Physics 102 Waves Moza M. Al-Rabban Professor of Physics Lecture 3 Traveling Waves

2 Traveling Waves The Goal is to learn the basic properties of traveling waves. You will learn to: Use the wave model and understand how it differs from the particle model. Understand how a wave travels through a medium. Recognize the properties of sinusoidal waves. Understand the important characteristics of sound and light waves. Use the Doppler effect to find the speed of wave sources and observers.

3 The Wave Model We will focus on the basic properties of waves using the wave model, which emphasizes the aspects on wave behavior common to all waves (e.g., water waves, sound waves, light waves, etc.) The wave model is built around the idea of traveling waves, wave disturbances that travel with a well-defined speed. We will begin by distinguishing three types of waves: 1.Mechanical waves can travel only within a medium, such as air or water. Examples: sound waves, water waves. 2.Electromagnetic waves are self-sustaining oscillations that require no medium and can travel through a vacuum. Examples: radio waves, microwaves, light, x-rays, gamma rays, etc. 3.Matter waves also can travel in vacuum and are the basis for quantum physics (i.e. quantum mechanics). Examples: quantum wave functions for electrons, photons, atoms, etc.

4 The medium of a mechanical wave is the substance through or along which the wave moves. For example, the medium of water waves is the water, the medium of a sound is the air, and the medium of a wave on a stretched string is the string. A medium must be elastic. The Disturbance of the medium. A wave disturbance is created by a source.

5 Waves and Energy Transport The disturbance propagates through the medium, and a wave does transfer energy, but the medium as a whole does not move! KE of the pebble just before hits the pond is partly converted into the energy carried off by water wave….. A wave transfers energy, but does not transfer any material or substance outward from the source. PHYSICS AT HOME Stretch a heavy rope between yourself and a friend and test out the transfer of energy from one to the other by sending wave pulses down the rope. Can you feel the energy transfer when the pulse arrives?

6 Two Types of Wave Motion A transverse wave is a wave in which the particles of the medium move perpendicular to the direction of wave motion. They can be polarized. Examples: waves on a string, electromagnetic waves. A longitudinal wave is a wave in which the particles of the medium move parallel to the direction of wave motion. They cannot be polarized. Example: sound waves.

7 Water Waves Water waves are a combination of transverse and longitudinal motion, because each particle of water participating in the wave motion travels in a circular path as the wave propagates. The particles stay in the same average position as the waves move to the right.

8 Traveling Waves Wave speed depends on the restoring forces in the medium. It does not depend on pulse size, shape, generation method, or distance traveled.

9 Waves on a String String linear density:  = m/L Example:

10 Waves on a String Waves on a string are produced by transverse motion of each particle of the string, participating in the wave motion by moving in a vertical path as the wave propagates. Note that although the wave moves to the right, the individual particles of the string return to their original positions.

11

12

13 Example 1: Speed of a Wave Pulse A 2.0 m long string with a mass of m=4.0 g is tied to a wall at one end, stretched horizontally by a pulley 1.5 m away, then tied to a physics book hanging from the string. Experiments find that a wave pulse travels at v=40 m/s. What is the mass M b of the book? To be precise, 327 g is the combined mass of the book and the short length of the string that hangs from the pulley.

14 Snapshot Graphs We can make a series of snapshots of wave motion showing wave displacement  y at all positions at a given instant. Each snapshot shows the wave displacement vs. position for one instant of time.

15 History Graphs We can also make a “history graph” of wave motion showing the time- dependent wave displacement  y at a given position vs. time. Each history graph shows the wave displacement vs. time for a particular particle of the medium.

16 Longitudinal Waves Longitudinal waves (e.g., sound) are produced in a compressible medium by longitudinal motion of each particle of the medium, participating in the wave motion by moving in a horizontal path as the wave propagates. This produces moving regions of compression and rarefaction in the medium. Note that although the wave moves to the right, the individual particles return to their original positions.

17 Moving Displacement Suppose we wish to move a parabolic function f(x) = x 2 so that it is centered at greater and greater values of the independent variable x. Then we change x to x-2, x- 4, etc. Similarly, if we wish to displace some arbitrary function f(x) by a distance d, we replace f(x) by f(x-d). If we wish to make the displacement increase with time, i.e., move the curve with velocity v, we make d=vt, so that the function becomes f(x-vt). Similarly, to displace the function in the negative x direction, we use f(x+vt).

18 Example: A Traveling Wave Pulse Draw snapshot graphs at t=0, 1 s, and 2s to show the displacement function where x is in m and t is in s, represents a traveling wave pulse that travels in the x direction without changing shape. That is, it is a traveling wave with speed v = 2 m/s.

End of Lecture 3