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From Spring 2000. Note :You should also see problems 4 and 5 from Sample Test 1
1. Ch. 18. (30 points)
In the diagram above, two speakers are shown. A common oscillator drives the speakers at a common frequency f . The two speakers are placed distances d1 and d2 from a detector D.
The speakers are first arranged as shown in Fig. A. In Fig. A, the two distances d1 and d2 are equal. Speaker 2 is then moved to the left. As Speaker 2 is moved, the sound decreases once to a minimum sound level of zero, then increases once again to a maximum at the final distance d2 = 1.518 m shown in Fig. B. Assume the speed of sound is v = 343 m/s. Assume d1 = 1.000 m.
2. (30 points) In the figure below, a laser beam of power 4.1 x102 W and diameter 2.3 mm is directed upward at a solid spherical bead (of diameter < 2.3 mm) . The radiation pressure exerted by the beam causes the bead to float in space with zero acceleration. The bead reflects 90 % of the radiation and absorbs the rest of it. The density of the bead is 0.20 x104 kg/m3.
(a) ( 18 points) What is the radius r of the bead ?
(b) (10 points) Suppose the magnetic field equations for the plane electromagnetic wave of the incident beam are:
See the axes on next page.
Write the electric field equations in the blanks below for the incident beam.(Use symbols.)
EX = __________________ EY = _________________ EZ = ____________________
(c) (2 points) What is the numerical value Em of the electric field amplitude ?
3. Extra Credit. A submarine is 300 m horizontally out from the shore and 100 m beneath the surface of the water. Please see the diagram below. A laser beam is sent from the sub so that it strikes the surface of the water at a point 210 m from the shore. If the beam just strikes the top of a building standing directly at the water's edge, find the height H of the building. Assume that nAIR = 1 and nWATER = 1.33.
4. EXTRA CREDIT. Ch. 36
An upright object 1.75 cm tall is placed 38.0 cm to the left of a converging lens having a focal length f1 = 28.0 cm. A converging lens of focal length f2 = 18.0 cm is placed 108 cm to the right of the first lens.