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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