SME
Oceanography · Problem type
Tsunami speed and travel time
Use this for “A tsunami crosses 3,000 km of ocean 4,000 m deep. How fast does it travel, and how many hours does it take?”
Diagram
d
L
=
4,000
200,000
=
0.02:
shallow
water
(d
<
L
20
):
the
orbits
are
flat
ellipses
down
to
the
floor,
and
c
=
√
gd
.
Wave speed c = 198 m/s.
Depths are stretched × 9.33 to show the orbits.
Wave heights are not to scale.
This is an example. Type your own values to start a new problem.
c (m/s)
=
g
×
d (m)
t (h)
=
x (km)
÷
c (m/s)
Formulas
c
=
√
9.81 ×
d
198.0909
=
√
9.81 × 4,000
t
=
x
×
1,000
c
÷
3,600
4.2068
=
3,000
×
1,000
198.0909
÷
3,600
Assumptions
•
A tsunami is a shallow-water wave: its wavelength, about 200 km, is far longer than the ocean is deep.
•
So its speed depends on the depth alone, c = √(gd), with g = 9.81 m/s².
•
The depth is taken as the same all the way across.
Step-by-step
WE KNOW
d = 4,000 m, x = 3,000 km
FIND
wave speed (c), travel time (t)
Step 1 · Find wave speed (c)
Use c = √(9.81 × d)
A shallow-water wave’s speed depends only on the depth.
c
=
√
9.81 × 4,000
c
=
√
39
,240
c
=
198.0909
m/s
Step 2 · Find travel time (t)
Use t = x × 1,000 ÷ c ÷ 3,600
Time is distance over speed: kilometers to meters, then seconds to hours.
t
=
3,000
×
1,000
198.0909
÷
3,600
t
=
3,000,000
198.0909
÷
3,600
t
=
15,145
3,600
t
=
4.2068
h
Check
Put the numbers back in. Both sides should match.
198.0909
=
√
9.81 × 4,000
✓
4.2068
=
3,000
×
1,000
198.0909
÷
3,600
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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