Chapter 16
3. (a) The motion from maximum displacement to zero is one-fourth of a cycle so 0.170 s is one-
fourth of a period. The period is
T
= 4(0.170 s) = 0.680 s.
(b) The frequency is the reciprocal of the period:
1
1
1.47Hz.
0.680s
f
T
=
=
=
(c) A sinusoidal wave travels one wavelength in one period:
1.40m
2.06m s.
0.680s
v
T
=
=
=
λ
7. Using
v
=
f
λ
, we find the length of one cycle of the wave is
λ
= 350/500 = 0.700 m = 700 mm.
From
f
= 1/
T
, we find the time for one cycle of oscillation is
T
= 1/500 = 2.00
×
10
–3
s = 2.00 ms.
(a) A cycle is equivalent to 2
π
radians, so that
π
/3 rad corresponds to one
‐
sixth of a cycle. The
corresponding length, therefore, is
λ
/6 = 700/6 = 117 mm.
(b) The interval 1.00 ms is half of
T
and thus corresponds to half of one cycle, or half of 2
π
rad.
Thus, the phase difference is (1/2)2
π
=
π
rad.

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