Physics: Simple Physics: Simple Harmonic Harmonic

Motion, Waves Motion, Waves and Energyand Energy

CHHS Physics

Mr. Puckett

What is a Wave?What is a Wave?Where have you seen or felt waves in your life?

– Oceans, lakes, stadium crowds, earthquakes, jump ropes, sound, pendulums…

A wave is a vibration or wiggle in time and space. It transfers energy.

The back and forth motion of a wave or pendulum is called simple harmonic motion (SHM)

Waves and Energy:Waves and Energy:

WAVES are nature's way of transferring energy without transferring matter. Waves are made from vibrations in molecules and energy.– Examples range from sound and

waves in water, to waves in light and electromagnetic force.

WAVE DIAGRAMWAVE DIAGRAM

Energy in Simple Harmonic Energy in Simple Harmonic Motion in Nature.Motion in Nature.

The Potential and Kinetic Energy we have studied is best examined by looking at simple harmonic motion. (SHM)

SHM is the oscillatory motion that results when an elastic material is subjected to the restoring force of an ideal spring. We will examine springs and pendulums

Conservation of Mechanical Conservation of Mechanical EnergyEnergy

Without friction, total mechanical energy remains constant.

½ mvf2 + mghf = ½ mvo

2 + mgho

SHM Vocabulary:SHM Vocabulary:

Period- The time required to complete one oscillatory cycle of motion. T = 1/f

Frequency- The number of cycles of motion per second. f = 1/T in units of Hertz.

Amplitude- the maximum distance that an oscillating object moves from equilibrium position.

Cycle- refers to the complete to and fro motion from some initial point back to that same point.

Examples of SHMExamples of SHM

Period of Simple Harmonic Period of Simple Harmonic MotionMotion

The time for one cycle through of the motion is called the Period (T).

Hooke’s Law: the Spring Hooke’s Law: the Spring Constant.Constant.

Hooke’s Law is the application of Newton’s second law F = ma to springs.

Formula: F = - kx where k is the spring constant and x is the distance the displacement. The negative sign is the “restoring” convention

Hooke’s Law of Springs Hooke’s Law of Springs ExamplesExamples

Hooke’s Law ProblemHooke’s Law Problem

The Potential Energy of a The Potential Energy of a Spring System:Spring System:

Just as when you pull back a rubber band to pop someone; the elastic effect of the rubber stores energy.

Springs likewise convert kinetic motion to Potential Energy: Elastic PE.

Formula: PE(elastic) = ½ kx2 =U It can convert the energy back to kinetic with

the release of the spring and the restoring force takes effect.

Pendulum: The Big Energy Pendulum: The Big Energy Exchanger.Exchanger.

The Trigonometry Analysis of The Trigonometry Analysis of the Pendulumthe Pendulum

Pendulum FormulasPendulum Formulas

The Frequency

The Period

Time period of a spring:

k

mT 2

Pendulum Length FormulaPendulum Length Formula

Frequencies and FunctionsFrequencies and Functions

When we look at different frequencies you are looking at different functions that you already know.

EM waves are transverse waves.

Frequencies you KnowFrequencies you Know

AM Radio - KHz (1,000 Hz)FM Radio - MHz ( 1,000,000 Hz)Microwave Oven – 2.5 GHzTV - 45 MHz to 10 GHzX-rays – 30-30,000 PHz (1015 Hz)Visible Light – 380 – 780 nm (10-9 m)Sound waves- 20 Hz – 20,000 Hz

QUALITIES AND QUALITIES AND MEASURES OF A WAVEMEASURES OF A WAVE:: FREQUENCY is the number

of complete vibrations per second measured at a fixed location per unit of time. It has the units of hertz (Hz). One vibration per second is = 1 Hz.

QUALITIES AND QUALITIES AND MEASURES OF A WAVEMEASURES OF A WAVE:: PERIOD is the shortest time interval in which the motion repeats itself. This is equal to the inverse of the frequency: T= 1/f

QUALITIES AND QUALITIES AND MEASURES OF A WAVEMEASURES OF A WAVE::WAVELENGTH is the shortest distance between points where the wave pattern repeats itself. The units are meters and the symbol is the (lambda)

QUALITIES AND QUALITIES AND MEASURES OF A WAVEMEASURES OF A WAVE::

D. AMPLITUDE is the maximum displacement from the resting position of equilibrium of the medium. The larger the amplitude, the larger the amount of work needed for the displacement and the larger the amount of energy transferred. The high points are called crests and the low points are troughs.

Speed of a WAVESpeed of a WAVE

The speed of any wave is calculated with the equation: speed = frequency x wavelength.

v = f λ Units: vel = m/s freq = Hz

wavelength = meters

What determines Speed of a Wave?What determines Speed of a Wave?

The speed of a mechanical wave is independent of amplitude or the frequency of the wave. It depends upon the nature of the medium it is transferred through, specifically the density or tension of the material. The denser the material, the faster the wave.

TYPESTYPES OF WAVES: OF WAVES:

a. MECHANICAL WAVES – the 2 kinds that move through matter– 1. TRANSVERSE WAVES move the

matter particles perpendicular to the direction of the motion of the wave. This type is shown in , lateral spring displacements and secondary earthquake waves.

TYPESTYPES OF WAVES: OF WAVES:

2. LONGITUDINAL WAVES move the matter particles parallel to the direction of the motion of the wave. This type is seen in compressional spring displacements and primary earthquake waves that move faster than secondary waves.

