Test1PhysicsSolutions

Test1PhysicsSolutions - Physics 2306 Fall 2007 First Exam...

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Physics 2306 Fall 2007 First Exam FORM A 1) The displacement of air molecules in a sound wave is given by s(x,t) = (0.20 cm) sin[(10 π radians/meter) x] sin[(3000 π radians/second) t] Which one of the following statements is true? A. The wave is a transverse wave and the displacement of air molecules and the pressure fluctuation are in phase. B. The wave is a transverse wave and the displacement of air molecules and the pressure fluctuation are 90 ° out of phase. C. The wave moves in the x-direction with a speed equal to 300 m/s. D. The wave is a transverse wave and the displacement of air molecules and the pressure fluctuation are 180 ° out of phase. E. The wave has an antinode at x = 0.25 meters. F. The wave is a longitudinal wave and the displacement of air molecules and the pressure fluctuation are in phase. G. The wave is a longitudinal wave and the displacement of air molecules and the pressure fluctuation are 180 degrees out of phase. H. The wave has a node at time equal to 0.0010 seconds. 2-5) The displacement of a string from equilibrium is given by y(x,t) = (0.030 m)cos[(4.0 π rad/meter)x + (1600 π rad/sec)t] 2) What is the amplitude (in meters) of the wave? A. 0.25 B. 2.0E-04 C. 0.030 D. 0.50 E. 0.0013 F. 6.3E-04 G. 4.0 π H. 1,600 π sin[(10 π radians/meter) x] is one for x = 0.25 meters which implies that the amplitude of the displacement is maximum at that position which implies an antinode at that position. General expression for a traveling wave is y(x,t) = A cos[ kx ± ω t] where A is the amplitude, k = 2 π / λ is the wave number, and ω = 2 π f = 2 π /T. Comparing the specific example given above to the general expression, you see that A = 0.030 m k = 4.0 π ω = 1600 π and that the wave is moving in the negative x-direction since there is a plus sign between kx and ω t.
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3) What is the period (in seconds) of the wave? A. 0.25 B. 2.0E-04 C. 0.030 D. 0.50 E. 0.0013 F. 6.3E-04 G. 4.0 π H. 1,600 π 4) What is the wavelength (in meters) of the wave? A. 0.25 B. 2.0E-04 C. 0.030 D. 0.50 E. 0.0013 F. 6.3E-04 G. 4.0 π H. 1,600 π 5) What is the velocity of propagation (in meters/second) of the wave (positive wave velocity is in the +x-direction and negative wave velocity is in the x-direction)? A. 6400 B. 6400 C. 4.0 D. 4.0 E. 1600 F. 1600 G. 400 H. 400 6) A pipe is open at one end. The frequency of sound from this pipe is 344 Hz? If this normal mode is the third harmonic, what is the length of the pipe (in meters)? Assume the speed of sound is 344 m/s. A. 0.75 B. 1.3 C. 2.0 D. 1.5 E. 1.0 F. 3.0 G. 2.5 H. 0.50 T = 2 π / ω = 2 π /1600 π λ = 2 π /k = 2 π /4.0 π The wave relation is ω = v k where v is the speed of the wave. Therefore v = ω /k =1600 π /4.0 π = 400 m/s The velocity is in the negative x-direction for the reason given in question 2. The length of a pipe that is open at one end is
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This note was uploaded on 04/02/2008 for the course PHYS 2306 taught by Professor Ykim during the Fall '06 term at Virginia Tech.

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Test1PhysicsSolutions - Physics 2306 Fall 2007 First Exam...

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