Problem Set 1. Due Friday December 2, 2005

• Text 1.2
• Text 1.3
• Text 1.7
• Text 1.9
• Text 1.11
• (For graduate students: Text 1.6)

• Text 1.4
• Text 1.21
• Text 1.22
• Text 1.25
• Text 1.28

• Text 2.2. Make an animation in Excel for this wave.
• Text 2.7
• Text 2.16
• Text 2.17
• Create a Maple animation of the shape of Example 2.3, travelling at c = 3 m/s.
• (For graduate students: Text 2.15. At very low frequencies, this mass will simply swing back and forth like a pendulum, so your equation for omega ought (at low frequencies) to give the frequency of a pendulum.)

• A rectangular membrane has length Ly = 0.40 m and width Lx = 0.20 m. Its lowest resonant frequency is 126 Hz. This membrane is given a sharp blow so that a small region between x = 0.08 m and 0.10m and between y = 0.18 m and 0.22 m is given a velocity v =0.38 m/s while the rest of the membrane is at rest. Find the coefficients of the 6 lowest-frequency modes of this membrane. This requires an analysis like was done in Section 2.5, pp. 47-49. You will have to carry out integrals in Maple over both x and y.
• Text problem 3.1

• Work out the odd-symmetry solutions for the flexural vibrations of a rod or bar free at both ends
• Write down the odd-symmetry wave functions
• Show that they satisfy the boundary conditions at a free end
• Write down the equation in kL/2 implied by satisfying the boundary conditions
• Find the lowest two odd-symmetry frequencies for a 12.7-mm diamter bar radius 0.8 m long made of aluminum
• A slinky is made up of 95 turns of flat steel wire, each of diameter 33.5 mm. The width of the flat wire is 1.26 mm and its thickness is 0.325 mm. Two flexural waves can propagate on this slinky. The first is one where flexing is against the thin direction ( 0.325 mm), basically perpendicular to the plane of a given loop of the slinky. The second is flexing radially, so the shape of a loop departs somewhat from circular.
• Find the total length of this slinky, stretched all the way out
• Take h = 0.325 mm and find the time it will take a 30-kHz wave to travel the length of the slinky
• Take h = 1.26 mm (for the second mode) and again find the travel time for a 30 kHz wave.
• From section 5.6 and the data on p. 628
• find the speed of torsional waves on a cylindrical steel bar
• by scouting around in the book, find an expression for the shear modulus G, and find poisson's ratio for steel from the listed value of G.
• Text problem 5.9

• a) Show that Eq. 15.6 follows from the previous equation, as indicated in the text.
• b) A highway noise barrier of 6x6 (0.14m x 0.14 m) wood members is erected. Take the density of the wood (use oak if you haven't already done the problem), and treat this barrier as a partition as was done in the beginning of sect 15.4. Calculate the transmission coefficient at 500 Hz and again at 1500 Hz
• Text problem 7.1. Also calculate the maximum particle displacement.
• Text problem 7.7
• Text problem 7.25 [See Sections 7.5 and 7.7 in the text. I don't get his answer for part a). For part b) the text's answer can't be right, since it is supposed to be a ratio.]

• Write a report for each of the four experiments you did in week 7. Something like 2 pages each.