Equilibrium Position Disturbance Period (T in sec) # sec T = # cycles Frequency (f in Hz) f = # cycles # sec Amplitude (A in cm, m or degrees [θ]) Other Harmonic Motion Basics Basic Definitions Pendulums Spring-Mass Systems Waves Where it comes to rest OR where it was before it was disturbed. At the bottom of the swing: point C. Equilibrium position Compressed Stretched trough crest Equilibrium position Halfway between crest and trough. Adding the initial energy OR moving the object away from equilibrium position; starts harmonic motion. Move the pendulum away from the equilibrium position; give it potential energy. Compress or stretch spring (move to one side and release). Giving energy to the medium (pushing down on water; moving a long spring side to side; etc). Amount of time it takes one cycle of the motion to repeat OR # sec T = = cycle f B A C D F E G H Time between any two repeated points on the wave: A to E; B to F; etc. f How many cycles occur in one second. How many times it swings back and forth # cycles = = T sec in one second. # of times it goes back and forth or up and down each second.. second # of cycles in sec. This graph shows: cycles in. sec, so the frequency = cycles Hz. sec = Amount of energy; strength of the motion; A = ½(side-to-side) A during cycle. Does not affect T or f. Dampens (see below) From A to C OR C to E. In degrees or radians. Amplitude From A to B OR B to C. Amplitude = cm From equilibrium to maximum displacement (crest or trough) A Amplitude = (side-to-side) Damping: gradual reduction of amplitude (loss of energy) over time. Amplitude does not affect period if <. Fspring = kx x distance from equilibrium position (in meters). More mass = lower equilibrium position (hanging springs only). vwave = f λ λ (lambda) is wavelength (in m) Wave speed depends only on medium it travels thru (water, air, etc). If medium changes (temperature; pressure; substance), v changes, too. Sound (Special Longitudinal Wave) Silence. db Any vibration of matter due to striking, rubbing, spinning, plucking, etc. Find frequency first, then calculate period. f = T Higher frequency = higher note or pitch. f = 66 Hz soprano f = Hz alto How loud a sound is; measured in decibels (db). +db = twice as loud. + db = times as loud, etc. More Ampl. = more pressure. compression (High pressure) rarefaction (Low pressure) cstephenmurray.com Copyright 9, C. Stephen Murray
Harmonic Motion Basics. Period, Frequency, or Amplitude? A. This increases as it vibrates back and forth faster. B. A wider swing means more of this. C. Time for one complete cycle to occur. D. If a pendulum swings slower this increases. E. Measured from the center to the extreme. F. Will decrease over time. G. In seconds. H. Contains the energy. I. Decreases when it vibrates back and forth slower. J. In Hz. K. Could be measured in degrees, cm, or meters. Position (cm) - - - - Position vs. Time.7.. Time (sec).. A. The pendulum s equilibrium position is: B. If the cycle begins at C going to the left, where does one cycle end? B. Where will the pendulum come to rest?. A pendulum has a period of. seconds. A. How many cycles will it undergo per second? B. What is its frequency?. A pendulum has a frequency of.6 Hz. Calculate the period of the pendulum. 7. The graph above shows the position of a pendulum moving back and forth over time. A. Mark one cycle on the above graph. B. How many total cycles are on the graph? C. The graph shows cycles in seconds. D. Calculate the frequency of the motion. E. What is the period of the graph? F. What is the equilibrium position? G. What is the amplitude of the graph? 8. How many centimeters are in a meter? 9. cm = m. Calculate the period of a pendulum that has a length of 68 cm.. A. Amplitude of Pendulum : B. Amplitude of Pendulum : C. Which has the most energy? D. Over time will the amplitude increase or decrease? E. This is called d.. A pendulum is cm long. Calculate its period.. A pendulum has a period of. seconds. How long is it? 6. Frequency is cycles per second, calculate the frequency of a pendulum that undergoes cycles in.6 seconds.. A spring moves back and forth, turning at points A and C. A. What is its amplitude? cm B. What distance does the spring travel in one complete cycle? cstephenmurray.com Copyright 9, C. Stephen Murray
=. sec cstephenmurray.com Copyright 9, C. Stephen Murray
