Work To move an object we must do work Work is calculated as the force applied to the object through a distance or: W F( d) Work has the units Newton meters (N m) or Joules 1 Joule = 1 N m Energy Work and Energy Examples There are 2 types of Energy that we will deal with, Kinetic energy and Potential Energy Potential Energy: is the energy of position or stored energy E p = F (Δd) Kinetic Energy: is the energy of motion E k = ½ mv 2 What amount of work is done by Jane as she lifts a box of mass 20.0 kg to a height of 1.5 m? W = F (x) g W = (20.0 kg)(9.81 m/s 2 )(1.5 m) W = 294 J What is the Kinetic energy of an object moving at 5.00 m/s that has a mass of 5.00 kg? E k = ½ mv 2 E k = ½(5.00 kg)(5.00 m/s) 2 E k = 62.5 J 1
What are Waves?? They are the motion of a disturbance. They are a means of transferring energy without the particle moving. Classifications of Waves Mechanical Waves 1-Dimensional (waves on a spring or rope) 2-Dimensional (waves in Water) 3-Dimensional (sound waves) All require a medium to travel through Governed by Newton s Laws Electromagnetic Waves 3-Dimensional (light, x-rays) Do not require a medium to travel through Governed by Electromagnetic Wave Theory Matter Waves 3-Dimensional (waves associated with electrons, protons etc) Do not require a medium to travel through Governed by Quantum Mechanics 2
Periodic Motion Motion that repeats itself over and over Ex: heart beats, ticking clock, moving on a swing The time it takes for one complete cycle of the motion is called the. Other Terms to Know Cycle One complete back and forth motion Frequency the number of cycles per unit time. It is measured in Hertz (Hz) Displacement the distance an object moves from the equilibrium position Amplitude the maximum displacement Simple Harmonic Motion (SHM) A type of periodic motion Objects that vibrate with SHM are called Simple Harmonic Oscillators An example of this is a mass on a spring, pendulums, and waves Mass on a spring When there is a mass on a spring, there are 2 forces that are acting on it. Gravity and the Tension of the spring Tension on the spring is governed by Hooke s Law 3
Hooke s Law F kx F is Force k is the spring constant X is the displacement When the spring is stretched F T > F g then the mass moves upwards When the spring is compressed F g > F T then the mass moves downwards Hooke s Law Example A mass of 15.0 kg is suspended from a spring. If the spring has a spring constant is 6.00 N/m, what is the restoring force of the spring when the mass is 0.30 m from equilibrium? F kx F -(6.00 N/m)(0.30 m) F -1.8 N MASS ON A SPRING Mass on a Spring Example e A M k = the spring constant in N m - 1 Stretch & Release T 2 m k A 0.23 kg object vibrates at the end of a horizontal spring (k = 32 N/m) along a frictionless surface. What is the period of the vibration? T = 2 (m/k) T = 2 (0.23 kg / 32 N/m) T = 0.53 s 4
Hooke s Law Cont. DAMPING DISPLACEMENT If there was no force to slow the motion down, it would continue forever The force that causes the slowing of the motion is called the Restoring Force The Restoring force is governed by the spring constant, k INITIAL AMPLITUDE THE AMPLITUDE DECAYS EXPONENTIALLY WITH TIME time Hooke s Law Cont. When there is a Restoring force, the systems will become damped Where is this idea of a damped system used in your daily life??? THE PENDULUM The period, T, is the time for one complete cycle. l T 2 l g 5
Pendulum Example Find the length of a pendulum that has a period of 0.90 s. T = 2 (l/g) 0.90 s = 2 (l / 9.81 m/s 2 ) l = (0.90 s / 2 ) 2 (9.81 m/s 2 ) l = 0.20 m Energy in SHM Work is done on an object when we apply a force over a distance W Fx For a spring, the work is moving the object to its maximum displacement W 1 2 Fx Energy in SHM Cont. Potential Energy stored in the spring is E p = ½ x And F F k x So E p = ½ k x 2 But the mass moves on the spring back and forth changing from Kinetic to potential Energy Kinetic Energy is: E k = ½ mv 2 Total Mechanical Energy is: E T = E p + E k E T = ½ k x 2 + ½ mv 2 Are there different Types of Waves?? You bet there are 6
