Assignment_6_09

# Assignment_6_09 - TA's Name_Section Your Name Physics 2214...

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TA's Name:_____________________________________Section: ____ Your Name: ____________________________________ Physics 2214 Assignment 6 Concepts: Boundary conditions Energy and Power in waves Reflection and Transmission of waves Reading: AG Notes on Superposition and Standing Waves (from website); Y&F, Vol. 1, Chapter 16 Assignment: Due in lecture on Thursday, March 5. Please turn in this sheet stapled to the top of your work. 1. Wave reflection and transmission. A wave is incident from medium 1 onto a boundary with a second medium 2, and the reflection and transmission coefficients are those we derived in lecture (in terms of Z, not v). What can you conclude about the ratios Z 2 /Z 1 and v 2 /v 1 in each case below, where Z is the characteristic impedance and v is the wave velocity? (a) The reflected wave in 1 has the same magnitude as the incident wave. (b) The transmitted wave has a larger amplitude than the incident wave. (c) The reflected wave is has opposite sign to the transmitted wave. (d) The transmitted wave amplitude is very small. (e) The wavelength of the transmitted wave is shorter than that of the incident wave. 2. How can T=2? In our analysis of wave reflection and transmission from a boundary between two media, we found that T = 1 + R, and that when R=1, T=2. This implied that the reflected wave in medium 1 has the same amplitude as the incident wave in 1, and that the transmitted wave in 2 has twice the amplitude of the incident wave. How is this possible? Let's focus on strings, where the tensions are constant, and on harmonic waves. (a) If T is close to 2, what does this imply about the ratio 2 1 / μ μ ? (b) For harmonic waves, the y acceleration at a given point is proportional to the wave amplitude and the square of frequency. How es the force that must be exerted on a piece of string of length x to produce a given displacement amplitude compare on the two sides of the boundary, i.e., what is in terms of its do 1 1 Δ F F 2 / 2 / μ μ ? When T=2, to what does this reduce?

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