Waves Notes and Worksheet (PDF)

PHYS 11 Introduction to Mechanical Waves Heath 7.1 – 7.4 Waves Waves are a __________________ that transfers _______________ from one point to another. Mechanical Mechanical waves are a special, easily observa...

PHYS 11 Introduction to Mechanical Waves Heath 7.1 – 7.4 Waves Waves are a __________________ that transfers _______________ from one point to another. Mechanical Mechanical waves are a special, easily observable type of wave. A mechanical wave occurs when energy travels through some ______________ by physically moving the particles within it. The medium (pl. media) is whatever matter the wave is _____________: water is the medium for surface waves on a lake; ___________ is (often) the medium for sound waves; or a rope might be the medium for a pulse traveling along it. Mechanical waves can occur in two distinct types: _________________ and ________________. These are defined based on how the medium __________________ (moves in a repetitive motion) relative to the motion of the wave itself. A transverse wave is what we normally think of when we imagine a wave. Here, the particles move ______________________ to the direction that the wave travels in. A wave moving along a rope or string is a good example of a transverse wave. 1 - The direction of wave motion (energy travel) and particle motion (oscillation) of a transverse wave. A longitudinal wave (or pressure wave or compression wave) is harder to visualize, but it is also perhaps more common in regular, everyday application: ____________________ are longitudinal waves. In this type of wave, the _________________ move in the __________________________ as the motion of the wave. 2 - The direction of wave motion (energy travel) and particle motion (oscillation) in a longitudinal wave. There are other types of mechanical waves, too. For example, water waves are actually a _________________ of transverse and longitudinal waves: water particles on the surface of a lake actually move in a ________________________ which has both up/down (transverse) and forward/backward (longitudinal) components of motion. ANIMATION URL: http://www.acs.psu.edu/drussell/demos/waves/wavemotion.html Generally speaking, there are two ways that we can produce a wave. Pulse A pulse is generated by rapidly _______________ (transverse) or _______________ (longitudinal) the medium and then returning it to normal. The result is a single wave chunk that moves along the medium, which we will draw in below: 3 - A transverse up-only pulse (top) and up-down pulse (bottom) traveling along a string. Periodic Wave A periodic wave is generated by repeatedly applying the same pulse 4 - A transverse up-only periodic wave (top) and up-down periodic wave (bottom) traveling along a string.  Unit  4  Waves  and  Optics  Day  2   The  Universal  Wave  Equation   Lets  Draw  a  wave   Medium:       Crest:     Trough:     Amplitude  (A):     Waves  with  higher  ________________  have  ___________  Energy     Wavelength  (λ):     Frequency  (f):   Waves  with  ____________  _______________  have  ___________     Energy   Ex,  8  waves  pass  in  2  seconds       Period  (T):   Ex:  Playing  middle  C  on  a  piano  produces  a  sound  with  a   Ex,  the  wave  in  last  example  would  have  a  period   frequency  of  256  Hz.  What  is  the  period  of  the  sound   of  _______________   wave?       Frequency  and  period  are  reciprocals,  that  is:     Wave  Transmission       In  general,  the  speed  of  any  wave  through  a  medium  is  _____________  regardless  of  the  ___________  of  the  wave.  For   example,  a  sound  wave  always  travels  at  ____________  in  air  at  sea  level  and  room  temperature  regardless  of  its  pitch   (__________)  or  volume  (_____________).  In  steel,  a  longitudinal  wave  always  travels  at  _____________  while  a   transverse  wave  always  travels  at  ______________.       Changes  to  the  composition  of  a  material  can  change  the  speed  of  wave  transmission.  Here  is  a  general  rule:     All  other  things  being  equal,  higher  _____________  means  faster  wave  travel.  Logically,  because  they  are  more  rigid,   the  particles  are  more  tightly  bound  together,  so  movement  by  one  particle  has  a  significant  effect  on  adjacent   particles.           Remember  that  speed  is       IF  we  look  at  a  single  wave  then:     (1)     (2)       This  gives  us  the  Universal  Wave  Equation:        Ex:  An  air  horn  sounds  at  a  frequency  of  220  Hz.  