Name: Period: Waves Ch : If you were to drop a rock in water you would make waves. You know that the waves move away from where you dropped the rock (linear motion), but when the waves pass, the water moves up and down (harmonic motion). Restoring force: To be harmonic motion, the waves have to have a restoring force. In water waves it is the water molecules. The water is compressed and expanded to cause the up and down (oscillating) motion. All waves do this with molecules they travel through. Waves combine harmonic motion and linear motion. Ocean waves travel: this is Linear Motion Ocean waves oscillate (move up and down): this is Harmonic Motion Waves can go through things: waves go through water; light waves can go through your skin; sound waves can goes through walls. If it can go through something, it is a wave. Two Types of Waves Transverse Wave (Perpendicular to direction of wave) Transverse waves (slinky moving side to side or up and down) moves perpendicular to the direction of the wave. Ocean waves are transverse waves, moving forward, but the oscillating up and down. Longitudinal waves (also called compression waves a slinky pushed and pulled) moves parallel (same direction) to the wave motion. Sound waves are longitudinal waves the sound moves forward and the oscillations move back and forth. Longitudinal Wave (Parallel to direction of wave) Earthquakes are made up of both transverse and longitudinal waves. The transverse waves do the most damage. Speed and Wavelength Different waves have different speeds and different wavelengths. New Terms: Wavelength (λ) the length of one cycle of the wave. Crest top peak Trough bottom peak Wavelength = m = (.7 m.7 m) The Speed (velocity) of a Wave velocity (m/sec) f = Hz λ = m v =? v = λ T v = f λ wavelength (m) period (sec) wavelength (m) frequency (Hz) Ex. Find the speed of a Hz wave that has a meter wavelength. v = fλ v = ( Hz) x ( m) v = m/s Amplitude = m Displacement (m) - - - - - Crest End of st cycle End of nd cycle Trough...7...7 Position (m) Amplitude = cm www.aisd.net/smurray Copyright, C. Stephen Murray
Name: Period: Ch :. Transverse wave. Longitudinal wave. Crest. Trough. Wavelength A. A wave where the oscillation is perpendicular to the direction of motion. B. The bottom of a wave. C. The top of a wave. D. A wave where the oscillation is in the same direction (parallel) as the motion. E. The length of one wave cycle. Wave Motion, Yes or No? FM radio: Music: A car going 7 m/s: A bulldozer: Clock pendulum: Earthquakes: Ocean waves: Cellphones: A wave has a wavelength of meters and a frequency of. Hz. What is its speed? Pendulum A is cm long and has a g mass on it. Pendulum B is cm long and has a g mass on it. Which one has a faster period? A wave is 8 meters long and has a frequency of Hz. Find speed. A wave has a period of seconds. Find its frequency. A wave has a frequency of Hz. Find its period. A wave has a speed of m/sec. If its frequency is Hz, what is its wavelength? Displacement (m) - - - - -...7 Displacement vs. Position...7. Position (m)..7 Mark cycle of the wave. Starting at m, where does the next cycle end: How many wavelengths long is the graph? Wavelength: Amplitude: If f =. Hz, find speed:...7 Displacement (m) - - - - -...7 Displacement vs. Position...7. Position (m)..7 Mark cycle of the wave. Starting at.7 m, where does the nd cycle end: Number of complete cycles: Wavelength: Amplitude: If f = Hz, find speed:...7 Position (cm) - - - - -.. Position vs. Time.. Time (sec). Mark cycle of the harmonic motion. Starting at. secs, when does half a cycle end: Number of complete cycles: Period: Frequency: Amplitude:. 6 www.aisd.net/smurray Copyright, C. Stephen Murray
Name: Period: What is Sound? Sound is the movement of compression waves (longitudinal waves) hitting our ears. These compression waves are alternating high and low pressure areas. The air molecules vibrate back and forth, but don t move. Speakers imitate sounds by pushing air and causing vibrations. sound source Sound Sound Wave Moving Through Air Molecules low pressure Tiny hairs inside the cochlea (inner ear) translate air pressure into electrical impulses that can be read by the brain. high pressure human ear cochlea How we graph sound: high pressure low pressure Sound needs a medium to travel through. Sound cannot travel through the vacuum of space. Space is silent (no matter what you hear in the movies). Ch : Frequency = Pitch We hear the frequency of sound as pitch. A higher frequency we hear as a higher pitch. A lower frequency we hear as a lower pitch. Humans can hear frequencies that are between Hz and, Hz! Higher Frequency = Higher Pitch Frequency (f) Wavelength (λ) Source Hz 7 m rumble of thunder Hz. m bass guitar, Hz 