Exam Results, HW4 reminder Exam: Class average = 14.1/20 ( at B/BC boundary) Exam scores posted this afternoon on Learn@UW Exam solutions will be posted on course web page HW3 (short) assigned at WileyPLUS - waves! Due Tuesday, Feb. 20 midnite COUNT 10 8 6 4 PHYSICS 107 EXAM 1 B B 2 B B C A A B A A D D D C C C F B A 0 0 2 4 6 8 10 12 14 16 18 20 SCORE Average Average at the B/BC boundary Exam Results Friday, Feb. 16 Phy107 Lecture 11 1 Friday, Feb. 16 Phy107 Lecture 11 2 Today: waves Have talked about Newton s laws, motion of particles, momentum, energy, etc. Basically a description of things that move. Waves are a different type of object They move (propagate), but in a different way Examples: Waves on a rope Sound waves Water waves Stadium wave! Wave Motion A wave is a sort of motion But unlike motion of particles A propagating disturbance The rope stays in one place The disturbance moves down the rope Friday, Feb. 16 Phy107 Lecture 11 3 Friday, Feb. 16 Phy107 Lecture 11 4 What is moving? Mechanical waves require: Some source of disturbance A medium that can be disturbed Some physical connection between or mechanism though which adjacent portions of the medium influence each other Waves move at a velocity determined by the medium The disturbance in the medium moves through the medium. Energy moves down the rope. Motion of a piece of the rope As the wave passes through, a piece of the rope vibrates up and down. As the pulse passes, there is kinetic energy of motion. Friday, Feb. 16 Phy107 Lecture 11 5 Friday, Feb. 16 Phy107 Lecture 11 6 1
Energy transport Moving rope sections have some energy of motion (kinetic). If rope section is not moving, kinetic energy is zero. Determine motion by looking at rope position at two different times. Zero velocity Zero velocity How does the wave travel Energy is transmitted down the rope Each little segment of rope at position x has some mass m(x), and moves at a velocity v(x), and has kinetic energy 1 2 m(x)v(x)2 Time=1.0 Time=1.1 sec Positive and negative velocities Friday, Feb. 16 Phy107 Lecture 11 7 Friday, Feb. 16 Phy107 Lecture 11 8 Waves on a whip Kinetic energy (1/2)mass x (velocity) 2 is transported down rope as wave pulse moves. Suppose the rope gradually tapers along its length. The wave pulse A. speeds up B. slows down C. keeps same speed Whip tapers from handle to tip, so that wave velocity increases. The forward crack The loop travels at velocity c, whereas a material point on top of the loop moves at velocity 2c. Friday, Feb. 16 Phy107 Lecture 11 9 Friday, Feb. 16 Phy107 Lecture 11 10 Wave on a whip Wave on a towel Numerical solutions of a realistic whip (a) Initial loop (b) whip when the tip reaches the fastest velocity (c) whip at time t=0.02 s Crack occurs as tip breaks sound barrier! Friday, Feb. 16 Phy107 Lecture 11 11 Towel tip breaks sound barrier on a good crack Friday, Feb. 16 Phy107 Lecture 11 12 2
How does the pulse propagate? Wave speed Think of balls and springs The speed of sound is higher in solids than in gases The molecules in a solid interact more strongly, elastic property larger The speed is slower in liquids than in solids Liquids are softer, elastic property smaller Speed of waves on a string Tension Mass per unit length Friday, Feb. 16 Phy107 Lecture 11 13 Friday, Feb. 16 Phy107 Lecture 11 14 Two ropes of different mass/length. On which does the pulse propagate fastest? A. Heavier rope B. Lighter rope C. Both the same Waves can reflect Whenever a traveling wave reaches a boundary, some or all of the wave is reflected Like a particle, it bounces back. But When it is reflected from a fixed end, the wave is inverted Friday, Feb. 16 Phy107 Lecture 11 15 Friday, Feb. 16 Phy107 Lecture 11 16 Magical waves Two pulses are traveling in opposite directions The net displacement when they overlap is the sum of the displacements of the pulses Note that the pulses are unchanged after the passing through each other Wave summary 1) Energy transfer along the direction of propagation. 2) Speed is characteristic of the medium elastic properties and inertia (mass) density 3) obey the principle of superposition - two superposed disturbances add or subtract Friday, Feb. 16 Phy107 Lecture 11 17 Friday, Feb. 16 Phy107 Lecture 11 18 3
Types of waves Wave on a rope was a transverse wave Transverse wave: each piece of the medium moves perpendicular to the wave propagation direction Longitudinal Waves In a longitudinal wave, the elements of the medium undergo displacements parallel to the motion of the wave A longitudinal wave is also called a compression wave Friday, Feb. 16 Phy107 Lecture 11 19 Friday, Feb. 16 Phy107 Lecture 11 20 Graph of longitudinal wave A longitudinal wave can also be represented as a graph Compressions correspond to crests and stretches correspond to troughs Here is a sound wave. It is a A. Transverse wave B. Longitudinal wave C. Mixed longitudinal and transverse Friday, Feb. 16 Phy107 Lecture 11 21 Friday, Feb. 16 Phy107 Lecture 11 22 Many waves continuously repeat Amplitude: maximum displacement of string above equilibrium Wavelength, λ: distance between two successive points that behave identically Periodic waves Amplitude Snapshot in time Period and frequency of a wave Period: time required to complete one cycle Unit = seconds Frequency = 1/Period = rate at which cycles are completed Units are cycles/sec = Hertz For instance, the distance between two crests Friday, Feb. 16 Phy107 Lecture 11 23 Friday, Feb. 16 Phy107 Lecture 11 24 4
Moving wave crests Period = 1 second Propagation speed = v Same period, slower wave velocity Period = 1 second Propagation speed = v/2 Friday, Feb. 16 Phy107 Lecture 11 25 Friday, Feb. 16 Phy107 Lecture 11 26 Freq., wavelength, velocity are related Period: Time interval between crests at some location, or Time for source to emit once cycle of the wave. Wavelength: Spatial distance between crests. Source emits a crest once every period T. This crest propagates at velocity v. By the time the source emits another crest T seconds later, the first crest has moved vt. So the distance between crests is vt. This is the wavelength of the wave Wavelength = velocity period Friday, Feb. 16 Phy107 Lecture 11 27 Equation form Velocity = Wavelength / Period v = λ / T, or v = λf f = Frequency = 1 / Period = 1/T Friday, Feb. 16 Phy107 Lecture 11 28 A sound wave is traveling through air when in encounters a large helium-filled balloon. The sound velocity inside the balloon is greater than in the air. Compare the wavelength of the sound wave inside and outside the balloon. A. λ inside = λ outside B. λ inside > λ outside λ 0 λ 1 C. λ inside < λ outside The frequency inside the balloon is the same as outside. Use λ = v / f to find that the wavelength is less λ = v / f Friday, Feb. 16 Phy107 Lecture 11 29 5