Physics 123 Practice Final Exam Spring 2005 Instructor: John McGill You might find the following information useful: g = 9.8 m/s2 εo = 8.85 x 10-12 C2/Nm2 µo = 4π x 10-7 Tm/A = 1.26 x 10-6 Tm/A c = 3.00 x 108 m/s Speed of Sound in air at 20°C = 343 m/s 1 nm = 10-9m 1 µm = 10-6m 1 mm = 10-3m 1 km = 103 m Name: Student ID#:

Problem 1 A beam of electrons with of wavelength of 7.5 x 10-6 m is incident on a pair of narrow rectangular slits separated by 0.75 mm. The resulting interference pattern is projected onto a screen 10.0 m from the slits. What is the separation of the interference maxima in the resulting interference pattern?

10.0 m

? λ = 7.5 µm 0.75mm

Problem 2 A 0.95 kg mass undergoes simple harmonic motion with an period of 2.0 s. a) What is the angular frequency of the oscillations? b) What is the magnitude of the net force on the mass when it is at a 5.0 cm displacement from the

equilibrium point of the motion?

Problem 3 An airplane flies directly toward a woman standing on the ground then pulls out of its dive and flies directly away from the woman, all at constant speed. The frequency of the sound that the woman hears while the airplane is approaching is twice the frequency of the sound that the woman hears as the airplane is flying away. What is the speed of the airplane? (Assume that the speed of sound is 343 m/s).

Problem 4 Light inside of a glass sphere is reflected along the perimeter of an equilateral triangle as shown above. If the light undergoes total internal reflection at each vertex of the triangle, what is the minimum value of the index of refraction of the glass? (Assume the index of refraction of air is 1).

60°

Problem 5 The intensity of light hitting the Earth from the sun is 1340 Watt/m2. a) If the distance from the earth to the sun is 1.50 x 1011 m, what is the total power output of the sun? b) What is the amplitude of electric field of the light from the Sun when it hits the earth? (Assume

that the electromagnetic wave is sinusoidal).

Problem 6 a) A seismic p-wave moves at 6.0 km/s and produces shaking at frequency of 5.0 Hz. What is the

wavelength of the seismic p-wave? b) A seismic s-wave produced by the same earthquake as the p-wave above, travels at a speed of 5.0

km/s and arrives at a seismograph 4.0 seconds later than the p-wave. How far is the earthquake from the seismograph?

Problem 7 A virtual image formed by a converging lens is twice as big as the object. If the object is 2.0 cm from the lens, what is the focal length of the lens?

Problem 8 A flute filled with air produces a pitch of 500 Hz. If the speed of sound in helium is 1000 m/s, what pitch will the same flute filled with helium produce? Assume the sound waves inside flute behave the same as waves on a stretched string the same length as the flute. (The speed of sound in air is 343 m/s)

Problem 9 Ocean surface waves undergo refraction at a boundary between deep and shallow water as shown above. The waves approach the boundary from deep water at a speed of 2.0 m/s and are incident on the boundary at an angle of 45° from the normal to the boundary. The ocean waves are then refracted in toward the normal to the boundary such that the refracted waves make an angle of 30.0° with the normal to the boundary. What is the speed of the waves in the shallow water?

Deep Water, ν = 2.0 m/s

Shallow Water, ν = ?

45°

30.0°

Boundary

Problem 10 An electromagnetic wave has a magnetic field with a magnitude of 2.0 x 10-7 Tesla directed directly west. a) What is the magnitude of the electric field associated with the wave? b) If the wave is propagating vertically upward, what is the direction of the electric field associated with

the wave?

North

East South

West

up = direction of propagation

Problem 11 A laser beam has an average intensity of 10.0 W/m2. a) What is the amplitude of the electric field in the laser beam? b) What is the amplitude of the magnetic field in the laser beam? c) The electromagnetic wave inside the laser tube is a standing wave. If the tube is 0.30 m long and

the laser light has a wavelength of 633 nm, how many anti-nodes are there inside the tube?

Physics 123 Spring 2003 Practice Final Exam Answer Key 1. h = λD/d = 10 cm 2. a) ω = 2π/T = 3.14 rad/s, b) F = mω2x = 0.47 N 3. vs = v/3 = 114 m/s 4. n = 1/sinθc = 2 5. a) P = 4πr2I = 3.79 x 1026 W, b) Em = 2 ocIµ = 1005 N/C

6. a) λ = v/f = 1.2 km, b) D = ∆t/(1/vs - 1/vp) = 120 km 7. f = 1/(1/p - 1/2p) = 4.0 cm 8. fHe = fair (vHe/vair) = 1460 Hz 9. v2 = v1 sinθ2/sinθ1 = 1.41 m/s 10. a) Em = cBm = 60 N/C, b) North 11. a) Em = 2 ocIµ = 86.8 N/C, b) Bm = Em/c = 2.89x10-7 T, c) n = 2L/λ = 950,000