7 cm fire truck siren, Hz 7 cm highest note of piano, Hz. cm whine of a jet turbine Elephants and submarines use infrasonic sound (too low to hear) to communicate over long distances. Very low frequencies (very bass) travel for very long distances and can penetrate through water (just like thru cars). Dog whistles use ultrasonic frequencies frequencies above human hearing, but perfect for dog ears! Amplitude = Loudness We hear pressure (the amplitude) of sound as loudness. It takes more energy to create a louder sound. Too loud of a sound can cause deafness. Loudness is measured in decibels (db) - db A quiet whisper, feet away db A house in the country 6 db Ordinary conversation, feet away 7 db City traffic 9 db A jackhammer, feet away db The threshold of physical pain from loudness A + db change we hear as twice as loud. A db sound is twice as loud as a db sound. A - db change we hear as half as loud. A db sound is half as loud as a db sound. www.aisd.net/smurray Speed of Sound (v s ) The speed of sound changes. Hotter (faster) molecules conduct sound faster. Also, just as heat travels faster in solids, so does sound. Material V s (m/sec) Air Helium 96 Water Wood Gold Steel 9 The speed of sound in air is about m/sec (66 mph). You can use v s = f λ. to find frequency or wavelength. AND use S = D/T to find distance or time (using v s for S). Ex. Find the wavelength of a Hz sound. v s = m/s f = Hz λ =? v = f λ so λ = v/f λ = ( m/s) ( Hz) λ =.7 m Ex. If you hear a sound seconds after you see the motion. How far away is it? Vs = m/s T = sec D =? v s = D/T so D = v s T D = ( m/s) X ( sec) D = m Motion faster than sound is called supersonic. Supersonic planes give their speed in multiples of Mach ( X the speed of sound). Mach = m/s (66mph) Mach = 68 m/s ( mph) A sonic boom is caused by an object breaking through the sound barrier. Supersonic planes, bullets, and bullwhips all make sonic booms. Copyright, C. Stephen Murray
Name: Period: Ch :. Sound. Sonic boom. Supersonic. Ultrasonic. Cochlea A. Faster than the speed of sound. B. A wave caused by alternating high and low pressure. C. The organ that detects sound waves. D. A pressure wave caused by an object going faster than sound. E. A sound higher than humans can hear.. Pitch. db. Space. Loudness. v s A. Where there is no sound because of its vacuum. B. How we hear changes of frequency of sound. C. m/s in air. D. How we measure loudness. E. The amplitude or strength of a sound. Displacement (m) - - - - -. Displacement vs. Position.. A wave s velocity is 9 m/sec with a frequency of 6 Hz. What is it s wavelength? Position (m).. Use the graph to answer these questions: λ = cycle is from m to ; / cycle is from m to. Amplitude (A) = Total cycles: ; It is a sound wave; find frequency: Is this frequency audible to humans (can we hear it)? Why is space silent? A sound wave has a wavelength of m. Find its frequency. If a sound wave s frequency is Hz. What is its period? If I increase the energy I give a sound wave what changes: If a wave s fourth harmonic has a frequency of Hz, what is its natural frequency and what is the frequency of H 6? What is the above wave s wavelength? If a wave s fundamental is 6 Hz, what harmonic has a frequency of 8 Hz? A railroad crew is repairing a rail. You hear the hammer. seconds after it is swung. How far away is the crew? You hear a plane seconds after you see it. Find the distance to the plane. Find its period: What harmonic is this? Could a human hear this frequency? Mark the nodes and anti-nodes. If a sound is db loud. Answer how many db these would be: ) A sound twice as loud: ) A sound half as loud: Compared to a db sound, you would hear a 6 db as: How many wavelengths is it? Find the fundamental frequency: th harmonic frequency: 8 Hz www.aisd.net/smurray Copyright, C. Stephen Murray
Sound Recap and Wave Interactions Properties of waves Constant even with interactions Once a wave exists its frequency never changes only way to change the frequency is to change the source. Velocity of a wave depends on the medium the only way to change the velocity is the change the medium through which the wave is traveling. Changes with interactions Amplitude can change when waves interact. Amplitude gives loudness and energy. Each waves possesses different energies so they can exchange energies in their interactions. Superposition Principles: adding waves Beats: Standing Waves:
Resonance: when one object vibrating at the same natural frequency of a second object forces that second object into vibrational motion.
