁnite, tensioned strings are connected to a point mass (of mass m) at x = 0 as shown in the ﬁgure below. String 1 has a mass per unit length of p u and a tension of T1; string 2 has a mass per unit length of pa and tension of T 2. A transverse force, f = F em, is applied to the mass. (i) Give an appropriate assumed solution for the displacement ﬁelds on both sides of the mass. Deﬁne terms as necessary. (ii) Draw a free body diagram of the forces acting on the mass. (iii) Express the boundary conditions that apply at x = 0 in equation form. (iv) Use the boundary conditions in conjunction with the assumed solution to solve for the complex amplitudes of the waves on both sides of the mass. (v) Derive an expression for the input mechanical impedance, Zin, experienced by the force. (vi) At what frequency will the transverse velocity of the mass be largest? /// 14' s E @ BOO @— m *9 DO ﬁ‘l a J: fFijt {12977. i—ds/x. : Prank“; .- L 3%9" LL? CL i p— L h e T"; ' T: 3 ma J x10 => ’T‘sa'MQ, +1Mk—syla—P == magi L .. T § T _ ﬂ = - 'Lé‘l. \‘3’; T L% +l" Wyhy' Problem 3. A plane wave propagating in C02 has the form p(x, y, Z, : Ae_j(5x+7y+6z)ejw, where A is complex. The density of C02 is 2 kg/m3 and the sound speed is 250 m/s. (i) What is the magnitude of the wave vector? What is the wavelength of the sound wave? (ii) What is the frequency of the wave? (iii) Specify the angle of propagation of the wave in terms of the polar angle, 6, and the azimuthal angle, (p. (iv) By using the linearized momentum equation, derive an expression for the vector intensity. 0’) (El = W 3 more: wfi thlcﬂ 4) A: 2:! 0.6M IN m ‘i’llo Hy V {TEE‘PE * 7,9: ...
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This note was uploaded on 12/26/2011 for the course ME 513 taught by Professor ### during the Fall '07 term at Purdue University-West Lafayette.

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midterm_solution - Name: M lZC/va ME 51300 Exam 1 — Fall...

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