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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.

  1. (12 points) What is the wavelength of the sound waves emitted from the speakers?
  2. (6 points) What is the frequency f ?
  3. (12 points) Suppose that Speaker 2 is moved more to the left as shown in Fig. C until the sound decreases once again to a sound level of zero. What is the distance d2 shown in Fig. C?

 

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.

  1. (4points) Determine the final position of the final image.
  2. (4 points) Determine the total magnification of the final image.
  3. (3 points) Is the final image upright or inverted?