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Unformatted text preview: Chapter 16 Problems 1, 2 , 3 = straightforward, intermediate, challenging Section 16.1 Propagation of a Disturbance 1. At t = 0, a transverse pulse in a wire is described by the function y = 6 x 2 + 3 where x and y are in meters. Write the function y ( x , t ) that describes this pulse if it is traveling in the positive x direction with a speed of 4.50 m/s. 2. Ocean waves with a crest-to-crest distance of 10.0 m can be described by the wave function y ( x , t ) = (0.800 m) sin[0.628( x – vt )] where v = 1.20 m/s. (a) Sketch y ( x , t ) at t = 0. (b) Sketch y ( x , t ) at t = 2.00 s. Note how the entire wave form has shifted 2.40 m in the positive x direction in this time interval. 3. A pulse moving along the x axis is described by y x , t ( 29 = 5.00 e- x + 5.00 t ( 29 2 where x is in meters and t is in seconds. Determine (a) the direction of the wave motion, and (b) the speed of the pulse. 4. Two points A and B on the surface of the Earth are at the same longitude and 60.0 ° apart in latitude. Suppose that an earthquake at point A creates a P wave that reaches point B by traveling straight through the body of the Earth at a constant speed of 7.80 km/s. The earthquake also radiates a Rayleigh wave, which travels along the surface of the Earth in an analogous way to a surface wave on water, at 4.50 km/s. (a) Which of these two seismic waves arrives at B first? (b) What is the time difference between the arrivals of the two waves at B ? Take the radius of the Earth to be 6 370 km. 5. S and P waves, simultaneously radiated from the hypocenter of an earthquake, are received at a seismographic station 17.3 s apart. Assume the waves have traveled over the same path at speeds of 4.50 km/s and 7.80 km/s. Find the distance from the seismograph to the hypocenter of the quake. Section 16.2 Sinusoidal Waves 6. For a certain transverse wave, the distance between two successive crests is 1.20 m, and eight crests pass a given point along the direction of travel every 12.0 s. Calculate the wave speed. 7. A sinusoidal wave is traveling along a rope. The oscillator that generates the wave completes 40.0 vibrations in 30.0 s. Also, a given maximum travels 425 cm along the rope in 10.0 s. What is the wavelength? 8. When a particular wire is vibrating with a frequency of 4.00 Hz, a transverse wave of wavelength 60.0 cm is produced. Determine the speed of waves along the wire....
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- Spring '08
- Physics, Rayleigh