1. Unit 9
Vibrations and waves

2. Vibrations occur in:
______________________________________
2. __________________________________
3. ______________________________________
4. ______________________________________
5. ______________________________________
6. ______________________________________
7. ______________________________________
8. ______________________________________
In addition, vibrations cause ___________ .
Vibrations can be understood by using
_____________________________ as models.
Earth and Sun
Vocal cords and eardrums
radios, speakers, and motors
atomic particles
buildings and bridges
musical instruments
solids: steel, wood, glass
liquids and gases
waves
pendulums and springs

3. that act on the pendulum bob at points A, B and C.
Ex 1: Draw the forces
that act on the pendulum
bob at points A, B and C. A C B
At A:
At B:
At C: T T T w w w
In all 3 cases, Fnet ___________________. This must be
true because ________________________________________
and so it is _______________________ .
does not equal 0
the bob is changing speed and direction
accelerating

4. The weight w can be ______________________________ :
resolved into components q q
This component
is ______________
to the motion and
is ____________ in
direction to the
____________
perpendicular
opposite
w||
w||
tension w┴ w┴ w w
equilibrium
w|| is the part of w that is ______________________motion.
w|| _______________ as q increases
w|| pulls the bob back towards __________________
w|| is called a ___________________ force.
parallel to the
increases
equilibrium
restoring

5. Ex 2: Vibrating mass m on a spring with constant k:
compression
stretching x x
spring m m
x =0
equilibrium
Draw the forces that act on
the mass at the points shown: FN FN FS FS w w
Except at x = 0, Fnet ____________________________
FS _________________ as x increases
FS pulls the mass back towards __________________
FS is also a ______________________ force.
does not equal zero
increases
equilibrium
restoring

6. harmonic
Simple _______________ motion (SHM):
--vibrations in an ______________ material
-- due to a restoring force that is __________
____________________ to a displacement.
elastic
directly
proportional
SHM occurs because of ____________________ :
Hooke's Law
F =
-kx
From Newton's 2nd Law, we know that F = ______ ma ma
= -kx
the 2nd time derivative of x
Calculus tells us that a = ___________________________:
m d2x
dt2
= -kx
The solutions to this equation are _____________________
sines and cosines

7. sine
______
curve: x
time
cosine
______
curve: x
time T
the period of vibration
T = ________________________
Both of these curves are ______________ and
describe the __________________________ that is
___________________________________________.
periodic
motion of an object
vibrating in simple harmonic motion

8. period T: the time for _________________________________
SI unit for T: _______________
one complete cycle or vibration
seconds, s
Ex: It takes a pendulum 40 seconds to complete 10
complete back and forth swings (10 cycles). What is
its period?
40 s
T = =
4 s 10
"cycles"
 Notice that ______________ is ignored as a unit.
# of complete cycles that occur
frequency f:
f =
time
Ex: Find the frequency of vibration for the above
example. 10
f =
0.25 =
40 s s

9. Other ___________ can be used for T and f. But when
the time is in _______________ , the unit for frequency is:
units
seconds (s) 1 or
s-1 s
This unit is called a _____________
It is _____________ from the fundamental unit ____ .
So the answer to the last example can be written:
hertz, Hz.
derived s
f =
0.25 s-1 =
0.25 Hz
Notice: T =
f =
4 s
0.25 s-1 =
¼ s-1
From this example, it can be seen that
period and frequency are _____________ :
T = 1 f
inverses