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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.

- (12 points) What is the wavelength of the sound waves emitted from the speakers?
- (6 points) What is the frequency
*f*? - (12 points) Suppose that Speaker 2 is moved more to the left as shown in Fig. C until the sound
__decreases__. What is the distance d2 shown in Fig. C?**once**again to a sound level of zero

2. (30 points) In the figure below, a laser beam of power 4.1 x10^{2} 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 x10^{4} kg/m^{3}.

(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.)

E_{X} = __________________ E_{Y} = _________________ E_{Z }= ____________________

(c) (2 points) What is the numerical value E_{m} 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 n_{AIR} = 1 and n_{WATER} = 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 f_{1} = 28.0 cm. A converging lens of focal length f_{2} = 18.0 cm is placed 108 cm to the right of the first lens.

- (4points) Determine the final position of the final image.
- (4 points) Determine the total magnification of the final image.
- (3 points) Is the final image upright or inverted?