16 - Wave Motion

Under what conditions 18 a solid can transport both

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Unformatted text preview: lid can transport both longitudinal waves and transverse waves, but a fluid can transport only longitudinal waves. Why? PROBLEMS 1, 2, 3 = straightforward, intermediate, challenging = full solution available in the Student Solutions Manual and Study Guide WEB = solution posted at http://www.saunderscollege.com/physics/ = Computer useful in solving problem = Interactive Physics = paired numerical/symbolic problems Section 16.1 Basic Variables of Wave Motion y(cm) Section 16.2 Direction of Particle Displacement Section 16.3 One-Dimensional Traveling Waves 1. At t 0, a transverse wave pulse in a wire is described by the function y 6 x2 2.00 cm/s –2.00 cm/s 4 A 2 B 2 4 6 8 10 12 14 16 18 20 x(cm) 3 where x and y are in meters. Write the function y (x, t ) that describes this wave if it is traveling in the positive x direction with a speed of 4.50 m/s. 2. Two wave pulses A and B are moving in opposite directions along a taut string with a speed of 2.00 cm/s. The amplitude of A is twice the amplitude of B. The pulses are shown in Figure P16.2 at t 0. Sketch the shape of the string at t 1, 1.5, 2, 2.5, and 3 s. Figure P16.2 3. A wave moving along the x axis is described by y(x, t ) 5.00e (x 5.00t )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 wave. 513 Problems 4. Ocean waves with a crest-to-crest distance of 10.0 m can be described by the equation 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. 5. 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 sends two waves toward point B. A transverse wave travels along the surface of the Earth at 4.50 km/s, and a longitudinal wave travels straight through the body of the Earth at 7.80 km/s. (a) Which wave arrives at point B first? (b) What is the time difference between the arrivals of the two waves at point B ? Take the radius of the Earth to be 6 370 km. 6. A seismographic station receives S and P waves from an earthquake, 17.3 s apart. Suppose that the waves have traveled over the same path at speeds of 4.50 km/s and 7.80 km/s, respectively. Find the distance from the seismometer to the epicenter of the quake. Section 16.4 Superposition and Interference WEB 7. Two sinusoidal waves in a string are defined by the functions y1 (2.00 cm) sin(20.0x 32.0t ) y2 (2.00 cm) sin(25.0x 40.0t ) and where y and x are in centimeters and t is in seconds. (a) What is the phase difference between these two waves at the point x 5.00 cm at t 2.00 s? (b) What is the positive x value closest to the origin for which the two phases differ by at t 2.00 s? (This is where the sum of the two waves is zero.) 8. Two waves in one string are described by the wave functions y1 3.0 cos(4.0x 1.6t ) y2 4.0 sin(5.0x 2.0t ) and where y and x are in centimeters and t is in seconds. Find the superposition of the waves y 1 y 2 at the points (a) x 1.00, t 1.00; (b) x 1.00, t 0.500; (c) x 0.500, t 0. (Remember that the arguments of the trigonometric functions are in radians.) 9. Two pulses traveling on the same string are described by the functions y1 5 4t )2 (3x (a) In which direction does each pulse travel? (b) At what time do the two cancel? (c) At what point do the two waves always cancel? Section 16.5 The Speed of Waves on Strings 10. A phone cord is 4.00 m long. The cord has a mass of 0.200 kg. A transverse wave pulse is produced by plucking one end of the taut cord. The pulse makes four trips down and back along the cord in 0.800 s. What is the tension in the cord? 11. Transverse waves with a speed of 50.0 m/s are to be produced in a taut string. A 5.00-m length of string with a total mass of 0.060 0 kg is used. What is the required tension? 12. A piano string having a mass per unit length 5.00 10 3 kg/m is under a tension of 1 350 N. Find the speed with which a wave travels on this string. 13. An astronaut on the Moon wishes to measure the local value of g by timing pulses traveling down a wire that has a large mass suspended from it. Assume that the wire has a mass of 4.00 g and a length of 1.60 m, and that a 3.00-kg mass is suspended from it. A pulse requires 36.1 ms to traverse the length of the wire. Calculate g Moon from these data. (You may neglect the mass of the wire when calculating the tension in it.) 14. Transverse pulses travel with a speed of 200 m/s along a taut copper wire whose diameter is 1.50 mm. What is the tension in the wire? (The density of copper is 8.92 g/cm3.) 15. Transverse waves travel with a speed of 20.0 m/s in a string under a tension of 6.00 N. What tension is required to produce a wave speed of 30.0 m/s in the same string? 16. A simple pendulum consists of a ball of mass M hanging from a uniform string of mass m and length L, with m V M. If the period...
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This note was uploaded on 03/24/2010 for the course PHYSICS 2202 taught by Professor Mihalisin during the Spring '09 term at Temple.

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