Semeser Review Session We will have a semeser review session on Wednesda, 1/10 a -4pm, here in room MPHY 03. If ou have a quesion(s ha ou would like me o go over, please drop me an email wih he problem saemen so ha I can prepare appropriael. I will spend his ime going over problems represenaive of he maerial presened in each of he chapers. Reminder our final will be held on Monda 1/15 from 3:30-5:30 here in MPHY 03. 1/4/014 Phsics 18 1
Chaper 15 Mechanical Waves
Goals for Chaper 15 To sud he properies and varieies of mechanical waves To relae he speed, frequenc, and wavelengh of periodic waves To inerpre periodic waves mahemaicall To calculae he speed of a wave on a sring To calculae he energ of mechanical waves To undersand he inerference of mechanical waves To analze sanding waves on a sring To invesigae he sound produced b sringed insrumens Coprigh 01 Pearson Educaion Inc.
Inroducion Earhquake waves carr enormous power as he ravel hrough he earh. Oher pes of mechanical waves, such as sound waves or he vibraion of he srings of a piano, carr far less energ. Overlapping waves inerfere, which helps us undersand musical insrumens. Coprigh 01 Pearson Educaion Inc.
Tpes of mechanical waves A mechanical wave is a disurbance raveling hrough a medium. Figure 15.1 below illusraes ransverse waves and longiudinal waves. Coprigh 01 Pearson Educaion Inc.
Periodic ransverse waves For he ransverse waves shown here in Figures 15.3 and 15.4, he paricles move up and down, bu he wave moves o he righ. Coprigh 01 Pearson Educaion Inc.
Periodic longiudinal waves For he longiudinal waves shown here in Figures 15.6 and 15.7, he paricles oscillae back and forh along he same direcion ha he wave moves. Follow Eample 15.1. Coprigh 01 Pearson Educaion Inc.
Describing waves NOTE: v propagaion = l / T = l f Coprigh 01 Pearson Educaion Inc.
The Wave Equaion Using F = ma on an elemen of he vibraing sring Coprigh 01 Pearson Educaion Inc.
The Wave Equaion Coprigh 01 Pearson Educaion Inc.
The Wave Equaion for (, T hesoluions for (,are f(-/v and g( /v wih v T Coprigh 01 Pearson Educaion Inc.
The soluions o he Wave Equaion wha do he look like??? Coprigh 01 Pearson Educaion Inc. Phsics 08 1
Coprigh 01 Pearson Educaion Inc. Phsics 08 13
Coprigh 01 Pearson Educaion Inc. Phsics 08 14
Coprigh 01 Pearson Educaion Inc. Choosing our favorie soluion k f v f k k v k A l l and, where wih cos(, (
Traveling waves Coprigh 01 Pearson Educaion Inc.
Coprigh 01 Pearson Educaion Inc. Paricle veloci and acceleraion of he medium! cos(, (, ( and sin(, (, ( hen cos(, ( k A a k A v k A
Coprigh 01 Pearson Educaion Inc. March 1 Energ carried in a wave, (, (, (, (, ( wih, ( F v F P F F
Average Power in a sine wave on a sring P(, F A sin ( k wih P ave 1 F A Noe: One half of he maimum power ransmied in he wave. Also noe he frequenc and ampliude dependence of hese mechanical waves. Coprigh 01 Pearson Educaion Inc.
Wave Inensi Inensi he ime averaged power per uni area P I ave 4r unis are was/meer Coprigh 01 Pearson Educaion Inc.
Reflecion from a fied end and a free end. Noe: The phase changes are differen for he wo refleced waves. Coprigh 01 Pearson Educaion Inc.
Superposiion of mechanical waves Coprigh 01 Pearson Educaion Inc.
The mahemaics of wave superposiion oal oal (, (, 1 wih also a soluion o he wave equaion (, Coprigh 01 Pearson Educaion Inc.
Sanding Waves on a sring (, Acos( k and 1 (, Acos( k hen A( cos( k cos( k oal using cos( a b cos a cos b sin asin b Coprigh 01 Pearson Educaion Inc.
Sanding waves (coninued oal oal A( cos( k (Asin ksin cos( k Coprigh 01 Pearson Educaion Inc.
Locaion of he nodes for a sanding wave on a sring. oal (Asin ksin for a sring fied a 0, he nodes will be locaed a poinswhere k m, wih 0, l /, l, 3 l /, l... Coprigh 01 Pearson Educaion Inc.
Normal Modes of a Sring The sring is rigidl held a boh ends, so we have wo ses of boundar condiions o be saisfied. L = n l/ Coprigh 01 Pearson Educaion Inc.
Normal Modes (coninued l L / n where n 1,,3,4.. f f n 1 n v / L he fundamenal frequenc n( v / L give he harmonic frequencies Coprigh 01 Pearson Educaion Inc.