If   Ex:  The  distance  between  successive  crests  in  a  series   the  speed  of  sound  in  air  is  330  m/s  what  is  the   of  water  waves  is  4.0  m,  and  the  crests  travel  8.6  m  in   wavelength  of  the  sound  wave?   5.0  s.  Calculate  the  frequency  of  a  block  of  wood     bobbing  up  and  down  on  these  water  waves.     Wave Worksheet 1-2 1. Suppose that a longitudinal wave moves along a Slinky at a speed of 5 m/s. Does one coil of the Slinky move through a distance of 5 m in one second? Justify your answer. 2. Give one example of a transverse wave and another of a longitudinal wave, being careful to note the relative directions of the disturbance and wave propagation in each. 3. What is the difference between propagation speed and the frequency of a wave? Does one or both affect wavelength? If so, how? 4. What is the period of 60.0 Hz electrical power? 16.7 ms 5. If your heart rate is 150 beats per minute during strenuous exercise, what is the time per beat in units of seconds? 0.400 s/beat 6. Find the frequency of a tuning fork that takes 2.50 × 10−3 s to complete one oscillation. 400 Hz 7. A stroboscope is set to flash every 8.00 × 10−5 s. What is the frequency of the flashes? 12500 Hz 8. Storms in the South Pacific can create waves that travel all the way to the California coast, which are 12,000 km away. How long in days does it take them if they travel at 15.0 m/s? 9.26 d 9. Waves on a swimming pool propagate at 0.750 m/s. You splash the water at one end of the pool and observe the wave go to the opposite end, reflect, and return in 30.0 s. How far away is the other end of the pool? 11.3 m 10. Wind gusts create ripples on the ocean that have a wavelength of 5.00 cm and propagate at 2.00 m/s. What is their frequency? 40.0 Hz 11. How many times a minute does a boat bob up and down on ocean waves that have a wavelength of 40.0 m and a propagation speed of 5.00 m/s? 7.50 times 12. What is the wavelength of an earthquake that shakes you with a frequency of 10.0 Hz and gets to another city 84.0 km away in 12.0 s? 700 m 13. Radio waves transmitted through space at 3.00 × 108 m/s by the Voyager spacecraft have a wavelength of 0.120 m. What is their frequency? 𝟐. 𝟓𝟎 × 𝟏𝟎𝟗 Hz 14. A person lying on an air mattress in the ocean rises and falls through one complete cycle every five seconds. The crests of the wave causing the motion are 20.0 m apart. Determine (a) the frequency and (b) the speed of the wave. 0.200 Hz, 4.00 m/s        Unit  4  Waves  and  Optics  Day  3   Wave  Interference     http://phet.colorado.edu/sims/html/wave-­‐on-­‐a-­‐string/latest/wave-­‐on-­‐a-­‐string_en.html     Boundary  Interactions     Waves  can  travel  from  one  medium  to  another.    The  interface  between  the  two  media  is  called  a  _____________.    Part   of  the  energy  of  the  wave  will  _______________  through  and  continue  on  as  a  new  wave  in  the  medium  (transmitted   wave),  while  some  of  the  energy  of  the  wave  will  _____________  _____________  and  continue  on  in  the  old  medium   (reflected  wave).    The  amount  of  transmission/reflection  depends  on  the  respective  ______________  of  the  two  media.     Fixed  End  Reflection     A  wave  pulse  reaching  the  end  of  a  medium  becomes   ________________  whenever  it   reflects  off  a  _________________   moves  from  a  ______________  medium  into  a   __________  medium         http://www.aplusphysics.com/courses/regents/waves/regents_wave_interference.html   Free  End  Reflection     A  wave  pulse  reaching  the  end  of  a  medium  remains   _______________  whenever  it   reflects  off  a  ____________   moves  from  a  ___________  medium  into   ______________  medium           Example  -­‐  A  wave  pulse  is  sent  along  a  string.    The  string  is  attached  to  a  thick  rope  that  is  attached  to  a  wall.    What   happens  when  the  wave  reaches  the  string/rope  boundary?    Is  the  reflected  wave  erect  or  inverted?              Note:    For  most  boundary  interactions:     Wavelength   Frequency   Speed   Amplitude   Incident  Wave           Reflected  Wave       Transmitted  Wave             Example:  A  wave  travelling  along  a  rope  has  a  speed  of  10.0  m/s  and  a  wavelength  of  5.00  m.    The  rope  is   connected  to  a  light  string  at  the  end,  and  the  transmitted  wave  has  a  speed  of  20.0  m/s.    