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AP- Waves & Sound. Ch 11-‐ 12 Giancoli. *Answers are given for the interesting questions ☺. Ch 11. *11. Is a rattle in a car ever a resonance phenomenon?

AP-­  Waves  &  Sound.    Ch  11-­‐  12  Giancoli  

*Answers  are  given  for  the  interesting  questions    

  Ch  11   *11.   Is  a  rattle  in  a  car  ever  a  resonance  phenomenon?  Explain.   A  rattle  in  a  car  is  very  often  a  resonance  phenomenon.    The  car  itself  vibrates  in  many  pieces,  because  there  are   many  periodic  motions  occurring  in  the  car  –  wheels  rotating,  pistons  moving  up  and  down,  valves  opening  and   closing,  transmission  gears  spinning,  driveshaft  spinning,  etc.    There  are  also  vibrations  caused  by  irregularities  in   the  road  surface  as  the  car  is  driven,  such  as  hitting  a  hole  in  the  road.    If  there  is  a  loose  part,  and  its  natural   frequency  is  close  to  one  of  the  frequencies  already  occurring  in  the  car’s  normal  operation,  then  that  part  will   have  a  larger  than  usual  amplitude  of  oscillation,  and  it  will  rattle.    This  is  why  some  rattles  only  occur  at  certain   speeds  when  driving.  

  *12.   Is  the  frequency  of  a  simple  periodic  wave  equal  to  the  frequency  of  its  source?  Why  or  why  not?   The  frequency  of  a  simple  periodic  wave  is  equal  to  the  frequency  of  its  source.    The  wave  is  created  by  the  source  moving  the   wave  medium  that  is  in  contact  with  the  source.    If  you  have  one  end  of  a  taut  string  in  your  hand,  and  you  move  your  hand   with  a  frequency  of  2  Hz,  then  the  end  of  the  string  in  your  hand  will  be  moving  at  2  Hz,  because  it  is  in  contact  with  your  hand.     Then  those  parts  of  the  medium  that  you  are  moving  exert  forces  on  adjacent  parts  of  the  medium  and  cause  them  to  oscillate.     Since  those  two  portions  of  the  medium  stay  in  contact  with  each  other,  they  also  must  be  moving  with  the  same  frequency.     That  can  be  repeated  all  along  the  medium,  and  so  the  entire  wave  throughout  the  medium  has  the  same  frequency  as  the   source.  

  *14.   Why  do  the  strings  used  for  the  lowest-­‐frequency  notes  on  a  piano  normally  have  wire  wrapped  around   them?   The  fundamental  frequency  of  oscillation  for  a  string  with  both  ends  fixed  is  

given  by  

.    Combining  these  two  relationships  gives  

.    The  speed  of  waves  on  the  string  is  

.    By  wrapping  the  string  with  wire,  the  mass  of  

the  string  can  be  greatly  increased  without  changing  the  length  or  the  tension  of  the  string,  and  thus  the  string  has  a  low   fundamental  frequency.  

  41.   (II)   A   cord   of   mass   0.65   kg   is   stretched   between   two   supports   28   m   apart.   If   the   tension   in   the   cord   is   150   N,  how  long  will  it  take  a  pulse  to  travel  from  one  support  to  the  other?     53.   (I)  A  violin  string  vibrates  at  294  Hz  when  unfingered.  At  what  frequency  will  it  vibrate  if  it  is  fingered  one-­‐ third  of  the  way  down  from  the  end?  (That  is,  only  two-­‐thirds  of  the  string  vibrates  as  a  standing  wave.)  

  54.   (I)  A  particular  string  resonates  in  four  loops  (as  shown  below)  at  a  frequency  of  280  Hz.  Name  at  least   three  other  frequencies  at  which  it  will  resonate.  

  55.   (II)  The  velocity  of  waves  on  a  string  is   are  two  adjacent  nodes?  

   If  the  frequency  of  standing  waves  is  475  Hz,  how  far  apart  

  56.   (II)  If  two  successive  overtones  of  a  vibrating  string  are  280  Hz  and  350  Hz,  what  is  the  frequency  of  the   fundamental?  

  57.   (II)  A  guitar  string  is  90  cm  long  and  has  a  mass  of  3.6  g.  The  distance  from  the  bridge  to  the  support  post   is    and  the  string  is  under  a  tension  of  520  N.  What  are  the  frequencies  of  the  fundamental  and   first  two  overtones?  

   

60.   (II)  The  length  of  the  string  in  the  figure  below   may  be  adjusted  by  moving  the  pulley.  If  the  hanging  mass   m   is   fixed   at   0.080   kg,   how   many   different   standing   wave   patterns   may   be   achieved   by   varying   L   between   10  cm  and  1.5  m?    

        Ch  12     *4.   When  a  sound  wave  passes  from  air  into  water,  do  you  expect  the  frequency  or  wavelength  to  change?   If  the  frequency  were  to  change,  the  two  media  could  not  stay  in  contact  with  each  other.    If  one  medium  vibrates  with  a   certain  frequency,  and  the  other  medium  vibrates  with  a  different  frequency,  then  particles  from  the  two  media  initially  in   contact  could  not  stay  in  contact  with  each  other.    But  particles  must  be  in  contact  in  order  for  the  wave  to  be  transmitted   from  one  medium  to  the  other,  and  so  the  frequency  does  not  change.    Since  the  wave  speed  changes  in  passing  from  air  into   water,  and  the  frequency  does  not  change,  we  expect  the  wavelength  to  change.    The  wave  travels  about  four  times  faster  in   water,  so  we  expect  the  wavelength  in  water  to  be  about  four  times  longer  than  it  is  in  air.  

