Waves/Vibrations Unit 6

Simple Harmonic Motion Any periodic motion that is the result of a restoring force. Every simple harmonic motion is a back-and-forth motion over the same path Recall: Hooke’s Law helps us to calculate the restoring force (Spring Force Fs) Fs= -kx

FOR ALL WAVES WE CAN CALCULATE THE PERIOD USING: Period & Amplitude The maximum displacement from the equilibrium position is called the amplitude. Period (T) is the time it takes for an object to complete one full cycle of motion. After a full period an object is back where it started measured in seconds Frequency – f – the number of complete cycles an object goes through per unit of time. measured in Hertz (Hz) FOR ALL WAVES WE CAN CALCULATE THE PERIOD USING: T=1/f

Simple Harmonic Motion At equilibrium position – velocity reaches a maximum. (when the object has a spring displacement of 0) At maximum displacement, (furthest stretch or compression of the spring), the restoring force (Fs) and acceleration reach a maximum.

Period of SHM We can calculate the period of an oscillating spring mass system using the following formula T= period of oscillation m= mass k= spring constant

The Simple Pendulum The restoring force of a pendulum is a component of the bob’s weight. (Fg) The only forces acting on the bob (mass at the end of the pendulum) are the force exerted by the string (tension) and the weight of the mass (Fg)

The Simple Pendulum As the displacement of the bob (mass) increases from equilibrium position to maximum to displacement, the Gravitational Potential Energy increases Therefore, at maximum displacement from equilibrium the bob has the GREATEST gravitational potential energy – because it is at its max height.

Period of a Pendulum We can calculate the period of a simple pendulum by the following formula

Types of Waves Transverse Waves when wave motion is perpendicular to the vibrations of a wave

Types of Waves Longitudinal Waves when wave motion is parallel to the vibrations of a wave. A longitudinal wave is also called a compression wave

Longitudinal Waves

Properties of Waves A wave is the motion of a disturbance There are different mediums in which a wave travels Ex: Water, Air, Glass etc. A pulse is a single traveling wave. Periodic or Traveling Wave – is a series of pulses within a medium creating periodic motion

Properties of Waves Amplitude Trough Crest Maximum displacement of a wave from its equilibrium position Trough Lowest point below equilibrium position on a wave Crest Highest point above equilibrium position on a wave Wavelength (λ llambda, measured in meters) The distance between two adjacent similar points of a wave (crest to crest OR trough to trough)

Fundamental Wave Equation We can relate the speed, frequency and wavelength of a wave with the following equation. v=fλ v= velocity (m/s) f= frequency (Hz) λ= wavelength (m)

Interference of Waves Two traveling waves can meet and pass through each other without being destroyed or even altered Waves obey the Superposition Principle If two or more traveling waves are moving through a medium, the resulting wave is found by adding together the displacements of the individual waves point by point Actually only true for waves with small amplitudes

Constructive Interference Two waves, a and b, have the same frequency and amplitude Are in phase The combined wave, c, has the same frequency and a greater amplitude

Constructive Interference Two pulses are traveling in opposite directions The net displacement when they overlap is the sum of the displacements of the pulses Note that the pulses are unchanged after the interference

Constructive Interference When two waves momentarily overlap and combine to form a larger wave. To create constructive interference, a crest must meet a crest or a trough must meet and trough.

Destructive Interference Two waves, a and b, have the same amplitude and frequency out of phase When they combine, the waveforms cancel

Destructive Interference Two pulses are traveling in opposite directions The net displacement when they overlap is decreased since the displacements of the pulses subtract Note that the pulses are unchanged after the interference

Destructive Interference When two waves momentarily overlap and combine to partially or totally cancel each other To create destructive interference, a crest must meet a trough

Ruben’s Tube Sound Intro Visual Representation of a Sound wave involving FIRE http://www.youtube.com/watch?v=QrgPK_JaKNA

Producing a Sound Wave Sound waves are longitudinal waves traveling through a medium A tuning fork can be used as an example of producing a sound wave

Pitch Pitch is related mainly, although not completely, to the frequency of the sound Pitch is not a physical property of the sound Frequency is the stimulus and pitch is the response It is a psychological reaction that allows humans to place the sound on a scale

Using a Tuning Fork A tuning fork will produce a pure musical note As the tines vibrate, they disturb the air near them As the tine swings to the right, it forces the air molecules near it closer together This produces a high density area in the air This is an area of compression

Using a Tuning Fork, continued As the tine moves toward the left, the air molecules to the right of the tine spread out This produces an area of low density This area is called a rarefaction

Categories of Sound Waves Audible waves Lay within the normal range of hearing of the human ear Normally between 20 Hz to 20,000 Hz Infrasonic waves Frequencies are below the audible range Earthquakes are an example Ultrasonic waves Frequencies are above the audible range Dog whistles are an example

Applications of Ultrasound Ultrasonic Waves – can be used to create images of very tiny objects. Most commonly used as a diagnostic and treatment tool in medicine.