What  is  the  wavelength  of   the  new  wave?    [13.3  m]       Wave  Superposition   When  two  waves  travel  in  the  same  medium   Two  waves  with  the  __________   Two  waves  with  the  same   they  affect  the  medium  independently.  To   frequency  and  phase.   frequency  and  _________  phase.     determine  their  overall  effect  we  use  the       principle  of  superposition.     Constructive  Interference:     Destructive  Interference:         Principle  of  Superposition:     The  total  amplitude  of  the  waves  is  equal  to...               Type   Type       Pattern:   Pattern:                   Type       Type   Pattern:       Pattern:               Type   Type       Pattern:   Pattern:           Example  -­‐  Pulse  A  is  traveling  towards  pulse  B.    Pulse  A  has  an  amplitude  of  +2.    Pulse  B  has  an  amplitude  of  –3.    Draw  a   diagram  of  this  interaction.    What  will  the  amplitude  of  the  resultant  wave  be?    What  type  of  interference  is  this?            Unit 4 Waves and Optics Day 4 2D Wave Interference Like 1D waves on a string, a 2D waves on a surface can ___________ with one another. This interaction is very complicated and difficult to model for most points, but it can be understood relatively easily using the concept of nodes and antinodes. We will generate a two-point-source interference pattern. To do this, we will begin with two point sources like the one shown to the right. Note the ________ (solid lines) and _________ (dotted lines), with the point source in the center. We are only drawing the upper half of the circular wave; the exact same thing would be found on the lower half of the page. The interference pattern generated by two such sources side-by-side can be produced by identifying ___________ and __________ where the two waves overlap one another. We will do this in the space below. Use solid dots for antinodes and hollow dots for nodes: ANTINODES: points where any two wavefronts interfere _____________ (crest/crest or trough/trough) NODES: points where are two wavefronts interfere _____________ (crest/trough) Nodal/Antinodal Lines As you fill in the nodes and antinodes, you will observe a pattern where you see lines forming between the two sources. These lines are called nodal and antinodal lines. The density of these lines depends on how ________________ the two sources are: If they are far apart relative to their wavelength, there are __________ lines, but they are small – very distant sources have tiny nodal/antinodal lines that are _________ to see If they are close together relative to their wavelength, there are ____________ lines, and they are much __________ ____________ or pronounced when you look for them Let’s try to build one on the next page Physics 11 Name:__________________ Two point sources oscillating in Phase: 2D interference Block:_________________ SCREEN Source Source # # 1 2 Legend: Solid Circles represent Crests Dashed Circles represent Troughs  Unit 4 Waves and Optics Day 5 Introduction to Sound Sound Frequency Sound is a ____________________ wave produced by a The ___________ of sound is determine by Frequency vibrating object. Imagine a flat surface moving back and forth inside a speaker. The vibrations of the speaker high-frequency → ____________-pitch (_________), surface result in compressions and rarefactions in the air. low-frequency → _____________-pitch (_________). Your _____________, in turn, perceive these vibrations as sound. Determine Max and Min Audible Frequencies 𝑓!"# :________________ 𝑓!"# :___________________ Side note: dogs can hear both lower and higher pitched sounds (15 Hz – 50 kHz) than humans, while cats can hear higher pitched sounds than dogs or humans but cannot hear low-pitched sounds that we can hear (60 Hz – 65 kHz). Speed of Sound Mach Number The speed of sound depends on its _______________ (more dense → faster) a ___________ of the object speed to the speed of sound, so you can calculate it from: 𝑣!"#$%& 𝑣 𝑀𝑎𝑐ℎ 𝑁𝑢𝑚𝑏𝑒𝑟 = = sound travels at ___________ in air at room temperature 𝑣!"#$% 343 or __________ in air at 0 °C. ex) What is the speed of a cruise missile travelling at Mach Sound travels faster in _________ air compared to 0.8? _________ air. Speed increases by about ______________________ of air temperature. 