VIBRATIONS AND WAVES Chapter 25

Wave Motion ■Waves consist of some sort of vibratory motion—motion that repeats itself over time. ■Examples include sound waves, visible light waves, radio waves, microwaves, water waves, sine and cosine waves, earthquake waves, waves on a string, and Slinky waves. ■A wave is a disturbance of a medium that transports energy through the medium without permanently transporting matter.

Types of Waves ■Two types of waves: –Transverse: the particles of the medium are displaced in a direction perpendicular to the direction of energy transport. (Electromagnetic waves such as visible light and microwaves are transverse waves.) –Longitudinal: the particles of the medium are displaced in a direction parallel to the direction of energy transport. (Sound waves and waves in a Slinky are examples.) ■AnimationAnimation TransverseLongitudinal

Characteristics of Waves

Frequency and Period

Wave Speed

Lab Activity ■Slinky Lab InteractiveSlinky Lab Interactive –Try different values for tension, density and damping. ■Complete and hand in slinky simulation sheet and wave properties worksheet.

Energy Transport in Waves

Boundary Behavior ■As a wave travels through a medium it may encounter a discontinuity—e.g., an obstacle or another medium. –Examples: sound waves reflecting off walls in a room, echoes in a canyon. ■Such a discontinuity is called a boundary and there are several types of wave behavior at a boundary. –Reflection –Refraction –Diffraction

Fixed End Reflection - 1 ■Assume that one end of an elastic rope is fixed. ■If an incident pulse is introduced at the left end of the rope, it will travel through the rope towards the right end of the medium. ■When the incident pulse reaches the boundary, two things occur: –A portion of the energy carried by the pulse is reflected and returns towards the left end of the rope. The disturbance that returns to the left after bouncing off the fixed end is known as the reflected pulse. Note that the reflected pulse is inverted. –A portion of the energy carried by the pulse is transmitted to the pole, causing the pole to vibrate.

Fixed End Reflection - 2 ■Some notable characteristics of the reflected pulse include: –The speed of the reflected pulse is the same as the speed of the incident pulse. –The wavelength of the reflected pulse is the same as the wavelength of the incident pulse. –The amplitude of the reflected pulse is less than the amplitude of the incident pulse. This is because some of the energy of the pulse was transmitted into the pole at the boundary.

Free End Reflection ■Suppose the end of the elastic rope were free to move. ■Unlike the fixed end case, the reflected pulse is not inverted. So an incident upward pulse is reflected as an upward pulse and a downward incident pulse is reflected as a downward pulse.

Wave Interference ■When two waves meet while traveling along the same medium they interfere with one another. ■The interference of waves causes the medium to take on a shape that results from the net effect of the two individual waves upon the particles of the medium. ■The interference may be –Constructive: the two waves have displacements in the same direction. –Destructive: the two waves have displacements in opposite directions. Constructive InterferenceDestructive Interference

Standing Waves ■Standing waves result from the interference of two or more waves in the same medium. ■Standing wave patterns are characterized by positions along the medium which are standing still. ■The positions where the medium is standing still are called nodes while the positions where the displacement is maximum are called anti-nodes. ■AnimationAnimation

Today’s Lab – 12/7 ■Experiment with this simulation: Standing Wave Maker InteractiveStanding Wave Maker Interactive ■Complete and hand in the Standing Wave Mathematics worksheet

Today’s Activities – 12/14 ■Wave on a String SimulationWave on a String Simulation –Experiment in Pulse mode with Fixed End and Loose End –Experiment with different values of Damping and Tension ■Standing Wave MakerStanding Wave Maker ■Standing WavesStanding Waves ■Standing Waves on a RopeStanding Waves on a Rope ■Waves on a StringWaves on a String