Douglass Houghton Workshop, Section 1, Mon 10/3/11
Worksheet Harbinger of Things to Come
1. Explain how you might use two long rulers to add numbers mechanically. (Example:
find 2 + 3 with two 6inch rulers.)
2. Explain how a slide rule is able to multiply numbers. It might help to recall that this
picture:
1
2
3
4
5
6
7
8
9
10
0
1
2
represents the function ln(
x
) if we find
x
on the top scale and read downward. Note
that the bottom scale is just like a regular ruler, in some units.
3. (This problem appeared on a Fall, 2008 Math 115 Exam) The speed of sound,
v
(
T
) (in
miles per hour), at an ambient temperature,
T
(in degrees Fahrenheit), is given by:
v
(
T
) = 740 + 0
.
4
T.
Objects which travel faster than the speed of sound create
sonic booms.
However, the
ambient temperature
T
in the Troposphere also decreases with height
h
(in miles) from
the earth’s surface according to the equation
T
(
h
) =

26
h
+
T
0
,
where
T
0
is the temperature at the surface.
(a) Find a formula which will give the speed of sound
S
as a function of height
h
,
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 Winter '08
 Conger
 Absolute Zero, sea level, Kelvin, Thermodynamic temperature

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