Transcript Vibrations and Waves

For this section we start with
Hooke’s Law.
But we already learned this.
(partially)
In another chapter we learned
That the Potential energy for
A spring is
PE = ½ mv2
But Hooke’s Law is about the
Force of a spring…
Felastic = -kx
If a mass of 0.55 kg attached to
A vertical spring stretches the
Spring 2 cm from its equilibrium.
What is the spring constant?
k = 270 N/m
A repeated motion, such as that
Of a spring, is called periodic
Motion.
At the equilibrium position, velocity
Reaches a maximum.
So a stretched or compressed
Spring has elastic potential energy.
At maximum displacement, spring
Force and acceleration is
At its maximum.
In simple harmonic motion,
The restoring force is proportional
To displacement.
Simple harmonic motion is the
Vibration about equilibrium
Position in which a restoring
Force is proportional to the
Displacement from equilibrium.
A simple pendulum consists of
A mass called a bob, which is
Attached to a fixed spring.
The restoring force of a
Pendulum is a component of
The bob’s weight.
So the forces acting on the bob
At any point include the force
Exerted by the string (y) and
The bob’s weight resolved into
Components in the y & x directions
For small angles, the pendulum’s
Motion is simple harmonic.
At any displacement, a simple
Pendulum has gravitational
Potential energy.
When measuring simple
Harmonic motion, there are
3 major parts…
Amplitude
Period
Frequency
Amplitude is the maximum
Displacement from equilibrium.
The period is the time it takes
To execute a complete cycle.
Frequency is the number of
Cycles (or vibrations)
Per unit time.
The SI unit for frequency is
s-1, or hertz (Hz).
There is a formula for this…
1
f=
T
T = Period
The period of a simple pendulum
Depends on string length
And free-fall acceleration.
T = 2π
L
g
What is the height if a pendulum
If it has a period of 12s?
L = 36m
You can do the same thing
For a spring…
The Period of a mass-spring
System depends on mass
And spring constant.
T = 2π
m
k
The body of a 1275 kg car is
Supported on a frame by four springs
Each of which has a constant of
2 X 104 . 2 people riding in the car
Have a combined mass of
153 kg. Find the period of
Vibration of the car when it is
Driven over a pothole on the road?
T = 0.84s
Transverse wave
Compression
Wave
A wave is the motion of
A disturbance through a medium.
A medium is the material through
Which a disturbance travels.
A mechanical wave is a wave
Whose propagation requires
The existence of a medium.
A pulse wave is a single
Non-periodic disturbance.
A periodic wave is a wave
Whose source is some form
Of periodic motion.
Sine waves describe particles
Vibrating with simple
Harmonic motion.
A transverse wave is a wave
Whose particles vibrate
Perpendicularly to the
Direction of the wave motion.
And a longitudinal wave is a
Wave whose particles
Vibrate parallel to the
Direction of wave motion.
There are 4 terms used to
Describe waves…
Crest
Trough
Wavelength
Speed
The crest is the highest point
Above the equilibrium position.
A trough is the lowest point
Below the equilibrium position.
The wavelength is the distance
Between 2 adjacent similar
Points of the wave.
And speed is obviously how
Fast the wave is moving.
A wave diagram
To find the speed of a wave
Is found through a new formula.
v=fλ
v = velocity
f = frequency
λ = wavelength
The string of a piano vibrates
With a frequency of 264 Hz. If the
Sound has a wavelength of
1.3 m, what is the speed?
v = 343 m/s
The law of superposition states
That because waves are not
Matter, but displacements of
Matter, two waves can occupy
The same space at the same time.
Although when waves
Interact with each other, they may
Be changed.
Constructive interference is
Interference in which individual
Displacements on the same side
Of the equilibrium position are
Added together to form the
Resultant wave.
Destructive interference is
Interference in which individual
Displacements on opposite
Sides of the equilibrium
Position are added together
To form the resultant wave.
At a free boundary, waves
Are reflected.
At a fixed boundary, waves
Are reflected and inverted.
A standing wave is a wave
Pattern that results when 2 waves
Of the same frequency,
Wavelength, and amplitude travel
In opposite directions and interfere
A node is a point in a standing
Wave that always undergoes
Complete destructive
Interference and therefore
Is stationary.
An antinode is a point on a
Standing wave, halfway
Between two nodes, at which
The largest amplitude occurs.
The law of reflection states
That the angle of incidence is
Equal to the angel of reflection.
Refraction is the change in
Direction of waves at the
Boundary of 2 different media.
Diffraction is the spreading of
Waves around the edge of a
Barrier.
Refraction
Law of
Reflection