Properties of Waves
Wave Motion The medium is what a wave or disturbance travels through Molecules vibrate up and down as the wave passes through The medium does not actually travel with the waves After a wave passes, the medium returns to its original position
Diagram of Wave Have you ever "done the wave" as part of a large crowd at a football or baseball game? A group of people jumps up and sits back down, some nearby people see them and they jump up, some people further away follow suit and pretty soon you have a wave travelling around the stadium. The wave is the disturbance (people jumping up and sitting back down), and it travels around the stadium. However, none of the individual people the stadium are carried around with the wave as it travels - they all remain at their seats. Longitudinal sound waves in air behave in much the same way. As the wave passes through, the particles in the air oscillate back and forth about their equilibrium positions but it is the disturbance which travels, not the individual particles in the medium. Transverse waves on a string are another example. The string is displaced up and down as the wave travels from left to right, but the string itself does not experience any net motion
Nomenclature A - Amplitude - the maximum displacement from equilibrium - Wavelength - Distance between any two successive identical points. f - Frequency - Number of cycles or oscillations per second. ( = 1/T) T - Period - Time to complete one full oscillation or cycle. (=1/f) Speed= frequency x wavelength
Parts of a Wave Crest: The highest point on the wave Trough: The lowest point on the wave
Simple Harmonic Motion A wave whose source vibrates with simple harmonic motion is called a sine wave It is called a sine wave because a graph of the trigonometric function y=sine x produces this curve when plotted
Plot of Amplitude vs. Position
Mechanical Waves Waves that require a medium are called mechanical waves Sound requires air or water to travel Light does not need a medium. It can travel through a vacuum.
Types of mechanical waves Transverse – vibrations of wave are perpendicular () to direction of wave motion Longitudinal – When the particles of a medium vibrate parallel () to direction of wave motion. Sound waves in air are longitudinal because air particles vibrate back and forth in a direction parallel to the wave motion Pulse- a wave that consists of a single traveling pulse wave Periodic- when you have more than one wave Harmonic
One, Two, & Three Dimensions One Dimension Spring / Slinky Two Dimension Ripples on water Three Dimension Sound / Earth Quake
Pulse wave A single oscillation sent through a media due to a non-repeating event. e.g. Sound from an explosion or crash. Splash from a stone dropped in water.
Periodic Wave Wave produced by an oscillation of the media which repeats with a regular period. e.g. Sound from a steady drum beat
Harmonic (Standing) Wave Created by a simple harmonic oscillations of the media. Standing waves have nodes and antinodes The resultant wave pattern does not move along the string The points at which the two waves cancel each other are called nodes Where the string vibrates with the larges amplitude is called the antinode.
Calculating Speed of a Wave v = f Speed= frequency x wavelength
Different types of waves
Wave Interactions Two different material objects can never occupy the same space at the same time. When two waves come together they do not bounce back as bumper boats. Because mechanical waves are not matter but rather the displacement of matter, who waves can occupy the same space at the same time
Displacement The combination of two overlapping waves is called superpositon. Displacement in the same direction produce constructive interference. When two waves are added together the resultant wave is larger than the individual displacements and this is constructive interference.
Destructive Interference Displacements in opposite directions produce destructive interference. When positive and negative displacements are added, the resultant wave is the difference between the pulses, this is called destructive interference.
Reflection of Waves At a free boundary, waves are reflected but not inverted At a fixed boundary, waves are reflected and inverted
Wave reflection
Reflection of a wave from a free end Animations courtesy of Paul Hewitt and borrowed from physicsclassroom.com
Reflection of a wave from a fixed end Animations courtesy of Paul Hewitt and borrowed from physicsclassroom.com
Transmission When a wave hits a surface or interface not all of the energy is reflected. Some is transmitted into the next medium. The transmitted wave is “non-inverted” and the “harder” the surface the less is transmitted.
Travel between media of different density Animations courtesy of Paul Hewitt and borrowed from physicsclassroom.com
Longitudinal Wave Animations courtesy of Paul Hewitt and borrowed from physicsclassroom.com
Standing Waves Created by the interference of two waves of the same frequency traveling in opposite directions. In a string or tube of limited length the reflections off the ends will create two traveling waves moving in opposite directions. Only certain wavelengths () will create standing waves in a string or tube of limited length . These wavelengths () correspond to frequencies (f = v/ ) called natural or resonant frequencies
Traveling Wave Animations courtesy of Paul Hewitt and borrowed from physicsclassroom.com
Standing Wave Animations courtesy of Paul Hewitt and borrowed from physicsclassroom.com
Fundamental Frequency Animations courtesy of Paul Hewitt and borrowed from physicsclassroom.com
Second Harmonic Animations courtesy of Paul Hewitt and borrowed from physicsclassroom.com
Third Harmonic Animations courtesy of Paul Hewitt and borrowed from physicsclassroom.com
Fourth Harmonic Animations courtesy of Paul Hewitt and borrowed from physicsclassroom.com
Fifth Harmonic Animations courtesy of Paul Hewitt and borrowed from physicsclassroom.com
Harmonics