phy2048 lecture31

phy2048 lecture31 - Chapter 16: Waves--I 161 What Is...

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Unformatted text preview: Chapter 16: Waves--I 161 What Is Physics? 162 Type of Waves 163 Transverse and Longitudinal Waves 164 Wavelength and Frequency 165 The Speed of a Traveling Wave 166 Wave Speed on a Stretched String 167 Energy and Power of a Wave Traveling Along a String 168 The Wave Equation 169 The Principle of Superposition for Waves 1610 Interference of Waves 1611 Phasor 1612 Standing Waves 1613 Standing Waves and Resonance Chapter 16 Homework 1, 7, 8, 14, 17, 20, 32, 42, 43, 47, 50, 58 Principle of Superposition y ( x, t ) = y1 ( x, t ) + y 2 ( x, t ) Overlapping waves algebraically add to produce a resultant wave (or net wave) Overlapping waves do not in any way alter the travel of each other Animations Interference of Waves Sample Problem 16-6. Two identical waves ym = 9.8 mm. (a) Find the amplitude of resultant wave when = 100. (13 mm) (b) What phase difference, in radian and wavelengths, will give the resultant wave an amplitude of 4.9 mm. (2.6 rad, 0.42 ) fully constructive fully destructive intermediate y1 ( x, t ) = y m sin(kx - t ) y 2 ( x, t ) = y m sin(kx - t + ) y ( x, t ) = [2 y m cos 1 ] sin(kx - t + 1 ) 2 2 x = kx = 2 Standing Waves y1 ( x, t ) = y m sin(kx - t ) y 2 ( x, t ) = y m sin( kx + t ) Nodes zero amplitude x=n 2 , for n = 0, 1, 2, ... y ( x, t ) = [2 y m sin kx] cos t Antinodes max amplitude 1 x = n + , for n = 0, 1, 2, ... 2 2 Standing Waves and Resonance Reflections Resonance f1 = v 1st harmonic 2 L Fundamental mode v = 2 f1 2nd harmonic L f2 = 3v f3 = = 3 f1 3rd harmonic 2L = 2L , for n = 1, 2, 3, ... n harmonic number n v v fn = = n = nf1 , for n = 1, 2, 3, ... 2L Example Sample Problem 16-8. m = 2.500 g, L = 0.800 m, T = 325.0 N Find wavelength , harmonic number n, and frequency f. What is the max transverse speed of the element at x = 0.180 m, and where does it occur? ...
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This note was uploaded on 04/17/2008 for the course PHY 2048 taught by Professor Chen during the Fall '08 term at UNF.

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phy2048 lecture31 - Chapter 16: Waves--I 161 What Is...

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