Ph002a, Fall 2009
Quiz
2
Due: 27 October 2009
sent from position r
: [email protected] and time f,
: oo along a
A traveling wave is
string, as shown:
Yt
}d'+
c:
y=o
Before the wave hits the right end, the string displacement is given by
(1)
where ,4 is the amplitude of the displacement (assumed to be small), and u
is the velocity at which the traveling wave propagates. The string is fixed at
the right end, which we take to be at tr
:
tr, as shown above.
At time t:0,
when the left end of the wave is at r
:
0, a clamp is applied
at $
:0
thus fixing the string at tr

0, as shown:
Y,T
+
k=0
We thus have at time t
:
0 a traveling wave on a string of length ,L with
ends at r:0
and r:,L
fixed.
1. Sketch the string configuration at time I
:
LlQu)
[1
point]
2. Write down an equation for the displacement y(r,t
:
0) at time f
:
0'
[0.5
point]
, .\
(+*,
for0<(rut)<L18,
ul:x.tl
<
"t"
.0,
otherwise,
,,/
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3. Write down an equation for the vertical string velocity
time t
:
0. (simply differentiate Eq. (1) with respect to time.)
[0.5
point]
4. In class we showed that the most general string motion (if both ends
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 Spring '09
 DUDKO
 mechanics, Trigraph, vertical string velocity, general string motion

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