01quiz_08

# 01quiz_08 - Physics 9B-C Quiz#1 Name key Last 4 of ID...

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Unformatted text preview: Physics 9B-C Quiz #1 Name: key 10/3/08 Last 4 of ID: Show that the general equation  y =y(kx + ∑t) , i.e.,  y  is a function of ( kx + ∑t)  and is a solution to  the second order wave equation.  The function  y () is unknown, but  y  & its derivatives exist and  are well-behaved and single-valued.  The wave has a phase velocity given by  v   =  ∑/ k  .   Explicitly write out all derivatives such as   dy du   .  Do not use the  y'  notation for derivatives. Method 1:   Start by applying the derivatives and using the chain rule. Let  u  =   kx  +  ∑ t:    ∂ y ∂ x = dy du ∂ u ∂ x = k dy du      so that   ∂ 2 y ∂ x 2 = d du ∂ y ∂ x ⎛ ⎝ ⎞ ⎠ ∂ u ∂ x = k 2 d 2 y du 2    (3 pts) Similarly for  dt, ∂ y ∂ t = dy du ∂ u ∂ t = +...
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## This note was uploaded on 10/23/2009 for the course PHY 9B taught by Professor Cheng during the Fall '08 term at UC Davis.

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