1Chapter 19Vibrations and Waves22Wave Description• Amplitude – the distance from the midpoint to crest (or trough) of the wave; the maximum displacement of the wave• Wavelength – the distance from the top of one crest to the next one• Frequency – the number of wavelengths in a unit of time– Unit – Hz (1/s)period1Frequency =• Waves can transfer energy from a source to a receiver without the transfer of matterWavelength can also be measure from trough to trough.33Wave Speed• The speed of a wave is related to both its period (1/frequency) and wavelength•Recall:• The wavelength is a measure of distance, and its period is the measure of how long it takes a crest to move the distance of one wavelength•Therefore:timedistancespeed =frequency*wavelengthperiodwavelengthspeed ==44Problem Solving: Wave Speed• What is the frequency of a wave if 25 crests pass you in 5 seconds? What is its period?• If this same wave has a wavelength of 0.25 m, what is the speed of the wave?s 2.0frequency1 period Hz 5s 5 waves25 frequency ==== m/s 1.25 Hz) m)(5 25.0( frequency *h wavelengt speed===55Transverse Wave• If you move a string up and down, you create a wave the moves left or right• Any wave whose amplitude is at a right angle (transverse) to the direction the wave moves is a transverse waveThe animation in this slide shows one transverse wave moving the the right. It will hit the fixed dot and reflect back to the left. The point here is to observe that the shape of the wave is at a right angle to the wave’s direction of motion.66Longitudinal Waves• Any wave whose amplitude is in the same direction as the wave’s propagation is called a longitudinal waveThe first animation here with springs shows that a compression moves from left to right. Since this wave’s amplitude is measured along the wave’s direction of motion, this is a longitudinal wave.The other 2 animations shows how a transverse wave in a guitar string creates compressions in the air. This is sounds and it is a longitudinal wave. The sound then travels to our ear drum where it makes another transverse wave.77Interference• When two waves run into each other they add together– Constructive – two waves interfere to make one larger wave– Destructive – two waves interfere to make one smaller (or no) wave• The waves will reemerge with the same shape they went inThe next slide shows some nice examples of these bullets.88InterferenceThe top three plots shows that 2 crests or 2 troughs will constructively interfere and make a wave with a larger amplitude. How when a crest meets a trough, the 2 will cancel out to no wave (but just momentarily).The bottom plot shows that after 2 waves are done interfering, the 2 waves will emerge unaffected as though they never ran into each other.99Doppler Effect• A moving sound source catches up to its own forward wave fronts –this increases its frequency•The source is also running away from the backward wave fronts –this lowers the frequencyDoppler Shift SimulationThe link here goes to a nice physics flashlet on the Doppler Effect (the link should work even in pdf format, if not go here: http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/doppler.htm).1010Problem Solving: Doppler Effect• The Doppler effect also applies when an observer is moving and the sound source is at rest. How does the frequency of the sound change when you are moving toward the sound? Away?–If you are moving toward a source, you will hit the wave fronts faster, so the frequency will sound higher. If you are moving away, each wave front must travel a little more than the one before to hit you, so the frequency sounds lower.1111Bow Waves• Bow waves are formed when the wave fronts from a source are moving faster than sound• The wave fronts will build up and form a V shape behind the object• This is what caused the “sound barrier”The bow wave is created by the interference of sound with itself (this can only happen when the sound source is moving faster than the speed of sound).1212Shock Waves• A shock wave is a 3D bow wave (so it is a cone instead of a V)• The shock wave has 2 parts, a high pressure part from the tip of the plane and a low pressure part from the tail of the plane• This variation of pressure causes the sound known as a sonic boom1313An F-14 Breaks the Sound BarrierThis is a movie showing an F-14 breaking the sound barrier. You could see the shock waves because they cause rapid expansion of the air right behind the wave and this causes that water in the air to condense and make the shock wave