. Explain how he is able to make the glass to shatter: Label the diagram indicating both pitch and volume:.. How many wavelengths are present in the wave below? What is the wavelength of the wave below?. What causes velocity to change? 6. What causes amplitude to change? 7. What is the equation for the velocity of a wave? 8. When you increase the frequency or wavelength of a wave without changing the medium, what happens to the velocity? 9. When you increase the frequency of a wave without changing the medium, what must happen to the wavelength?. You decrease the wavelength by ½ without changing the medium, what happens to the frequency?. You have a wave with a wavelength of m and a frequency of 87 Hz. What s the waves velocity?. You have a wave traveling at m/s with a frequency of Hz. What is the wavelength?
Standing Wave Lab Change the frequency of the oscillator until you find a harmonic. You will know because the amplitude (antinode) will be big and the oscillator will be quieter. wavelength (λ) = antinodes. You will need to find the first 6 harmonics for your string. 6 7 8 9 th harmonic Measuring the wavelength wavelength Node Anti-node Node Anti-node Fill in the following table for each harmonic. Difference between frequencies: f f = f f = f f = f f = f 6 f = H (# of AN) Answer the questions on the back. 6 f (Hz) λ (m) V (= f λ) (in m/s) Standing Wave Lab Change the frequency of the oscillator until you find a harmonic. You will know because the amplitude (antinode) will be big and the oscillator will be quieter. wavelength (λ) = antinodes. You will need to find the first 6 harmonics for your string. 6 7 8 9 th harmonic Measuring the wavelength wavelength Node Anti-node Node Anti-node Fill in the following table for each harmonic. Difference between frequencies: f f = f f = f f = f f = f 6 f = H (# of AN) Answer the questions on the back. 6 f (Hz) λ (m) V (= f λ) (in m/s) Standing Wave Lab Change the frequency of the oscillator until you find a harmonic. You will know because the amplitude (antinode) will be big and the oscillator will be quieter. wavelength (λ) = antinodes. You will need to find the first 6 harmonics for your string. 6 7 8 9 th harmonic Measuring the wavelength wavelength Node Anti-node Node Anti-node Fill in the following table for each harmonic. Difference between frequencies: f f = f f = f f = f f = f 6 f = H (# of AN) Answer the questions on the back. 6 f (Hz) λ (m) V (= f λ) (in m/s) cstephenmurray.com Copyright 9, C. Stephen Murray
Lab Questions:. How many antinodes is one wavelength?. How many wavelengths is the first harmonic?. How do you find the wavelength of the first harmonic?. What did you notice about the difference between the frequencies each harmonic (left side of the table)?. What did you notice about the speed of the wave (v)? 6. As the frequency went up (bigger number) the wavelength went: Tighten the string slightly. Find the fourth or fifth harmonic and find the wavelength, frequency, and wave speed. 7. What changes occurred? Lab Questions:. How many antinodes is one wavelength?. How many wavelengths is the first harmonic?. How do you find the wavelength of the first harmonic?. What did you notice about the difference between the frequencies each harmonic (left side of the table)?. What did you notice about the speed of the wave (v)? 6. As the frequency went up (bigger number) the wavelength went: Tighten the string slightly. Find the fourth or fifth harmonic and find the wavelength, frequency, and wave speed. 7. What changes occurred? Lab Questions:. How many antinodes is one wavelength?. How many wavelengths is the first harmonic?. How do you find the wavelength of the first harmonic?. What did you notice about the difference between the frequencies each harmonic (left side of the table)?. What did you notice about the speed of the wave (v)? 6. As the frequency went up (bigger number) the wavelength went: Tighten the string slightly. Find the fourth or fifth harmonic and find the wavelength, frequency, and wave speed. 7. What changes occurred? cstephenmurray.com Copyright 9, C. Stephen Murray
