16 - Wave Motion

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Unformatted text preview: of oscillation for the pendulum is T, determine the speed of a transverse wave in the string when the pendulum hangs at rest. 17. The elastic limit of a piece of steel wire is 2.70 109 Pa. What is the maximum speed at which transverse wave pulses can propagate along this wire before this stress is exceeded? (The density of steel is 7.86 103 kg/m3.) 18. Review Problem. A light string with a mass per unit length of 8.00 g/m has its ends tied to two walls separated by a distance equal to three-fourths the length of the string (Fig. P16.18). An object of mass m is sus3L/4 L/2 L/2 2 and m y2 5 (3x 4t 6)2 2 Figure P16.18 514 CHAPTER 16 Wave Motion the period of vibration from this plot and compare your result with the value found in Example 16.3. 24. 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. 25. 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? 26. Consider the sinusoidal wave of Example 16.3, with the wave function pended from the center of the string, putting a tension in the string. (a) Find an expression for the transverse wave speed in the string as a function of the hanging mass. (b) How much mass should be suspended from the string to produce a wave speed of 60.0 m/s? 19. Review Problem. A light string with a mass of 10.0 g and a length L 3.00 m has its ends tied to two walls that are separated by the distance D 2.00 m. Two objects, each with a mass M 2.00 kg, are suspended from the string, as shown in Figure P16.19. If a wave pulse is sent from point A , how long does it take for it to travel to point B ? 20. Review Problem. A light string of mass m and length L has its ends tied to two walls that are separated by the distance D. Two objects, each of mass M, are suspended from the string, as shown in Figure P16.19. If a wave pulse is sent from point A, how long does it take to travel to point B ? L 4 A B L 2 M M Figure P16.19 WEB y Problems 19 and 20. y Section 16.6 Reﬂection and Transmission Section 16.7 Sinusoidal Waves 23. (a) Plot y versus t at x 0 for a sinusoidal wave of the form y (15.0 cm) cos(0.157x 50.3t ) , where x and y are in centimeters and t is in seconds. (b) Determine (0.25 m) sin(0.30x 40t ) where x and y are in meters and t is in seconds. Determine for this wave the (a) amplitude, (b) angular frequency, (c) angular wave number, (d) wavelength, (e) wave speed, and (f) direction of motion. 30. A transverse wave on a string is described by the expression 21. A 30.0-m steel wire and a 20.0-m copper wire, both with 1.00-mm diameters, are connected end to end and are stretched to a tension of 150 N. How long does it take a transverse wave to travel the entire length of the two wires? 22. A series of pulses, each of amplitude 0.150 m, are sent down a string that is attached to a post at one end. The pulses are reﬂected at the post and travel back along the string without loss of amplitude. What is the displacement at a point on the string where two pulses are crossing (a) if the string is rigidly attached to the post? (b) if the end at which reﬂection occurs is free to slide up and down? 50.3t ) At a certain instant, let point A be at the origin and point B be the ﬁrst point along the x axis where the wave is 60.0° out of phase with point A. What is the coordinate of point B ? 27. 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 wave pulses along the wire. 28. A sinusoidal wave traveling in the x direction (to the left) has an amplitude of 20.0 cm, a wavelength of 35.0 cm, and a frequency of 12.0 Hz. The displacement of the wave at t 0, x 0 is y 3.00 cm; at this same point, a particle of the medium has a positive velocity. (a) Sketch the wave at t 0. (b) Find the angular wave number, period, angular frequency, and wave speed of the wave. (c) Write an expression for the wave function y (x, t ). 29. A sinusoidal wave train is described by the equation D L 4 (15.0 cm) cos(0.157x y WEB (0.120 m) sin( x/8 4 t) (a) Determine the transverse speed and acceleration of the string at t 0.200 s for the point on the string located at x 1.60 m. (b) What are the wavelength, period, and speed of propagation of this wave? 31. (a) Write the expression for y as a function of x and t for a sinusoidal wave traveling along a rope in the negative x direction with the following characteristics: A 8.00 cm, 80.0 cm, f 3.00 Hz, and y(0, t ) 0 at t 0. (b) Write the expression for y as a function of x and t for the wave in part (a), assuming that y(x, 0) 0 at the point x 10.0 cm. 32. A transverse sinusoidal wave on a string has a period T 25.0 ms and travels in the negative x direction with a speed of 30.0 m/s. At t 0, a particle on the string...
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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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