Sound WavesHard
Question
Y(x, t) = 
represents a moving pulse where x and y are in meter and t is in second. Then,
represents a moving pulse where x and y are in meter and t is in second. Then, Options
A.pulse is moving in positive x-direction
B.in 2 s it will travel a distance of 2.5 m
C.its maximum displacement is 0.16 m
D.its is a symmetric pulse
Solution
The shape of pulse at x = 0 and t = 0 would be as shown, in figure (a)
y(0, 0) =
= 0.16
From the figure it is clear that ymax = 0.16 m.
Pulse will be symmetric (Symmetry is checked about ymax)if at t = 0
y(x) = y(-x)
From the given equation,
and
at t = 0
or y(x) = y(-x)
Therefore, pulse is symmetric.
Speed of pulse
At t = 1 s
and x = - 1.25 m
value of y is again 0.16 m, i.e., pulse has travelled a distance of 1.25 m in 1 s in negative x-direction or we can say that he speed of pulse is 1.25 m/s and it is travelling in negative x-direction. Therefore, it will travel a distance of 2.5 m in 2 s. The above statement can be better understood from figure (b).
y(0, 0) =
= 0.16 From the figure it is clear that ymax = 0.16 m.
Pulse will be symmetric (Symmetry is checked about ymax)if at t = 0
y(x) = y(-x)
From the given equation,
and
at t = 0or y(x) = y(-x)
Therefore, pulse is symmetric.
Speed of pulse
At t = 1 s
and x = - 1.25 m
value of y is again 0.16 m, i.e., pulse has travelled a distance of 1.25 m in 1 s in negative x-direction or we can say that he speed of pulse is 1.25 m/s and it is travelling in negative x-direction. Therefore, it will travel a distance of 2.5 m in 2 s. The above statement can be better understood from figure (b).
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