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Unformatted text preview: homework 23 FIERRO, JEFFREY Due: Apr 20 2008, 11:00 pm 1 Question 1, chap 16, sect 1. part 1 of 1 10 points Earthquakes produce two kinds of seis- mic waves: The longitudinal primary waves (called P waves) and the transverse secondary waves (called S waves). Both S waves and P waves travel through the Earths crust and mantle, but do so at dif- ferent speeds; the P waves are always faster than the S waves, but their exact speeds de- pend on depth and location. For the purpose of this exercise, we assume the P waves speed to be v P = 9930 m / s while the S waves travel at a slower speed of v S = 4710 m / s. Suppose a seismic station detects a P wave and then t = 66 . 1 s later detects an S wave. How far away is the earthquake center? Correct answer: 592 . 245 km (tolerance 1 %). Explanation: Suppose the earthquake happens at time t = 0 at some distance d . The P wave and the S wave are both emitted at the same time t = 0, but they arrive at different times, respectively t P = d/v P and t S = d/v S . The S wave is slower, so it arrives later than the P wave, the time difference being t = d v S- d v P = d ( v P- v S ) v P v S . Consequently, given this time difference and the two waves speeds v P and v S , we find the earthquake center being d = v P v S t v P- v S = (9930 m / s) (4710 m / s) (66 . 1 s) (9930 m / s)- (4710 m / s) = 592 . 245 km . away from the seismic station. Question 2, chap 16, sect 2. part 1 of 1 10 points A harmonic wave is traveling along a rope. The oscillator that generates the wave com- pletes 46.0 vibrations in 24.5 s. A given crest of the wave travels 409 cm along the rope in a time period of 11.8 s. What is the wavelength? Correct answer: 0 . 184608 m (tolerance 1 %). Explanation: Basic Concepts: v = f f = number of vibrations t x = v t Given: n = 46 . 0 vibrations t = 24 . 5 s x = 409 cm t = 11 . 8 s Solution: = v f = x t n t = x t n t = (409 cm)(24 . 5 s) 46(11 . 8 s) 1 m 100 cm = 0 . 184608 m Question 3, chap 16, sect 2. part 1 of 3 10 points The transverse displacement of a stretched string from equilibrium as a function of time and position is given by y = a sin( b x + ct ) , where a = 0 . 65 m, b = 2 . 9 m 1 , and c = 43 s 1 , and x is in meters and t is in seconds. The wave 1. travels in the- x direction. correct homework 23 FIERRO, JEFFREY Due: Apr 20 2008, 11:00 pm 2 2. is stationary. 3. travels in the + x direction. 4. travels in the + y direction. 5. travels in the y direction....
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This note was uploaded on 05/11/2008 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas at Austin.
- Spring '08