Longitudinal Transverse Surface Types of Waves Transverse waves The wave particles vibrate perpendicular to the transfer of energy An example of this is a wave on a string Waves in solids are transverse waves Transverse waves Crests Highest part of a wave Troughs The low points of the wave Longitudinal Waves The wave particles vibrate parallel to the transfer of energy An example of this is a sound wave Waves in gases and liquids usually are longitudinal waves 7
What the waves look like Compressions The close together part of the wave Rarefactions The spread-out parts of a wave Surface Waves These are waves that move particles in both longitudinally and transversely Ex: Water waves 8
Wave Characteristics All waves have 5 Characteristics Frequency Period Wavelength Velocity Amplitude Wave Characteristics Cont. Frequency (f) the number of cycles or oscillations per second. Measured as 1/s, or s -1, or Hertz (Hz) 1 Hz = 1 cycle per second Ex: A car travels 8 times around a track in 4 seconds. What is the frequency? f = #cycles/time = 8/4 = 2 Hz Wave Characteristics Cont. Period (T) The time required for one cycle to be completed Measured in seconds (s) T = 1/f Ex: What is the period from the previous question? T = 1/f = ½ = 0.5 s Wave Characteristics Cont. Wavelength (l) The distance between successive parts of a wave. The parts can be either the Crest or the Trough of the wave 9
Wave Characteristics Cont. Velocity (v) The speed of a wave through a medium depends on the Elasticity and the density of the medium V = (elasticity/density) The speed of the wave can also be determined using the wave characteristics v = l/ T or v = lf Which is known as the Universal Wave Equation Which is a form of uniform motion: v = Δd/Δt Velocity Example Ex: What is the velocity of a wave with a frequency of 10 Hz and a wavelength of 10 m? v = lf v = 10 Hz * 10 m v = 100 m/s Wave Characteristics Cont. Amplitude (x) The maximum displacement from equilibrium (or rest position) of a wave Wave Characteristics 10
10 Characteristics of Waves 1. Propagation 2. Reflection 3. Polarization 4. Refraction 5. Diffraction 6. Interference 7. Diffusion 8. Color 9. Dispersion 10.Scattering Propagation How a wave moves from one position to another All the motion is in a straight line Wave speed is determined by the medium that it is traveling in Calculated using either v = Δd/Δt v = fλ Reflection The bouncing of a wave off a reflective boundary Law of Reflection Θ i = Θ reflection v, f, T, and λ DO NOT CHANGE 11
Polarization When the displacement of the particles is in the same plane Passing a wave through a slit aligned in a direction produces a polarized wave If 2 slits that are perpendicular are used, the wave is destroyed Does not occur in Longitudinal waves only Transverse waves Refraction Occurs when a wave meets a boundary at an angle Where the wave and the boundary meet, the angle taken from the normal is called the Angle of Incidence Θ i Refraction Cont. v and λ must change because you are going into a new medium The speed will decrease when the wave refracts to the normal The speed will increase when the wave refracts away from the normal To calculate the angles, speed, and wavelengths λ 1 = sin Θ 1 = v 1 = n 2 λ 2 sin Θ 2 v 2 n 1 Refraction Cont. n refers to the Index of Refraction and is an indication of the density in comparison to the density of air i refers to the incident medium and r to the refractive medium In this form, the equations are only to be used with mechanical waves 12
Refraction Example Waves travel from deep water into shallow water. If the angle of incidence is 30.0 o, and the angle of refraction is 20.0 o, what is the index of refraction? sinθ 1 = n sinθ 2 sin 30.0 o = n n = 1.46 sin 20.0 o Diffraction Are waves able to bend around corners? Yes they can, this is called Diffraction How much they bend depends on the wavelength and the size of the opening the λ the the diffraction and vice versa the opening the the diffraction Diffraction Interference Occurs when 2 waves simultaneously act on the same particles 2 types of Interference Constructive Interference Destructive Interference Also known as the Principle of Superposition 13
