PHYSICS 220 Lecture 19 Waves What is a Wave A wave is a disturbance that travels away from its source and carries energy. A wave can transmit energy from one point to another without transporting any matter between the two points. Examples: Stadium waves (people move up & down) Water waves (water moves up & down) Sound waves (air moves back & forth) Seismic waves (earth moving up & down) Electromagnetic waves (what moves??) Lecture 19 Purdue University, Physics 220 1 Lecture 19 Purdue University, Physics 220 2 Why are Waves Important? Transport energy from one place to another Electromagnetic waves transport energy (electromagnetic energy in the form of light) from the Sun to the Earth. Sound waves transport energy from speakers to our ear drums. In waves, energy is transported over large distances, but matter is not. Power The power carried by a wave equals the energy emitted by the source (and carried away by the wave) per unit time. [watts]=[joules/second] Lecture 19 Purdue University, Physics 220 3 Lecture 19 Purdue University, Physics 220 4
Intensity Average power per unit area carried by the wave past a surface which is perpendicular to the direction of propagation of the wave. For spherical waves, the intensity decreases with distance: I = P 4!r 2 Plane wave Light produced by laser good example Intensity does not change with distance from the source. Unit: W/m 2 I! A 2 Lecture 19 Purdue University, Physics 220 5 Lecture 19 Purdue University, Physics 220 6 Demo 1S - 16 For frequency watch one point For wavelength look at one time Types of Waves Transverse: The medium oscillates perpendicular to the direction the wave is moving. Water (more or less) Slinky Circular waves --- water waves Longitudinal waves --- sound Transverse -- light For velocity watch one peak Longitudinal: The medium oscillates in the same direction as the wave is moving. Sound Slinky Lecture 19 Purdue University, Physics 220 8
http://www.youtube.com/watch?v=g49mahyengc&feature =related Waves on a String http://www.youtube.com/watch?v=uhcse1jjato&feature= related http://www.youtube.com/watch?v=agucwnbretu&featur e=related http://www.youtube.com/watch?v=xa5xw0sgn_i&featu re=related velocity = T µ µ = linear mass density = m L T = Tension Lecture 19 Purdue University, Physics 220 9 Lecture 19 Purdue University, Physics 220 10 Question Suppose that a longitudinal wave moves along a Slinky at a speed of 5 m/s. Does one coil of the slinky move through a distance of five meters in one second? A) Yes B) No y(x,t) = A sin("t kx) A = Amplitude= Maximum displacement of a point on the wave # =Wavelength: Distance between identical points on the wave T=Period: Time for a point on the wave to undergo one complete oscillation. f = frequency =1/T " = angular frequency= 2$/T k = wave number = 2$/# Harmonic Waves v =! T =! f = " k Lecture 19 Purdue University, Physics 220 11 Lecture 19 Purdue University, Physics 220 12
Period and Velocity! Period: The time T for a point on the wave to undergo one complete oscillation.! Speed: The wave moves one wavelength # in one period T so its speed is v = # / T. v =! T =! f = ( 2" f )! 2" = # k Lecture 19 Purdue University, Physics 220 13 Harmonic Waves Exercise y(x,t) = A cos("t kx) Label axis and tic marks for a graph showing an observation of the wave y(x,t) = 2 cos(4t 2x) at x=0. Recall: T = 2 $ /" What is the period of this wave? T = 2 $ / " = 2 $/ 4 = 1.58 s +2-2 $/4 3$/4 $ / 2 Lecture 19 Purdue University, Physics 220 14 t What is the velocity of this wave? v = "/k= 4/2 m/s=2m/s Wave Properties Wave Description The speed of a wave is a constant that depends only on the medium, not on amplitude, wavelength or period (similar to SHM) # and T are related! # = v T or # = 2$ v / " (since T = 2$ / " ) or # = v / f (since T = 1/ f ) Recall f = cycles/sec or revolutions/sec " = 2$f = radians/second Intensity I! A 2 v = # / T # wavelength: distance between crests (meters) T period: the time between crests passing fixed location (seconds) v speed: the distance one crest moves in a second (m/s) f frequency: the number of crests passing fixed location in one second (1/s or Hz) " angular frequency: =2$f (rad/s) v =! T f = 1 T v =! f Lecture 19 Purdue University, Physics 220 15 Lecture 19 Purdue University, Physics 220 16
Direction y(x,t) = Acos(!t " kx) A wave y = A cos("t - kx) travels in +x direction A wave y = A cos("t + kx) travels in -x direction %t Exercise The wavelength of microwaves generated by a microwave oven is about 3 cm. At what frequency do these waves cause the water molecules in your burrito to vibrate? A) 1 GHz B) 10 GHz C) 100 GHz k! 1 "! " 1 T!t " kx = const!#t " k#x = 0 #x #t =! k 1 GHz = 10 9 cycles/sec The speed of light is c = 3x10 8 m/s Lecture 19 Purdue University, Physics 220 17 Lecture 19 Purdue University, Physics 220 18! Recall that v = #f H H Exercise f = v! = 3 " 108 m s.03m = 10 10 Hz = 10GHz Makes water molecules wiggle Superposition Principle When two or more waves pass through the same region the actual displacement is the sum of the separate displacements. y!(x,t) = y 1 (x,t) + y 2 (x,t) If two waves pass through the same region they continue to move independently. O 1 GHz = 10 9 cycles/sec The speed of light is c = 3x10 8 m/s Lecture 19 Purdue University, Physics 220 19 Lecture 19 Purdue University, Physics 220 20
Superposition Mathematical Description y(x,t) = A cos("t kx) Wavelength: The distance # between identical points on the wave. Amplitude: The maximum displacement A of a point on the wave. Angular Frequency ": " = 2 $ f Wave Number k: k = 2 $ / # Recall: f = v / # y Wavelength # Amplitude A A x Lecture 19 Purdue University, Physics 220 21 Lecture 19 Purdue University, Physics 220 22 Wave Speed y(x,t) = Acos(!t " kx) Phase:!t " kx = const!#t " k#x = 0 #x #t =! k = v A wave y = A cos("t - kx) travels in +x direction A wave y = A cos("t + kx) travels in -x direction Lecture 19 Purdue University, Physics 220 23