LONGITUDINAL WAVESLONGITUDINAL WAVES

TYPESTYPES OF WAVES: OF WAVES:

3. SURFACE WAVES are a mixture of transverse and longitudinal waves. This is the type found in water.

4. IMPULSE WAVE is a single disturbance that travels through a medium

5. TRAVELING WAVE is a continuous wave produced by a source that is vibrating with simple harmonic motion.

SURFACE WAVESURFACE WAVE

Surface waves are a combination of longitudinal and transverse waves.

TYPESTYPES OF WAVES: OF WAVES:

B. ELECTROMAGNETIC WAVES do not require matter to move through.– Examples are electromagnetic

waves such as light, x-rays, microwaves, and radiation.

Properties of a WaveProperties of a Wave

2. 2. QUALITIES AND QUALITIES AND MEASURES OF A WAVEMEASURES OF A WAVE::

F.      VELOCITY - is the speed of the wave and is found with the equation:

VELOCITY (v) = lambda () x frequency (f). The speed of a mechanical wave is independent of amplitude or the frequency of the wave. It depends upon the nature of the medium it is transferred through, specifically the density or tension of the material. The denser the material, the faster the wave.

3. 3. WAVES AT A WAVES AT A BOUNDARYBOUNDARY: :

An INCIDENT WAVE is any wave that encounters a boundary during its travels.– . When a wave hits a solid

boundary, it bounces back and turns into a REFLECTED WAVE and returns the original direction. However, the wave is inverted from its original direction.

Wave inversion Wave inversion

INTERFERENCE OF INTERFERENCE OF WAVESWAVES::

A. Principle of SUPERPOSITION says that when two independent waves passing through a medium meet; the result is the ALGEBRAIC SUM of the DISPLACEMENTS caused by the individual waves.

INTERFERENCE OF INTERFERENCE OF WAVESWAVES::

B. INTERFERENCE is the result of the superpositioning of two independent waves acting on each other.

Interference Interference

CONSTRUCTIVE CONSTRUCTIVE INTERFERENCEINTERFERENCE

a. CONSTRUCTIVE INTERFERENCE - is when the waves displace the medium in the same direction at the same time. They simply reinforce each other and add to the amplitude. The amount of reinforcement is found by the algebraic sum of the two wave amplitudes.

DESTRUCTIVE DESTRUCTIVE INTERFERENCEINTERFERENCE

DESTRUCTIVE INTERFERENCE - is when the waves displace the medium in different directions at the same time. If the amplitudes of the two pulses are equal but opposite, the displacement produces a net ZERO DISPLACEMENT. If the amplitudes are unequal, the destructive interference will not be complete and there will be some net but reduced wave amplitude

INTERFERENCE DIAGRAMINTERFERENCE DIAGRAM

Constructive Destructive

5. 5. STANDING WAVESSTANDING WAVES STANDING WAVES : A standing wave is a

wave pattern that results when two waves of the same frequency, wavelength and amplitude travel in opposite directions and interfere.

The wave appears stationary. The period of this wave is equal to the

time it takes for the wave to travel to a fixed point and back. That means the nodes and antinodes stay in the same position. This shows the property of RESONANCE where the wave is reinforced in synch.

STANDING WAVESSTANDING WAVES

a. A NODE is a position in a wave where the medium displacement is zero and is not moving. This is the result of maximum destructive interference.

b. An ANTINODE is the position where the displacement is at its maximum. This is the result of maximum constructive interference

Standing WaveStanding Wave

Bow WavesBow WavesWhen a boat exceeds the speed with which the ripple waves in front travel, the boat overtakes the waves. The overtaken waves form a bow wave — a single wave made up of all the ripple waves that would have propagated ahead of the boat but could not move fast enough to do so.

Shock WavesShock WavesAlmost the same thing happens when the jet breaks the sound barrier. When the jet exceeds the speed of sound — the sound waves can’t get out of the way of the jet. So, they scrunch together and form a kind of "bow wave" that is called a shock wave — a sonic boom. The only difference is that the boat wave forms a 2-dimensional "V" on the water surface and the shock wave forms a 3-dimensional cone.

Sound barrier link

Reflection, Refraction, DiffractionReflection, Refraction, Diffraction

Reflection is where a wave hits a barrier and is bounced back ( reflected like echo’s or spring reflections off fixed objects).

Refraction is the bending of a wave due to entering a different density medium. Like light bending through glasses and contacts.

Diffraction is the spreading out of a wave when it hits a barrier and goes around it. Like light and water around a barrier.

LAW OF REFLECTIONLAW OF REFLECTIONThe Incoming Light Ray Angle is Equal

to the Outgoing Ray angle. Angle of incident wave to normal is equal to the

angle of reflection at a solid boundary.

INDEX OF REFRACTIONINDEX OF REFRACTIONA measure of the density of a medium

that can slow the velocity of a wave.Formula for light: n = c/v where n =

index of refraction, c = speed of light, v is velocity of light in the medium.

Diffraction ExamplesDiffraction Examples

The Doppler EffectThe Doppler Effect

The Doppler effect refers to the change in pitch of a sound due to the motion of either the source or the listener. If they are approaching each other, the pitch is higher. If they are moving apart, the pitch is lower. This is also the basis of a modern radar system that shows weather movement well. The formula would be:

  f ‘ = f((v +/-vo) / (v -+ vs))

The Doppler EffectThe Doppler Effect

ENERGY IN SHMENERGY IN SHM

Energy of an object in simple harmonic motion is the mechanical energy ( PE + KE)

E = ½ mv2 + ½ kx2 Recall that the period of a SHM is T = 2 L/g (pendulum) OR 2 m/k ( spring )

Sound WavesSound Waves