𝒗𝒔𝒐𝒖𝒏𝒅 = Ex) What is the speed of sound at 5 °C air? Ex) A bass guitar produces a 70-Hz sound wave at room temperature. Determine the length of the sound wave. Ex) A 250-Hz sound wave is 1.42 m long. Determine the speed of sound in air for this situation and the corresponding air temperature Sound Volume Volume of a sound (or its intensity) is based on the ___________________ of the wave. Higher amplitude waves → more ______________ = _______________ volume. We use the decibel scale (units decibels, or dB) to measure the intensity of a sound. There is a fancy way to relate decibels to the power delivered to your ear by the sound wave, but the simplest way to think of it is this: 0 dB is an arbitrarily defined, incredibly low-intensity sound For every increase of 10 dB, the sound is 10x more intense. See the table below: Sound Intensity (dB) Intensity Compared to Base Level 0 Base Level 10 10 x 20 100 x 30 1000 x Beat An interference pattern between two sounds of slightly different __________________. What you hear is a beat with periodic variation in volume. 𝒇𝒃𝒆𝒂𝒕 = 𝒇𝟐 − 𝒇𝟏  Unit 4 Waves and Optics Day 6 Standing Wave and Diffraction Standing waves are caused by _______________ and How to create Standing Waves? _________________ interference When a wave hits a ___________________ it will Areas of complete destructive interference have reflect and _________ its amplitude. ____________________ and are called ____________ If a series of waves are sent along a string the Areas of complete constructive interference have reflected pulse will…… __________________ are called ____________ Standing waves have fixed ______________________ called ________________. If the waves are sent at just the right _____________ we will create a standing wave Two fixed ends (Standing wave in a rope. Ex, string instruments: guitar) I------------------------------L---------------------------------I One open End – standing wave in Air Column Mouthpiece – pressure varies as you blow (varying pressure = ____________) A B C D pressure fixed at the closed end = ___________ Ex) Use the graphic below to answer these questions 1) Which harmonic is shown in each of the strings below? 2) Label the nodes and antinodes on each of the standing waves shown below. 3) How many wavelengths does each standing wave contain? 4) Determine the wavelength of each standing wave. Ex) A clarinet is essentially a tube that is open at only one end. Sketch the wave patterns associated with the first and third harmonic of a clarinet that is 67.5 cm long. What frequencies would these waves have if the clarinet was played at 21.0oC? (128 Hz, 383 Hz) Diffraction When waves hit a ____________________ (hole) or a ________________________ (like a corner) they bend around. Forming ___________________ waves that spread out. The ___________________ the aperture compared to the wavelength, the more pronounced this effect is (Lets see and sketch some examples). Wide gap → Narrow gap → Large wavelength → __________ diffraction effect __________ diffraction effect __________ diffraction effect  Unit 4 Waves and Optics Day 7 Doppler Effect Have you ever listened to an ambulance drive by quickly with their sirens going? What did it sound like? _______ pitch as the ambulance was coming, ________ pitch as it was leaving This phenomenon is called ___________________ after Christian Doppler, who first labeled it in 1842. when the truck is moving, it produces a sound wave when the truck is still, the sounds waves move (compression), move, produce another sound wave, etc. outward in all the directions at the same ___________ and ____________ since it moves between sound production, the air compressions (sound) are____________________ in front of the truck and ___________________ behind the truck Short _____→ higher __________→ _______ pitch long _____→ Lower __________→ _______ pitch 𝑓! = frequency observed 𝑣! = speed of the source ±/∓ Use the top signs when 𝒗𝒘 ± 𝒗𝒐 𝑓! = frequency of source 𝑣! = speed of the observer the object is moving 𝒇𝒐 = 𝒇𝒔 ( ) 𝒗𝒘 ∓ 𝒗𝒔 𝑣! = speed of wave (sound) _____________ the other object Ex) What frequency is received by a mouse just before being dispatched by a hawk flying at it at 25.0 m/s and emitting a screech of frequency 3500 Hz? Take the speed of sound to be 331 m/s. Ex) You are driving down the road at 20 m/s when you approach a car going the other direction at 15 m/s with their radio playing loudly. If you hear a certain note at 600 Hz, what is the original frequency? (Assume speed of sound is 343 m/s) Ex) A duck is flying overhead while you