Constructive Interference When 2 waves come together and the resulting wave is GREATER than either of the original waves Destructive Interference When 2 waves come together and the resulting wave is SMALLER than either of the original waves Diffusion The ability of the wave to spread The Other Characteristics 8. Color 9. Dispersion 10.Scattering All of these characteristics will be discussed during Light waves 14
2-Dimensional Waves Speed varies with respect to the depth Small depth, small speed and vice versa Amplitude varies with respect to the depth Small depth, big amplitude Tsunami Tsunami Warning On December 26, they were playing in the sea when Tilly suddenly found the water was bubbling, like on top of a beer. She immediately realized tsunami was coming because the scene reminded her of a geography lesson about Hawaii's 1946 tsunami. Right away, Tilly told her parents, sister and other tourists to escape quickly, but at first they were in half belief. However, seeing Tilly's serious and firm expression, people started to be convinced of the seriousness of the thing and instantly left the beach. At last over 100 tourists were ended up in safety with no death http://www.phy.ntnu.edu.tw/java/propagation/propagation.html 15
Ripple Tank Most of the characteristics of waves can be seen through the use of a ripple tank 3-Dimensional Waves 3-D Waves Cont. Ex: Sound waves These move as longitudinal waves in air and transverse waves in solids These waves carry energy that will stimulate the ear drum Sound is produced by the compression and rarefaction of the medium The average person can hear frequencies from: infrasonic 20 Hz to 20000 Hz ultrasonic All sound waves have v, f, T, and λ Frequency of sound waves is the # of vibrations per second This is also called the PITCH 16
Doppler Effect Have you ever noticed that as a siren moves towards you, the sound gets louder and when it moves away the sound is quieter? This is called the Doppler Effect Doppler Effect The Doppler Effect states that the frequency of the observed sound is related to the velocity of the sound, the velocity of the observer and the frequency of the original sound f O v vo f ( ) I v v S Doppler Effect Cont. V o is + if the observer is moving towards the sound V o is if the observer is moving away from the sound V s is if the source is moving toward the receiver V s is + if the source is moving away from the receiver Doppler Effect Example A car is travelling 29 m/s toward a stationary sound (whistle) that has a frequency of 625 Hz. If the speed of sound is 337 m/s, what is the apparent frequency of the sound as heard by the driver of the car? 17
Doppler Effect Example Cont. f O v vo f ( ) I v v S = 625 Hz (337 m/s + 29 m/s) 337 m/s - 0 m/s f o = 679 Hz 3-D Wave Cont. Amplitude is the maximum displacement from equilibrium In the case of sound, the amplitude is the volume of the sound Sound Intensity The intensity of a sound, or its loudness, is measured in Decibels, db 0 db is the threshold of hearing An increase in 10 db s means that the intensity increases by a factor of 10 An increase from 40dB to 60 db means that 60 db is 100 times as intense as 40 db Speed of Sound in Air At sea level the speed of sound is 331 m/s Velocity of the sound wave depends on the temperature v = (331 + 0.6T) m/s Where T is in o C 18
What is the speed of sound at 20 o C and at -20 o C? v = (331 + 0.6T) m/s = 331 m/s +0.6(20 o C) = 331 m/s + 12 m/s v = 343 m/s v = (331 + 0.6T) m/s = 331 m/s + 0.6(-20 o C) = 331 m/s - 12 m/s v = 319 m/s Diffraction This is the bending of a wave around a corner. You can hear a person s voice as it passes through a doorway or window even if you are around a corner. This is because the opening acts as a barrier causing the sound wave to bend around it. Diffraction Cont. Those waves with long wavelengths will diffract more than those with a smaller wavelength The size of the opening also plays a role in this Lower frequencies will diffract more because of their long wavelengths Refraction The speed of sound is dependant on the temperature that the air is at Sound will travel faster in warm air than in cold air 19
