Chapter 15: Wave Motion 15-1 Characteristics of Wave Motion 15-2 Types of Waves: Transverse and Longitudinal 15-3 Energy Transported by Waves 15-4 Mathematical Representation of a Traveling Wave 15-5 The Wave Equation 15-6 The Principle of Superposition 15-7 Reflection and Transmission 15-8 Interference Chapter opener. Caption: Waves—such as these water waves—spread outward from a source. The source in this case is a small spot of water oscillating up and down briefly where a rock was thrown in (left photo). Other kinds of waves include waves on a cord or string, which also are produced by a vibration. Waves move away from their source, but we also study waves that seem to stand still (“standing waves”). Waves reflect, and they can interfere with each other when they pass through any point at the same time.

Problem 49 49. (II) The balance wheel of a watch is a thin ring of radius 0.95 cm and oscillates with a frequency of 3.10 Hz. If a torque of 1.1X10-5 Nm causes the wheel to rotate 45°, calculate the mass of the balance wheel.

14-6 The Physical Pendulum and the Torsional Pendulum A physical pendulum is any real extended object that oscillates back and forth. The torque about point O is: Substituting into Newton’s second law gives: Figure 14-16. Caption: A physical pendulum suspended from point O.

14-6 The Physical Pendulum and the Torsional Pendulum For small angles, this becomes: which is the equation for SHM, with

14-6 The Physical Pendulum and the Torsional Pendulum A torsional pendulum is one that twists rather than swings. The motion is SHM as long as the wire obeys Hooke’s law, with Figure 14-18. Caption: A torsion pendulum. The disc oscillates in SHM between θmax and –θmax . (K is a constant that depends on the wire.) For the torsional pendulum: τ=-Kθ, K depends on the stiffness of the wire

15-1 Characteristics of Wave Motion All types of traveling waves transport energy. Study of a single wave pulse shows that it is begun with a vibration and is transmitted through internal forces in the medium. Continuous or periodic waves start with vibrations, too. If the source vibrate sinusoidally, then the wave will have a sinusoidal shape. Figure 15-2. Motion of a wave pulse to the right. Arrows indicate velocity of cord particles.

Sound It Out 1) yes 2) no 3) it depends on the medium the wave is in Does a longitudinal wave, such as a sound wave, have an amplitude?  Click to add notes low high normal air pressure x A

 Sound It Out A x 1) yes 2) no 3) it depends on the medium the wave is in Does a longitudinal wave, such as a sound wave, have an amplitude?  All wave types—transverse, longitudinal, surface—have all of these properties: wavelength, frequency, amplitude, velocity, period. low high normal air pressure x A

The Wave At a football game, the “wave” might circulate through the stands and move around the stadium. In this wave motion, people stand up and sit down as the wave passes. What type of wave would this be characterized as? 1) polarized wave 2) longitudinal wave 3) lateral wave 4) transverse wave 5) soliton wave Click to add notes

The Wave At a football game, the “wave” might circulate through the stands and move around the stadium. In this wave motion, people stand up and sit down as the wave passes. What type of wave would this be characterized as? 1) polarized wave 2) longitudinal wave 3) lateral wave 4) transverse wave 5) soliton wave The people are moving up and down, and the wave is traveling around the stadium. Thus, the motion of the wave is perpendicular to the oscillation direction of the people, and so this is a transverse wave.

Wave Motion I 1) 2) 3) 4) 5) zero Consider a wave on a string moving to the right, as shown below. What is the direction of the velocity of a particle at the point labeled A ? A Click to add notes

Wave Motion I 1) 2) 3) 4) 5) zero Consider a wave on a string moving to the right, as shown below. What is the direction of the velocity of a particle at the point labeled A ? A The velocity of an oscillating particle is (momentarily) zero at its maximum displacement.

Wave Motion II 1) 2) 3) 4) 5) zero Consider a wave on a string moving to the right, as shown below. What is the direction of the velocity of a particle at the point labeled B ? B Click to add notes

Wave Motion II 1) 2) 3) 4) 5) zero Consider a wave on a string moving to the right, as shown below. What is the direction of the velocity of a particle at the point labeled B ? The wave is moving to the right, so the particle at B has to start moving upward in the next instant of time. B

15-2 Types of Waves: Transverse and Longitudinal Problem 6. (II): A cord of mass 0.65 kg is stretched between two supports 8.0 m apart. If the tension in the cord is 140 N, how long will it take a pulse to travel from one support to the other?

15-2 Types of Waves: Transverse and Longitudinal Example 15-2: Pulse on a wire. An 80.0m-long, 2.10mm-diameter copper wire is stretched between two poles. A bird lands at the center point of the wire, sending a small wave pulse out in both directions. The pulses reflect at the ends and arrive back at the bird’s location 0.750 seconds after it landed. Determine the tension in the wire. Solution: We need to find the mass per unit length of the wire; this comes from the cross-sectional area and the density of copper (8900 kg/m3). Then the tension is 353 N.