stand still. As it moves away, you hear its quack at 190 Hz. Because you are a brilliant naturalist, you know that this type of duck quacks at 200 Hz. How fast is the duck flying? Sonic Boom: The image below shows how wavefronts travel for an object traveling slower than the speed of sound, equal to the speed of sound and faster than the speed of sound: In case (1), the different spacing at the In case (2), at the leading edge all of In case (3), anyone standing on the front and behind the object as it the wave fronts are stacked up: this ground as the line of sound waves hits moves to the right explains why you creates a VERY high-pressure zone in experiences a _________________: all hear different pitches as an front of the object. of those stacked up sound waves ambulance gets closer and then drives make a very loud noise that hits you past you: at the front, the wave fronts all at once, sounding like an explosion. are packed closer together, so it sounds high-pitched; the opposite is true at the back Worksheet 7: Doppler Effect and Sonic Booms 1. The pitch of a sound depends on the ______________ of the sound waves that reach the _____________. 2. In each case, tell whether the pitch rises or drops: a. The source of a sound moves away from the observer, who stands still. _____ b. The source stays still and the observer moves toward the source. ______ c. The source and observer move toward each other. ___________ d. The source stays still, and the observer moves away. ___________ 3. All the cases above are examples of the ____________ Effect. Calculation 1. When you hear a sonic boom, you often cannot see the plane that made it. Why is that? 2. When a car is at rest, its horn emits a frequency of 600 Hz. A person standing in the middle of the street hears the horn with a frequency of 580 Hz. Should the person jump out of the way? Account for your answer. 3. (a) What frequency is received by a person watching an oncoming ambulance moving at 110 km/h and emitting a steady 800-Hz sound from its siren? The speed of sound on this day is 345 m/s. (b) What frequency does she receive after the ambulance has passed? (878 Hz, 735 Hz) 4. (a) At an air show a jet flies directly toward the stands at a speed of 1200 km/h, emitting a frequency of 3500 Hz, on a day when the speed of sound is 342 m/s. What frequency is received by the observers? (b) What frequency do they receive as the plane flies directly away from them? 5. What frequency is received by a mouse just before being dispatched by a hawk flying at it at 25.0 m/s and emitting a screech of frequency 3500 Hz? Take the speed of sound to be 331 m/s. 6. A spectator at a parade receives an 888-Hz tone from an oncoming trumpeter who is playing an 880-Hz note. At what speed is the musician approaching if the speed of sound is 338 m/s? (3.05 m/s) 7. A commuter train blows its 200-Hz horn as it approaches a crossing. The speed of sound is 335 m/s. (a) An observer waiting at the crossing receives a frequency of 208 Hz. What is the speed of the train? (b) What frequency does the observer receive as the train moves away? (12.9 m/s, 193 Hz) 8. Suppose you are stopped at a traffic light, and an ambulance approaches you from behind with a speed of 18 m/s. the siren on the ambulance produces sound with a frequency of 955 Hz. The speed of sound I air is 343 m/s. What is the wavelength of the sound reaching your ears? ( 0.340 m)  Worksheet  3:  Waves  transmission  and  Interference   1) A  wave  travelling  along  a  spring  has  a  speed  of  12.0  m/s  and  a  wavelength  of  8.00  m.    After  transmission,  the   wave  has  a  speed  of  20.0  m/s.    What  is  the  wavelength  of  the  new  wave?    [13.3  m]   2) The  distance  between  the  crest  and  the  trough  of  a  wave  is  2.6  m.    When  the  wave  moves  to  a  new  medium   with  a  speed  of  9.5  m/s  and  a  wavelength  of  1.00  m,  what  is  the  speed  in  the  initial  medium?    [49  m/s]   3) A  wave’s  length  changes  from  150  m  to  225  m  when  it  switches  media.    What  is  the  new  speed  of  the  wave  if  it   was  initially  moving  at  2.00  km/s?    [3.0  x  103  m/s]   4) The  frequency  of  a  wave  moving  at  25.0  m/s  is  50.0  Hz.    If  the  wavelength  increases  by  20.0  m  when  it  switches   media,  what  is  the  speed  of  the  wave  in  the  second  medium?    [1030  m/s]   5) Blue  light  in  air  has  a  frequency  of  4.75  x  10-­‐7  Hz.    