Refraction Cont. During the day, your voice will tend to rise because of refraction. The air above is colder than the air below During the night, your voice will tend toward the ground because the air below is colder At night or over water your voice will travel further Interference When 2 sound waves that of different frequencies, when they meet you will hear a beat The waves will be move from in-phase to out of phase The will come when the frequency are in phase This is call the Beat Frequency Beat Frequency The beat frequency is the result of the interference of 2 waves It is calculated as follows: # of beats = f 1 f 2 Natural Frequency The frequency at which an object will vibrate Ex: swinging on a swing, windows rattling when a truck goes by The tendency for an object to vibrate at it s natural frequency is called RESONANCE 20
Resonance There are 2 types of Resonance Mechanical Acoustical Mechanical Resonance Mechanical Resonance is created when one object is forced to vibrate at its natural frequency by a physical force being placed on the object Examples of this would include marching on a bridge or the Tacoma Bridge Disaster Acoustical Resonance Resonance can occur when a standing wave is generated The wavelength for resonance to occur is called the resonant frequency Examples of this include the guitar, violin, cello, or any other string instrument Acoustical Resonance Cont. A resonant frequency can also be set up in a wind instrument The sound travels through the pipe of the instrument and is reflected back If the wavelength of the sound waves are matched, the waves will create a standing wave pattern The sound emitted will have the same frequency as that of the waves in the pipe 21
Resonance in Air Columns When a tuning fork is held over an open end of a hollow tube of a certain length then Resonance may be heard This is caused by the interference produced by the standing waves Standing Waves Occurs when 2 waves of equal wavelength and amplitude travel in opposite directions on the same medium They have alternating nodes and antinodes Standing Waves Cont. The distance between nodes is ½ λ This is also true for the distance between antinodes Node: area where there is zero amplitude Antinode: Area where amplitude is a maximum Terminology Natural Frequency: the frequency that a medium vibrates Resonant Frequency: the frequency that causes an air column to vibrate Fundamental Frequency: the lowest natural frequency. Also called the First Harmonic 2 nd Harmonic: Frequency of 2 x the fundamental 3 rd Harmonic: Frequency of 3 x the fundamental 22
Closed At One End Resonance can only occur if there is an ANTINODE at the open end and a NODE at the closed end This is necessary for a standing wave to be produced for resonance The length of the air column must be equivalent to ¼ of the wavelength produced by the tuning fork Closed At One End Cont. Resonance can also occur when the length of the tube is ¾ λ The 1 st resonance occurs when the air column length is ¼ λ The 2 nd resonance occurs when the air column length is ¾ λ Each successive resonance will occur when the lengths are 5/4, 7/4. Open At Both Ends Resonance can only occur if there is an ANTINODE at both ends This is necessary for a standing wave to be produced for resonance The length of the air column must be equivalent to ½ λ Open At Both Ends Cont. The 1 st resonance occurs when the air column length is ½ λ of the tuning fork The 2 nd resonance occurs when the air column length is 2/2 λ of the tuning fork Each successive resonance occurs when the air column length is 3/2, 4/2, 23
Earthquakes The power of Resonance Earthquakes occur when the ground moves This moving earth produces 2 types of waves: Primary or P waves and Secondary or S waves Primary Waves The Primary waves are the first to come from the earthquake These waves are able to pass through the crust of the Earth as well as the core of the Earth The waves will refract as they pass through the core Secondary Waves Secondary waves are the second waves to be felt during an earthquake These waves can only move through the crust of the Earth These waves will reflect off the core 24
Generate an Earthquake 25