Wave Properties

What do you think? Consider different types of waves, such as water waves, sound waves, and light waves. What could be done to increase the speed of any one of these waves? Consider the choices below. Change the size of the wave? If so, in what way? Change the frequency of the waves? If so, in what way? Change the material through which the wave is traveling? If so, in what way? When asking students to express their ideas, you might try one of the following methods. (1) You could ask them to write their answers in their notebook and then discuss them. (2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups. The most important aspect of eliciting student’s ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally. One common student idea is that changing the size (amplitude) of the wave will affect the speed. If this is mentioned, ask them why it will change the speed and in what way (i.e. Do bigger waves move faster or slower?). Others may expect frequency to affect the speed. Ask them to clarify why they believe that to be true. Facilitate a discussion between those that think one of these factors will affect the speed and those that do not think so.

Wave Motion A wave is a disturbance that propagates through a medium. What is the meaning of the three italicized terms? Apply each word to a wave created when a child jumps into a swimming pool. Mechanical waves require a medium. Electromagnetic waves (light, X rays, etc.) can travel through a vacuum. A disturbance is a change from equilibrium position. This occurs when the child pushes down on the water. Propagates means that the wave continues to travel outward from the disturbance. This occurs as the wave moves toward the other side of the pool. The medium is the material through which the wave travels. In this case, it is the water. Be sure students understand that “through a vacuum” means that no medium is required.

Wave Types The wave shown is a pulse wave. Starts with a single disturbance Repeated disturbances produce periodic waves.

Wave Types If a wave begins with a disturbance that is SHM, the wave will be a sine wave. If the wave in the diagram is moving to the right, in which direction is the red dot moving in each case? Students may struggle and think, for example, in (a) that the red point is moving downward because it looks like it is going “downhill.” Help them visualize where the rope will be in the next instant. Answers: moving upward (b) stopped but will move downward (c) moving downward (d) stopped but will move upward

Transverse Waves A wave in which the particles move perpendicular to the direction the wave is traveling The displacement-position graph below shows the wavelength () and amplitude (A). particle motion Ask students to draw the wave on the left, and to identify in their diagrams the directions of wave motion (a horizontal line) and particle motion (a vertical line). Point out to students that, even though the graph on the right looks like the wave, it is really the measured values for displacement as a function of position. This is important because a subsequent slide will show a longitudinal wave and a graph of density-position, and that graph does not look at all like the wave. Instead, it looks like a transverse wave. It is important that students understand what is being graphed, and that graphs are mathematical models rather than pictoral representations. wave direction

Transverse Wave Click below to watch the Visual Concept. file:///F file:///F:/Honors%20Physics/Topics/T8-Vibrations%20and%20Waves/videos/70355.html

Longitudinal Wave A wave in which the particles move parallel to the direction the wave is traveling. Sometimes called a pressure wave In your notes, sketch a graph of density vs. position for the spring shown below. After the white rectangle appears on the slide, do not click again until after students have had a chance to draw the graph. At that point, click again to reveal the graph for students. To help students draw the graph, you might show the axis for density and position (it is covered in the diagram to hide the answer). Point out to students that even though the graph looks “transverse,” is really just a mathematical model of the density of the longitudinal wave. It is a good idea to show students both types of waves on a slinky after discussing the definitions of the waves. The spring is most dense (or compressed) at x1 and x3, while it is least dense at x2 and x4. In the next chapter, students will find that sound waves are longitudinal. Later they will study the properties of light waves, which are transverse. particle motion wave direction

Longitudinal Wave Click below to watch the Visual Concept. file:///F:/Honors%20Physics/Topics/T8-Vibrations%20and%20Waves/videos/70356.html

Wave Speed Use the definition of speed to determine the speed of a wave in terms of frequency and wavelength: A wave travels a distance of one wavelength (l) in the time of one period (T), so Because frequency is inversely related to period: Have students work through the derivation before showing them the steps on this slide. The next slide explores this equation in more detail.

Wave Speed SI unit: s-1  m = m/s The speed is constant for any given medium. If f increases,  decreases proportionally. Wavelength () is determined by frequency and speed. Speed only changes if the medium changes. Hot air compared to cold air Deep water compared to shallow water Point out that speed is not in any way dependent on the amplitude. Also, even though the equation makes it appear that speed depends on frequency, it does not. Increasing the frequency does NOT change the speed. Instead, it decreases the wavelength so that the speed remains constant. Students should note that at an outdoor concert, they hear all the instruments at the same time even though they are producing different frequencies and amplitudes. The web site listed below has an excellent simulation of transverse waves. http://phet-web.colorado.edu/web-pages/index.html Choose “Go To Simulations” then choose “Waves and Sound” then “Wave on a string.” Set the simulation for “No End” to avoid reflections and “oscillate” to produce a periodic wave. Turn off damping. Adjust the tension to the center and frequency to 15 so the waves move more slowly and it is easier for students to observe: (1) The particles move up and down in SHM while the wave moves to the right. (2) Increasing the amplitude does not change the wave speed or the wavelength. (Try different amplitudes and observe the speed.) (3) Increasing the frequency does not change the speed but does decrease the wavelength. (Try increasing the frequency and observe the speed and wavelength.)

Characteristics of a Wave Click below to watch the Visual Concept. Visual Concept

Waves Transfer Energy Waves transfer energy from one point to another while the medium remains in place. A diver loses his KE when striking the water but the wave carries the energy to the sides of the pool.

Waves Transfer Energy Wave energy depends on the amplitude of the wave. Energy is proportional to the square of the amplitude. If the amplitude is doubled, by what factor does the energy increase? Answer: by a factor of four

Now what do you think? Consider different types of waves, such as water waves, sound waves, and light waves. What could be done to increase the speed of any one of these waves? Consider the choices below. Change the size of the wave? If so, in what way? Change the frequency of the waves? If so, in what way? Change the material through which the wave is traveling? If so, in what way? When asking students to express their ideas, you might try one of the following methods. (1) You could ask them to write their answers in their notebook and then discuss them. (2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups. The most important aspect of eliciting student’s ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally. One common student idea is that changing the size (amplitude) of the wave will affect the speed. If this is mentioned, ask them why it will change the speed and in what way (i.e. Do bigger waves move faster or slower?). Others may expect frequency to affect the speed. Ask them to clarify why they believe that to be true. Facilitate a discussion between those that think one of these factors will affect the speed and those that do not think so.