What  is  the  wavelength  in  glass  for  blue  light  if  it  travels  at   2.00  x  108  m/s?    [4.21  x  1014  m]   6) Draw  the  reflected  pulses  on  the  blank  media.     7) a               8)              9)               10)     Wave Worksheet #5: Assume the speed of sound in air is 343 m/s unless otherwise noted. 1. The speed of sound, like all waves, depends on the _________________ through which it travels. Sound travels fastest in ______________ (solids, liquids, gases) and slowest in ______________. 2. The speed of sound in air depends on the _____________________ of the air. At 0°C, the speed of sound in air is ______________ m/s. For every degree above 0°C, the speed _____________ by 0.6 m/s. For every degree below 0oC, the speed__________________by 0.6 m/s. The equation is: 𝑣!"#$% =_________m/s + 0.6 ______ 3. What is the speed of sound at 35°C? _____________ 4. What is the speed of sound at -20°C? ______________ 5. Other than the velocity/temperature equation, there are two important equation involving the speed of sound: V=_____ x ______ V= --------- Rearrange one equation to solve for: f = _________ ; l =__________ Rearrange the other to solve for: d = __________ ; t = __________ 6. A 320 Hz tuning fork will produce a wave of what wavelength in air at 22°C? 7. We see a bolt of lightning and 4 s later we hear the thunderclap. If the speed of sound in air is 343m/s, how far away is the lightning? 8. How many seconds will it take an echo to reach your ears if you yell toward a mountain 82 m away on a day when the air temperature is 0°C? 9. You look up and see a helicopter pass directly overhead. 3.10s later you hear the sound of the engine. If the air temperature is 23.0°C, how high was the helicopter flying? 10. Navy ships use sonar (sound navigation and ranging) to detect submarines. A sound pulse sent by the ship reflects off the submarine. If the submarine is 2.2 km away from the ship, and the speed of sound in seawater is 1400 m/s, how long will it take the sound pulse to travel out and back? 11. A person is listening with his ear against the rail for an oncoming train. When the train is 1.65 km away, how long will it take him to hear the sound of the whistle? (The speed of sound in steel is 5200 m/s.) How long would it take his friend who is standing nearby to hear the same whistle if the air temperature is 0°C? 12. If a ship captain sounds a foghorn toward an iceberg and hears the echo 4.6 s later, how far away is the iceberg? (air temperature is -10 °C) Think about this one. If you make a mistake, the ship could run into the iceberg!!!  Wave Worksheet #6: Standing wave 1) A standing wave in a rope has a frequency of 28 Hz at the second harmonic. a. If the wavelength is 0.20 m, what is the distance between nodes? (0.10 m) b. What is the speed of the waves that make up the standing wave? (5.6 m/s) c. What would the frequency of a rope vibrating at the third harmonic be? (42 Hz) 2) An 85 cm long guitar string is plucked and vibrates at the fourth harmonic. What is the frequency of the sound produced if the speed of sound is 332 m/s? (780 Hz) 3) Two children playing with a 6.0 m long skipping rope produce a standing wave pattern with five “loops”. If the skipping rope is vibrating at 85 vibrations per minute, what is the speed of the vibration producing the standing wave pattern? (3.4 m/s) 4) Hollow wind chimes open at both ends resonate best at their third harmonic. How long should a chime be to produce a sound of 128 Hz when the temperature is 19 °C? (4.0 m) 5) A tuba can be considered a tube open at both ends. A tuba with a length of 7.0 m is played at its fundamental note at a temperature of 21 °C. What is the frequency of the fundamental? (25 Hz) 6) A flute is essentially a tube that is open at both ends. Sketch the wave patterns associated with the first and third harmonic of a flute that is 67.5 cm long. What frequencies would these waves have if the flute was played at 21.0 °C? (1020 Hz, 763 Hz) 7) A tuning fork was sounded over an adjustable air column open at one end. It was found that the distance between the fundamental and the 2nd overtone was 90.0 cm. What was the frequency of the tuning fork if the air temperature was 0 °C? (370 Hz) 8) Two clarinets are plated at the same time in a room with a temperature of 21 °C. One clarinet is 1.20 m long and the second is 1.22 m long. What beat frequency would you hear if both were played at their fundamental frequency at the same time? (1.2 Hz)