Two pulses traveling on the same string are described by the following equations, where k = 2 and w = 7. 5 -5 (kx - wt)² + 2 (kx + wt - 6)² + 2 (a) In which direction does the first pulse travel? O O Y₁ +X -X +y -Y X At t = 0 the maximum of this function occurs at x = 0. If t is a little bigger than zero, where does the maximum occur? In which direction does the second pulse travel? O +x -X Y₂ +y (b) At what instant do the two pulses cancel for all x? t = 0.42 s (c) At what point do the two pulses cancel at all times t? x = 0.42 X Remember that A² = B² implies either A = B or A = -B. m
Two pulses traveling on the same string are described by the following equations, where k = 2 and w = 7. 5 -5 (kx - wt)² + 2 (kx + wt - 6)² + 2 (a) In which direction does the first pulse travel? O O Y₁ +X -X +y -Y X At t = 0 the maximum of this function occurs at x = 0. If t is a little bigger than zero, where does the maximum occur? In which direction does the second pulse travel? O +x -X Y₂ +y (b) At what instant do the two pulses cancel for all x? t = 0.42 s (c) At what point do the two pulses cancel at all times t? x = 0.42 X Remember that A² = B² implies either A = B or A = -B. m
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Transcribed Image Text:Two pulses traveling on the same string are described by the following equations, where k = 2 and w = 7.
5
Y₂
(kx - wt)² + 2
Y₁ =
(a) In which direction does the first pulse travel?
O +x
O-x
O+y
O-Y
At t = 0 the maximum of this function occurs at x = 0. If t is a little bigger than zero, where does the maximum occur?
In which direction does the second pulse travel?
+X
-X
-5
(kx + wt - 6)² + 2
O +y
-Y
(b) At what instant do the two pulses cancel for all x?
t = 0.42
S
(c) At what point do the two pulses cancel at all times t?
x = 0.42
X
Remember that A² = B² implies either A = B or A = -B. m
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