Example 12-1 Frequency and Period
(a) What is the oscillation period of your eardrum when you are listening to the A4 note on a piano (frequency
440 Hz)? (b) A bottle floating in the ocean bobs up and down once every 2.00 min. What is the frequency of this
oscillation?
Set Up
We’ll use Equation 12-1 to find the period
T from the frequency f and vice versa.
Solve
(a) The period of this oscillation is the reciprocal of the frequency. Note that a cycle is not a
true unit but simply a way of counting, so we
can remove it from the final answer as needed.
(b) The frequency of this oscillation is the
r­ eciprocal of the period. To get a result in Hz,
we must first convert the period to seconds.
Note that the period is the number of seconds
per cycle, so we can add “cycle” to the
calculation as needed.
Reflect
Frequency and period:
1
1
and T = f =
T
f
(12-1)
1
1
1
1
s
=
=
=
f
440 Hz
440 cycles>s
440 cycle
= 2.27 * 1023 s
T =
60 s
= 120 s
1 min
1
1
1
1 cycle
f =
=
=
=
T
120 s
120 s>cycle
120 s
= 8.33 * 1023 Hz
T = 2.00 min *
Since frequency and period are the reciprocals of each other, a large value of f (high frequency) corresponds to a small value
of T (short period) as in (a) and a small value of f (low frequency) corresponds to a large value of T (long period) as in (b).