Figure 16. 1 A pulse traveling down a stretched rope Figure 16.1  A pulse traveling down a stretched rope. The shape of the pulse is approximately unchanged as it travels along the rope. Fig. 16.1, p.488

Figure 16. 2 A transverse pulse traveling on a stretched rope Figure 16.2  A transverse pulse traveling on a stretched rope. The direction of motion of any element P of the rope (blue arrows) is perpendicular to the direction of wave motion (red arrows). Fig. 16.2, p.488

Figure 16. 3 A longitudinal pulse along a stretched spring Figure 16.3  A longitudinal pulse along a stretched spring. The displacement of the coils is in the direction of the wave motion. Each compressed region is followed by a stretched region. Fig. 16.3, p.488

Active Figure 16.4  The motion of water elements on the surface of deep water in which a wave is propagating is a combination of transverse and longitudinal displacements, with the result that elements at the surface move in nearly circular paths. Each element is displaced both horizontally and vertically from its equilibrium position. Fig. 16.4, p.489

y = f (x – vt) Figure 16.5  A one-dimensional pulse traveling to the right with a speed v. (a) At t = 0, the shape of the pulse is given by y = f(x). (b) At some later time t, the shape remains unchanged and the vertical position of an element of the medium any point P is given by y = f(x – vt). Fig. 16.5, p.489

Figure 16. 6 Graphs of the function y(x, t) = 2/[(x – 3 Figure 16.6  Graphs of the function y(x, t) = 2/[(x – 3.0t)2 +1] at (a) t = 0, (b) t = 1.0 s, and (c) t = 2.0 s. Fig. 16.6, p.491

Active Figure 16.7  A one-dimensional sinusoidal wave traveling to the right with a speed v. The red curve represents a snapshot of the wave at t = 0, and the blue curve represents a snapshot at some later time t. At the Active Figures link at http://www.pse6.com, you can watch the wave move and take snapshots of it at various times. Fig. 16.7, p.491

Active Figure 16.8  (a) The wavelength  of a wave is the distance between adjacent crests or adjacent troughs. (b) The period T of a wave is the time interval required for the wave to travel one wavelength. At the Active Figures link at http://www.pse6.com, you can change the parameters to see the effect on the wave function. Fig. 16.8, p.492

Active Figure 16.10  One method for producing a sinusoidal wave on a string. The left end of the string is connected to a blade that is set into oscillation. Every element of the string, such as that at point P, oscillates with simple harmonic motion in the vertical direction. At the Active Figures link at http://www.pse6.com, you can adjust the frequency of the blade. Fig. 16.10, p.495

Active Figure 16.10  One method for producing a sinusoidal wave on a string. The left end of the string is connected to a blade that is set into oscillation. Every element of the string, such as that at point P, oscillates with simple harmonic motion in the vertical direction. At the Active Figures link at http://www.pse6.com, you can adjust the frequency of the blade. Fig. 16.10a, p.495

Active Figure 16.10  One method for producing a sinusoidal wave on a string. The left end of the string is connected to a blade that is set into oscillation. Every element of the string, such as that at point P, oscillates with simple harmonic motion in the vertical direction. At the Active Figures link at http://www.pse6.com, you can adjust the frequency of the blade. Fig. 16.10b, p.495

Active Figure 16.10  One method for producing a sinusoidal wave on a string. The left end of the string is connected to a blade that is set into oscillation. Every element of the string, such as that at point P, oscillates with simple harmonic motion in the vertical direction. At the Active Figures link at http://www.pse6.com, you can adjust the frequency of the blade. Fig. 16.10c, p.495

Active Figure 16.10  One method for producing a sinusoidal wave on a string. The left end of the string is connected to a blade that is set into oscillation. Every element of the string, such as that at point P, oscillates with simple harmonic motion in the vertical direction. At the Active Figures link at http://www.pse6.com, you can adjust the frequency of the blade. Fig. 16.10d, p.495

Figure 16.11  (a) To obtain the speed v of a wave on a stretched string, it is convenient to describe the motion of a small element of the string in a moving frame of reference. (b) In the moving frame of reference, the small element of length ∆s moves to the left with speed v. The net force on the element is in the radial direction because the horizontal components of the tension force cancel. Fig. 16.11, p.497

Figure 16.12  The tension T in the cord is maintained by the suspended object. The speed of any wave traveling along the cord is given by v = √T/μ. Fig. 16.12, p.498

Figure 16.13  If the block swings back and forth, the tension in the cord changes, which causes a variation in the wave speed on the horizontal section of cord in Figure 16.12. The forces on the block when it is at arbitrary position B are shown. Position A is the highest position and C is the lowest. (The maximum angle is exaggerated for clarity.) Fig. 16.13, p.498

Active Figure 16.14  The reflection of a traveling pulse at the fixed end of a stretched string. The reflected pulse is inverted, but its shape is otherwise unchanged. Fig. 16.14, p.499

Active Figure 16.15  The reflection of a traveling pulse at the free end of a stretched string. The reflected pulse is not inverted. Fig. 16.15, p.500

Figure 16.16  (a) A pulse traveling to the right on a light string attached to a heavier string. (b) Part of the incident pulse is reflected (and inverted), and part is transmitted to the heavier string. See Figure 16.17 for an animation available for both figures at the Active Figures link. Fig. 16.16, p.500

Active Figure 16.17  (a) A pulse traveling to the right on a heavy string attached to a lighter string. (b) The incident pulse is partially reflected and partially transmitted, and the reflected pulse is not inverted. At the Active Figures link at http://www.pse6.com, you can adjust the linear mass densities of the strings and the transverse direction of the initial pulse. Fig. 16.17, p.500

Figure 16.18 (a) A pulse traveling to the right on a stretched string that has an object suspended from it. (b) Energy is transmitted to the suspended object when the pulse arrives. Fig. 16.18, p.501

Figure 16.18 (a) A pulse traveling to the right on a stretched string that has an object suspended from it. Fig. 16.18a, p.501

Figure 16.18 (b) Energy is transmitted to the suspended object when the pulse arrives. Fig. 16.18b, p.501

Figure 16.19 A sinusoidal wave traveling along the x axis on a stretched string. Every element moves vertically, and every element has the same total energy. Fig. 16.19, p.501

Figure 16.20  An element of a string under tension T. Fig. 16.20, p.503