Quiz 1 Rubric
Summary
The four letter grades refer to Parts A, B, and C of Question 1. Part B of of Question 1 is
broken into two parts, with a letter assigned to each. In the following table we describe the letter
grade values. Note that the letter grade shown applies to that particular question, not the whole
quiz.
Question #1 Part A (50% of the grade):
This question asked us to draw an x vs. t graph for a tsunami wave. We note that in the
statement of the problem we are told that the wave travels 600 km in 40 minutes,
with a
maximum trough to crest distance of 10 m. We recall here that the velocity of a wave is given by
v=
Δx
Δt
=
λ
T
,
where
Δx
is the distance covered by the wave in a time
Δt
. Here we then associate the tsunami a
wave speed of
v=
Δx
Δt
=
600
km
40
min
.
=
15
km
min
.
=
250
m
s
.
Note that we DO NOT know what the wavelength (
λ
) or period (T) is. These two
quantities
cannot be extracted from the given information. Recall that the speed is medium dependent, and
the period source dependent. You know the speed of the medium, but nothing of the source
–
any
frequency would work. To determine the form of the x vs. t graph, we recall FNT 6 from DLM
01. For this part we consider a wave moving in the positive x direction, so that there is a negative
sign in front of the xterm of the
Φ
x,t
equation. It is instructive to consider the lines of constant
total phase
,
Φ
, in order to see how x and t are related for a given point on the wave. Setting the
total phase equal to a constant number, C, we have
.
Solving for x, we have
where v is the familiar velocity of a wave. This equation has the same form as a linear equation:
y=mx+b
. The graph we must draw, then, is a linear graph with a slope of
v=
15
km/min. , the
velocity. To properly describe the wave on an x vs. t graph, we must include several lines of total
phase. The easiest lines of total phase are those corresponding to crests and troughs. A sample
graph is given below, where we have drawn the lines of total phase corresponding to C=
3
2
π
(trough),
1
2
π
(crest),
−
1
2
π
(trough), and
−
3
2
π
(crest):
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We note that the solid lines correspond to crests, and the dashed lines correspond to troughs.
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 Spring '08
 schore
 Derivative, Frequency, Velocity

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