Download presentation

Presentation is loading. Please wait.

Published byNatalia St. ives Modified over 2 years ago

2
Physics 151: Lecture 35, Pg 1 Physics 151: Lecture 35 Today’s Agenda l Topics çWaves on a string çSuperposition çPower

3
Physics 151: Lecture 35, Pg 2 Review: Wave Properties... The speed of a wave (v) is a constant and depends only on the medium, not on amplitude (A), wavelength ( or period (T). remember : T = 1/ f and T = 2 / and T are related ! l Travleing 1-D wave: y(x,t):

4
Physics 151: Lecture 35, Pg 3 Bats can detect small objects such as insects that are of a size on the order of a wavelength. If bats emit a chirp at a frequency of 60 kHz and the speed of soundwaves in air is 330 m/s, what is the smallest size insect they can detect ? a.1.5 cm b.5.5 cm c. 1.5 mm d.5.5 mm e.1.5 um f.5.5 um Example

5
Physics 151: Lecture 35, Pg 4 Write the equation of a wave, traveling along the +x axis with an amplitude of 0.02 m, a frequency of 440 Hz, and a speed of 330 m/sec. A.y = 0.02 sin [880 (x/330 – t)] b.y = 0.02 cos [880 x/330 – 440t] c.y = 0.02 sin [880 (x/330 + t)] d.y = 0.02 sin [2 (x/330 + 440t)] e.y = 0.02 cos [2 (x/330 - 440t)] Example

6
Physics 151: Lecture 35, Pg 5 For the transverse wave described by y = 0.15 sin [ (2x - 64 t)/16] (in SI units), determine the maximum transverse speed of the particles of the medium. a. 0.192 m/s b. 0.6 m/s c. 9.6 m/s d. 4 m/s e. 2 m/s Example

7
Physics 151: Lecture 35, Pg 6 Lecture 34, Act 4 Wave Motion l A heavy rope hangs from the ceiling, and a small amplitude transverse wave is started by jiggling the rope at the bottom. l As the wave travels up the rope, its speed will: (a) increase (b) decrease (c) stay the same v l Can you calcuate how long will it take for a pulse travels a rope of length L and mass m ?

8
Physics 151: Lecture 35, Pg 7 Superposition l Q: l Q: What happens when two waves “collide” ? l A: l A: They ADD together! çWe say the waves are “superposed”. see Figure 16.8 See text: 16.4 Animation-1 Animation-2

9
Physics 151: Lecture 35, Pg 8 Aside: Why superposition works l It can be shown that the equation governing waves (a.k.a. “the wave equation”) is linear. çIt has no terms where variables are squared. x = Bsin( t)+ Ccos( t) l For linear equations, if we have two (or more) separate solutions, f 1 and f 2, then Bf 1 + Cf 2 is also a solution ! l You have already seen this in the case of simple harmonic motion: linear in x !

10
Physics 151: Lecture 35, Pg 9 Superposition & Interference l We have seen that when colliding waves combine (add) the result can either be bigger or smaller than the original waves. l We say the waves add “constructively” or “destructively” depending on the relative sign of each wave. will add constructively will add destructively l In general, we will have both happening see Figure 16.8 See text: 16.4

11
Physics 151: Lecture 35, Pg 10 Superposition & Interference l Consider two harmonic waves A and B meeting. çSame frequency and amplitudes, but phases differ. l The displacement versus time for each is shown below: What does C(t) = A(t) + B(t) look like ?? A( t) B( t)

12
Physics 151: Lecture 35, Pg 11 Superposition & Interference l Add the two curves, A = A 0 cos(kx – t) B = A 0 cos (kx – t - ) l Easy, çC = A + B C = A 0 (cos(kx – t) + cos (kx – t + )) çformula cos(a)+cos(b) = 2 cos[ 1/2(a+b)] cos[1/2(a-b)] çDoing the algebra gives, C = 2 A 0 cos( /2) cos(kx – t - )

13
Physics 151: Lecture 35, Pg 12 Superposition & Interference A( t) B( t) l Consider, C = 2 A 0 cos( /2) cos(kx – t - ) C(kx- t) Amp = 2 A 0 cos( /2) Phase shift = /2

14
Physics 151: Lecture 35, Pg 13 Lecture 35, Act 1 Superposition l You have two continuous harmonic waves with the same frequency and amplitude but a phase difference of 170° meet. Which of the following best represents the resultant wave? A) E) D) C) B) Original wave (other has different phase)

15
Physics 151: Lecture 35, Pg 14 Lecture 35, Act 1 Superposition The equation for adding two waves with different frequencies, C = 2 A 0 cos( /2) cos(kx – t - /2). The wavelength (2 /k) does not change. The amplitude becomes 2A o cos( /2). With =170, we have cos(85°) which is very small, but not quite zero. Our choice has same as original, but small amplitude. D)