The Doppler Effect http://www.youtube.com/watch?v=z0EaoilzgGE A Doppler effect is experienced whenever there is relative motion between a source of waves and an observer. When the source and the observer are moving toward each other, the observer hears a higher frequency When the source and the observer are moving away from each other, the observer hears a lower frequency

The Doppler Effect Although the Doppler Effect is commonly experienced with sound waves, it is a phenomena common to all waves Assumptions: The air is stationary All speed measurements are made relative to the stationary medium

Forced Vibrations A system with a driving force will force a vibration at its frequency When the frequency of the driving force equals the natural frequency of the system, the system is said to be in resonance

An Example of Resonance Pendulum A is set in motion The others begin to vibrate due to the vibrations in the flexible beam Pendulum C oscillates at the greatest amplitude since its length, and therefore frequency, matches that of A

Other Examples of Resonance Child being pushed on a swing Shattering glasses Tacoma Narrows Bridge collapse due to oscillations by the wind Upper deck of the Nimitz Freeway collapse due to the Loma Prieta earthquake

Tacoma Narrows http://www.youtube.com/watch?v=3XE5qU0c5qU

Characteristics of Light What your eye recognizes as “white” light is actually light that can be separated into six elementary colors of the visible spectrum: red, orange, yellow, green, blue and violet However, not all light is visible to the human eye The spectrum includes MORE than just visible light

The Nature of Light Light can be described as both a wave and a particle Experiments can be devised that will display either the wave nature or the particle nature of light In some experiments light acts as a wave and in others it acts as a particle Particles of light are called “photons”

The Electromagnetic Spectrum Light can be found in a variety of forms including radiation Examples include: X Rays, microwaves, radio waves which all have similar properties to visible light These are considered examples of electromagnetic waves.

The Electromagnetic Spectrum Electromagnetic waves vary based upon frequency and wavelength. Although specific ranges for frequency and wavelength are indicated on the table, in reality, the spectrum is continuous Meaning, there is no definite division between types of waves and even some ranges actually overlap with one another.

c = 3.0 x 108 m/s Using the Spectrum All electromagnetic waves move at the speed of light We will denote the speed of light with the letter, c. c = 3.0 x 108 m/s

Fundamental Wave Equation for Light Waves The fundamental wave equation discussed previously relating speed, frequency and wavelength can be re-written to be specific for electromagnetic waves. c= fλ

Example pg. 522 Sample 14A The AM radio band extends from 5.4 x 105 Hz to 1.7 x 106 Hz. What are the longest and shortest wavelengths in this frequency range?

Brightness Brightness decreases by the square of the distance from the source. The further you get from a light source, the less bright the light appears to be. The further away from the light source, the more spread out the light gets.

Reflection of Light The texture of a surface affects how it reflects light When light is reflected, the angle of incidence an the angle of reflection are equal to each other.

Law of Reflection The normal is a line perpendicular to the surface It is at the point where the incident ray strikes the surface The incident ray makes an angle of θi with the normal The reflected ray makes an angle of θr with the normal θi = θr

Refraction When a ray of light traveling through a transparent medium encounters a boundary leading into another transparent medium, part of the ray is reflected and part of the ray enters the second medium The ray that enters the second medium is bent at the boundary This bending of the ray is called refraction

Refraction of Light The incident ray, the reflected ray, the refracted ray, and the normal all lie on the same plane The angle of refraction, θ2, depends on the properties of the medium

Refraction Light may refract into a material where its speed is lower The angle of refraction is less than the angle of incidence The ray bends toward the normal

Refraction Light may refract into a material where its speed is higher The angle of refraction is greater than the angle of incidence The ray bends away from the normal

Index of Refraction When light passes from one medium to another, it is refracted because the speed of light is different in the two media The index of refraction, n, of a medium can be defined

Snell’s Law of Refraction n1 sin θ1 = n2 sin θ2 θ1 is the angle of incidence 30.0° in this diagram θ2 is the angle of refraction

Total Internal Reflection Total internal reflection can occur when light attempts to move from a medium with a high index of refraction to one with a lower index of refraction Ray 5 shows internal reflection

Critical Angle A particular angle of incidence will result in an angle of refraction of 90° This angle of incidence is called the critical angle