Transcript Vibrations & Waves

Honors Physics
Then we will no longer be infants, tossed back and
forth by the waves.
Ephesians 4:14

Back and forth motion
that is caused by a
force that is directly
proportional to the
displacement.

The displacement
centers around an
equilibrium position.
Fs x

One of the simplest type of simple harmonic
motion is called Hooke's Law.

This is primarily in reference to springs.
Fs  x
k  Constant
of Proportion ality
k  Spring Constant(U
F s  kx
or
 kx
nit : N/m)
The negative sign tells us
that “F” is a restoring
force; it works in the
opposite direction of the
displacement.
Common formulas which are set equal to Hooke's law
are Newton’s Second Law and weight.
A 0.55 kg mass is attached to a vertical spring, which stretches 36
cm from it’s original equilibrium position. What is the spring
constant?
Fs   kx
F g  mg
F g   Fs
mg   kx
k 
mg
x
( 0 . 55 kg )(  9 . 81
m
s

0 . 36 m
2
)
 15
n
m
A load of 50 N attached to a spring hanging vertically stretches the
spring 5.0 cm. The spring is now placed horizontally on a table and
stretched 11.0 cm. What force is required to stretch the spring this
amount?
F   kx
k 
F
x

 (  50 N )
0 . 05 m
F   kx  (  1000
N
m
 1000
N
m
)( 0 . 11 m )   110 N
The amplitude, A, of a wave is the
same as the displacement ,x, of a
spring. Both are in meters.
Crest
Equilibrium Line
Trough
CREST
Equilibrium Line
• Period (T): the time for one
revolution or one complete
oscillation (one crest and
trough).
• Oscillations could also be
called vibrations and cycles.
• Ts = sec/cycle
Trough
• In the wave above we have
1.75 cycles or waves
(vibrations or oscillations).
• Assume that the wave
crosses the equilibrium line
in one second intervals.
• T = 3.5 seconds/1.75
cycles. T = 2 sec.



The Frequency of a wave is the inverse of Period.
That means that the frequency is cycles/sec.
The commonly used unit is Hertz (HZ).
Period  T 
seconds

cycles
Frequency
 f 
cycles
seconds
T 
1
f
f 
1
T
3 .5 s
 2s
1 . 75 cyc

1 . 75 cyc
3 . 5 sec
 0 .5 c
s
 0 . 5 Hz

The period of a Spring-Mass System is:
◦ Proportional to 2
◦ Inversely proportional to the square root of the spring
constant
◦ Proportional to the square root of the mass on the spring
T  2
m
k
• The greater the mass, the larger the
period
• The greater the spring constant
(more stiff), the smaller the period
A 125 N object vibrates with a period of 3.56 seconds when
hanging from a spring. Find the spring constant.
T  2
m
k
4 m
2
k 
T
2
125 N
4 (
)
m
9 . 81 2
N
s
k 
 39 . 7
2
( 3 . 56 s )
m
2

The period of a pendulum is:
◦ Proportional to 2 (it’s sweeping out an arc of a circle)
◦ Inversely proportional to the square root of gravity
◦ Proportional to the square root of the length of the
pendulum
T  2
L
g
The height of a tower is unknown, but a pendulum, extending
from the ceiling almost touches the floor. If the period of the
pendulum is 12 s, what is the approximate height of the
tower?
T  2
2
L
L
g
2
(12 s ) ( 9 . 81
L
4
4
2
m
s
2
T g
)
2
 36 m
A Wave is a vibration or disturbance in space.
A Medium is the substance that all sound waves
travel through and need to have in order to move.
Longitudinal Wave - A fixed point will move parallel with the wave motion
2 areas:
Compression - an area of high molecular density and pressure
Rarefaction - an area of low molecular density and pressure
Transverse Wave - A fixed point will move perpendicular with the wave motion.
Wave parts: Crest, Trough, Wavelength, Amplitude, Frequency, Period
All waves have 4 basic properties:
Amplitude
Wavelength
Frequency f
Speed c
λ lambda
Amplitude – the maximum
distance the wave moves
up and down.
The more energy a wave
has the greater the
amplitude.
Wavelength – the distance between two corresponding
parts of a wave
Short Waves can
complete more
cycles than Long
Waves in the same
amount of time.
Frequency – the number of complete waves that pass a
given point
Frequency is measured in the unit called Hertz (Hz).
A wave that occurs
every second has a
frequency of 1 Hz.
Speed – the distance a wave travels in a given amount of
time.
The speed of sound
through air is 331 m/s.
You can find the speed of a wave by multiplying the wave’s
wavelength in meters by the frequency (cycles per second).
Since a “cycle” is not a standard unit this gives you m/s.
A harmonic wave is traveling along a rope. It is observed that
the oscillator that generates the wave completes 40.0
vibrations in 30.0 s. Also, a given maximum travels 425 cm
along a rope in 10.0 s . What is the wavelength?
f 
40 . 0 cycles
30 . 0 s

4
Hz
v
4 . 25 m
10 . 0 s
3
v  f
 
v
f
0 . 425
4
3
 0 . 425
m
s
m
s  0 . 319 m
Hz
Wave Behavior
Superposition - The combination of two overlapping waves
Interference - The result of superposition
A standing wave is produced when a wave that is traveling is
reflected back upon itself.
Two main parts of standing
waves:

Antinodes – Areas of
maximum amplitude

Nodes – Areas of zero
amplitude
Interference is the
interaction between
waves that meet
There are two
types of
interference:
Constructive and
Destructive
When an object hits a surface it can not pass, it bounces back.
This is called reflection.
The bending of waves
due to a change in
speed is called
refraction.
When a wave moves around a barrier or through an
opening in a barrier, it bends and spreads out. This is
known as diffraction.