16
Physics 151: Lecture 35, Pg 15 Wave Power l A wave propagates because each part of the medium communicates its motion to adjacent parts. çEnergy is transferred since work is done ! l How much energy is moving down the string per unit time. (i.e. how much power ?) P See text: 16.8

17
Physics 151: Lecture 35, Pg 16 Wave Power... l Think about grabbing the left side of the string and pulling it up and down in the y direction. l You are clearly doing work since F. dr > 0 as your hand moves up and down. l This energy must be moving away from your hand (to the right) since the kinetic energy (motion) of the string stays the same. P See text: 16.8

18
Physics 151: Lecture 35, Pg 17 How is the energy moving? l Consider any position x on the string. The string to the left of x does work on the string to the right of x, just as your hand did: x x F Power P = F. v v see Figure 16-15 See text: 16.8

19
Physics 151: Lecture 35, Pg 18 Power along the string. Since v is along the y axis only, to evaluate Power = F. v we only need to find F y = -Fsin -F if is small. We can easily figure out both the velocity v and the angle at any point on the string: l If Recall sin cos for small tan x F v y vyvy dy dx See text: 16.8

20
Physics 151: Lecture 35, Pg 19 Power... l So: l But last time we showed that and See text: 16.8

21
Physics 151: Lecture 35, Pg 20 Average Power l We just found that the power flowing past location x on the string at time t is given by: l It is generally true that wave power is proportional to the speed of the wave v and its amplitude squared A 2. l We are often just interested in the average power moving down the string. To find this we recall that the average value of the function sin 2 (kx - t) is 1 / 2 and find that: See text: 16.8

22
Physics 151: Lecture 35, Pg 21 Recap & Useful Formulas: y x A l Waves on a string l General harmonic waves tension mass / length

23
Physics 151: Lecture 35, Pg 22 Lecture 35, Act 2 Wave Power l A wave propagates on a string. If both the amplitude and the wavelength are doubled, by what factor will the average power carried by the wave change ? i.e. P final /P init = X (a) 1/4 (b) 1/2 (c) 1 (d) 2 (e) 4 initial final

24
Physics 151: Lecture 35, Pg 23 3-D Representation Waves, Wavefronts, and Rays l Up to now we have only considered waves in 1-D but we live in a 3-D world. l The 1-D equations are applicable for a 3-D plane wave. l A plane wave travels in the +x direction (for example) and has no dependence on y or z, Wave Fronts RAYS

25
Physics 151: Lecture 35, Pg 24 Waves, Wavefronts, and Rays l Sound radiates away from a source in all directions. l A small source of sound produces a spherical wave. l Note any sound source is small if you are far enough away from it. 3d representation Shading represents density wave fronts rays

26
Physics 151: Lecture 35, Pg 25 Waves, Wavefronts, and Rays l Note that a small portion of a spherical wave front is well represented as a plane wave.

27
Physics 151: Lecture 35, Pg 26 Waves, Wavefronts, and Rays l If the power output of a source is constant, the total power of any wave front is constant. l The Intensity at any point depends on the type of wave.

28
Physics 151: Lecture 35, Pg 27 l You are standing 10 m away from a very loud, small speaker. The noise hurts your ears. In order to reduce the intensity to 1/2 its original value, how far away do you need to stand? Lecture 35, Act 3 Spherical Waves (a) 14 m (b) 20 m (c) 30 m (d) 40 m

29
Physics 151: Lecture 35, Pg 28 Two ropes are spliced together as shown. A short time after the incident pulse shown in the diagram reaches the splice, the ropes appearance will be that in Lecture 35, Act 4 Traveling Waves Can you determine the relative amplitudes of the transmitted and reflected waves ?

30
Physics 151: Lecture 35, Pg 29 l You are standing 0.5 m away from a very large wall hanging speaker. The noise hurts your ears. In order to reduce the intensity you walk back to 1 m away. What is the ratio of the new sound intensity to the original? Lecture 35, Act 3b Plane Waves (a) 1 (b) 1/2 (c) 1/4 (d) 1/8 speaker 1 m

31
Physics 151: Lecture 35, Pg 30 Recap of today’s lecture l Chapter 16 çWaves on a string çSuperposition çPower

Similar presentations

Presentation is loading. Please wait....

OK

Sound Physics 202 Professor Lee Carkner Lecture 9.

Sound Physics 202 Professor Lee Carkner Lecture 9.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on ramayana in sanskrit Ppt on earth movements and major landforms in mexico Ppt on avalanche photodiode detector Ppt on direct broadcasting satellite Ppt on fibonacci numbers Ppt on group 14 elements Ppt on online examination system project in java Ppt on small business plan Ppt on computer graphics notes Ppt on limits and continuity worksheets