Harmonic Motion In Class Review ) Which harmonic is λ long? ) Which has antinodes? ) Which has nodes? ) Calculate the wavelength of harmonic. ) Calculate the string s wave speed.. m 6) What is the wavelength of the fundamental? 7) What is the natural frequency of this string? 8) Which one has the greatest amplitude? 9) What is the wave speed for harmonic? ) These are the frequencies at which the string is r. 6 Hz ) A pendulum swings faster. A. Does the cycle occur more or less frequently? B. Therefore, does the frequency go up or down? C. Is the period faster or slower? ) How do you make a pendulum go faster ( ways)? D. Therefore, does the period go up or down? E. If the period goes up the frequency goes up or down? F. Is this direct or inverse relationship? ) Pendulum A, B, or C: A. Has the smallest period? B. Has the biggest amplitude? ) What is the same between pendulum A and B? ) What is the same between pendulum B and C? 6) Does A or B have the highest frequency? 7) What is the amplitude of pendulum C? 8) Find the period of pendulum B. A º B º C º 9) How do you change the period of a spring? ( ways) A M M B C ) Which of the three springs will have the fastest period? ) Why? ) How far does Spring A travel side-to-side? 6) How far will Spring C travel in one complete cycle? ) Which spring was disturbed the most? ) Why? 7) If M = g, find the period of Spring A. ) What is Spring B s amplitude? cstephenmurray.com Copyright 9, C. Stephen Murray
Position (cm) - - - -. Position vs. Time..7 Time (sec)...7 Displacement (m) - - - - -. Wave Graph Position (m). 8) A. Amplitude = B. Equilibrium position = C. Mark a crest and a trough. D. # of cycles = E. Period = F. Frequency = 9) A. Where will it come to rest? B. Amplitude? C. # of wavelengths D. Length of the graph = E. Calculate the wavelength. ) If a sound wave has a wavelength of cm, A. Calculate its frequency. 6) f = 8 Hz; f = 8 Hz. A. How many beats will you hear? B. What causes the beats? B. What is its speed if you double the amplitude? ) Sound is generally faster in: A. Solids or gases? B. Helium or oxygen? C. Tight things or loose things? D. Denser objects or less dense objects? ) What is the speed of sound in space? ) Which has a higher frequency: long or short wavelengths? ) Higher frequency: bird or elephant? ) Which has the shorter wavelength: a bird or an elephant? ) A longitudinal wave is moving up, which way are the vibrations moving? 7) A race car is moving towards you. A. Is the pitch of car higher or lower than normal? B. Is the wavelength of the sound longer or shorter? C. What is this called? D. What will happen when it passes you? 8) What is timbre? 9) Sound waves are longitudinal or transverse? ) How different is 6 db from db? 6) Draw what will happen when the wave passes. ) For motion to be harmonic: A. It has to have a r force. B. This force has to pull to the m. ) Give an example of motion that repeats, but is NOT harmonic motion. ) A person yells up to a ceiling and hears the echo.6 seconds later. How high is the ceiling? ) A g object is hung onto a spring. It stretches 8 cm. Find the spring s spring constant. 7) The above pictures show: 8) Echoes occur when sound. 9) Light bends as it passes from air to glass: ) Sound dying out in a soft boundary is called: ) When two waves interact with each other, causing a greater amplitude: ) When two waves interact with each other, causing a smaller amplitude: ) When one object vibrates from the energy of another wave (like one tuning fork causing another to vibrate): cstephenmurray.com Copyright 9, C. Stephen Murray
cstephenmurray.com Copyright 9, C. Stephen Murray
cstephenmurray.com Copyright 9, C. Stephen Murray