  *5.   What  evidence  can  you  give  that  the  speed  of  sound  in  air  does  not  depend  significantly  on  frequency?   Listening  to  music  while  seated  far  away  from  the  source  of  sound  gives  evidence  that  the  speed  of  sound  in  air  does  not   depend  on  frequency.    If  the  speed  were  highly  frequency  dependent,  then  high  and  low  sounds  created  at  the  same  time  at  the   source  would  arrive  at  your  location  at  different  times,  and  the  music  would  sound  very  disjointed.    The  fact  that  the  music   “stays  together”  is  evidence  that  the  speed  is  independent  of  frequency.  

  *6.   The  voice  of  a  person  who  has  inhaled  helium  sounds  very  high-­‐pitched.  Why?   The  sound-­production  anatomy  of  a  person  includes  various  resonating  cavities,  such  as  the  throat.    The  relatively  fixed   geometry  of  these  cavities  will  determine  the  relatively  fixed  wavelengths  of  sound  that  a  person  can  produce.    Those   wavelengths  will  have  associated  frequencies  given  by  

.    The  speed  of  sound  is  determined  by  the  gas  that  is  filling  

the  resonant  cavities.    If  the  person  has  inhaled  helium,  then  the  speed  of  sound  will  be  much  higher  than  normal,  since  the   speed  of  sound  waves  in  helium  is  about  3  times  that  in  air.    Thus  the  person’s  frequencies  will  go  up  about  a  factor  of  3.    This  is   about  a  1.5  octave  shift,  and  so  the  person  sounds  very  high  pitched.  

  *14.   Consider  the  two  waves  shown  in  the  figure  below.    Each  wave  can  be  thought  of  as  a  superposition  of   two   sound   waves   with   slightly   different   frequencies.     In   which   of   the   waves,   (a)   or   (b),   are   the   two   component  frequencies  farther  apart?  Explain.                   From the two waves shown, it is seen that the frequency of beating is higher in Figure (a) – the beats occur more frequently. The beat frequency is the difference between the two component frequencies, and so since (a) has a higher beat frequency, the component frequencies are further apart in (a).  

 

     

 

    15.   Is  there  a  Doppler  shift  if  the  source  and  observer  move  in  the  same  direction,  with  the  same  velocity?   Explain.       *17.   Figure  12–32  shows  various  positions  of  a  child  in  motion  on  a  swing.  A  monitor  is  blowing  a  whistle  in   front  of  the  child  on  the  ground.  At  which  position,  A  through  E,  will  the  child  hear  the  highest  frequency   for  the  sound  of  the  whistle?  Explain  your  reasoning.     The  highest  frequency  of  sound  will  be  heard  at  position  C,   while  the  child  is  swinging  forward.    Assuming  the  child  is   moving  with  SHM,  then  the  highest  speed  is  at  the  equilibrium   point,  point  C.    And  to  have  an  increased  pitch,  the  relative   motion  of  the  source  and  detector  must  be  towards  each  other.     The  child  would  also  hear  the  lowest  frequency  of  sound  at   point  C,  while  swinging  backwards.  

 

      24.   (I)  The  A  string  on  a  violin  has  a  fundamental  frequency  of  440  Hz.  The  length  of  the  vibrating  portion  is   32  cm,  and  it  has  a  mass  of  0.35  g.  Under  what  tension  must  the  string  be  placed?  

  25.   (I)  An  organ  pipe  is  112  cm  long.  What  are  the  fundamental  and  first  three  audible  overtones  if  the  pipe   is  (a)  closed  at  one  end,  and  (b)  open  at  both  ends?     32.   (II)   How   far   from   the   mouthpiece   of   the   flute   in   Example   12–10   should   the   hole   be   that   must   be   uncovered  to  play  D  above  middle  C  at  294  Hz?     39.   (I)  A  piano  tuner  hears  one  beat  every  2.0  s  when  trying  to  adjust  two  strings,  one  of  which  is  sounding   440  Hz.  How  far  off  in  frequency  is  the  other  string?  

  *41.   (I)  A  certain  dog  whistle  operates  at  23.5  kHz,  while  another  (brand  X)  operates  at  an  unknown   frequency.  If  neither  whistle  can  be  heard  by  humans  when  played  separately,  but  a  shrill  whine  of   frequency  5000  Hz  occurs  when  they  are  played  simultaneously,  estimate  the  operating  frequency  of   brand  X.   The  5000  Hz  shrill  whine  is  the  beat  frequency  generated  by  the  combination  of  the  two  sounds.       This  means  that  the  brand  X  whistle  is  either  5000  Hz  higher  or  5000  Hz  lower  than  the  known-­frequency  whistle.    If  it  were   5000  Hz  lower,  then  it  would  be  in  the  audible  range  for  humans.    Since  it  cannot  be  heard  by  humans,  the  brand  X  whistle   must  be  5000  Hz  higher  than  the  known  frequency  whistle.    Thus  the  brand  X  frequency  is  

 

  45.   (II)  You  have  three  tuning  forks,  A,  B,  and  C.  Fork  B  has  a  frequency  of  441  Hz;  when  A  and  B  are  sounded   together,  a  beat  frequency  of  3  Hz  is  heard.  When  B  and  C  are  sounded  together,  the  beat  frequency  is  4   Hz.  What  are  the  possible  frequencies  of  A  and  C?  What  beat  frequencies  are  possible  when  A  and  C  are   sounded  together?