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Answers to Ch 12 Sound
Updated 5/27/07
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12.1 Sound Waves

Section 12.1 Review Q, pg 413: 
[1] A greater frequency is perceived as a higher pitch.
[2] Echolocation can find objects about one wavelength long. 
    Since λ = Speed/f, the higher the frequency the smaller the
    object (fish) that can be located.  Thus, a dolphin can locate a
    fish as small as: λ = 1450 m/s/220000 Hz = 0.006 m = 6 mm long.
[3] The compressions in a sound wave are created by the collisions of
    molecules.  Since the molecules in water are closer together the
    collisions take place more frequently and the sound moves faster.
[4] No, because plane waves are flat and not curved.  As the wave
    moves farther from its source it becomes more flat, less curved,
    and can approximate a plane wave.
[5] To the right
[6] To the left.
[7] The dolphin is catching up to the fish.

Ch 12 Review Q, pg 434:  Q 1-12
[1] Because air molecules vibrate in a direction parallel to the
    direction of wave motion.
[2] Diagrams should depict a sine curve that begins and ends at its
    lowest point and that has three crests and tow troughs. 
[3] Frequency is an objective measure of the rate of particle
    vibration.  Pitch is a subjective quality that depends on the
    listener.
[4] Infrasonic waves are below 20 Hz, audible waves are between 20
    and 20,000 Hz, and ultrasonic waves are greater than 20,000 Hz.
[5] Molecules that have more motion (higher temperature) can transfer
    their vibrations more easily.  This is less noticeable in liquids
    and solids because the particles are closer together.
[6] the siren’s pitch will drop.
[7] Because their short wavelengths can image small objects.
[8] Frequency doubles; Speed remains constant.
[9] Sound travels faster through the ground.
[10] Notes that are played at the same time reach your ears at the
     same time.
[11] The driver of the van.
[12] Greater than 40 kHz

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12.2 Intensity & Resonance

Practice A, pg 415
[1a] 8.0x10-4 W/m2   [b] 1.6x10-3 W/m2   [c] 6.4x10-3 W/m2 
[2] 8.91x10-3 W/m2   
[3] 2.3x10-5 W      
[4] 4.5 W  
[5] I =  P   --->1.2x10-3 = 0.35 ---> r2x1.2x10-3 = 0.35  
        4πr2                4πr2                    4π 
                                               
r2 =    0.35     ----> r2 = 23.2 --->r = √23.2 = 4.8 m
    (4π1.2x10-3)   Note parenthesis
 

Section 12.2 Review Q, pg 420: 
[1] The intensity has increased by a factor of 100 (102)
[2] no; because the sensation of loudness is approximately
    logarithmic in the human ear.
[3] The second tuning fork will pick up the vibrations of the
    first tuning fork, and a faint sound will be heard from the
    second fork.  This occurs because the two forks have the
    same natural frequency, which is the condition required for
    resonance.
[4] 2.0x104 m
[5] a,d,f;  c,e
 

Ch 12 Review, Q 13-23. pg 434: 
[13] Intensity is power per area; decibel level is a measure of
     relative intensity
[14] 90dB, 30 dB, 20 dB, 60 dB (Answers may vary slightly.)
[15] Because the threshold of hearing depends on both frequency
     and intensity.
[16] When forced vibration is the same as the natural frequency
     of a vibrating system.
[17] The sound intensity from the orchestra is 100 times that
     from the violin.
[18] 9 machines (for a total of 10)
[19] Because intensity decreases with distance and the sound has
     traveled from the source to a reflecting surface and back
     (and because of imperfect reflection).
[20] The swing’s amplitude is maximized when the pushes match
     the swing’s natural frequency.
[21] Vibrations could set the bridge in motion if they match one
     of the bridge’s natural frequencies.
[22] 70 dB 
[23] 7.96x10-2 W/m2 

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12.3 Harmonics

Practice B, pg 427
[1] 440 Hz      
[2] 260 Hz, 520 Hz, 780 Hz 
[3a] 82.1 Hz     [b] 115 Hz     [c] 144 Hz    
[4] 440 m/s
 

Section 12.3 Review Q, pg 431: 
[1] 524 Hz     
[2] 346 m/s    
[3] 388 Hz and 396 Hz 
[4] the odd harmonics
[5] b, c
 

Ch 12 Review, Q 24-35, pg 435: 
[24] The lowest possible frequency of a vibrating system; 
     They are integral multiples of the fundamental frequency.
[25a] 4.0 m      [b] 2.0 m     [c] 1.3 m     [d] 1.0 m
[26] Because a closed end is a node, an open end is an antinode.
[27] The instruments have different harmonics present at various
     intensity levels.
[28] The guitar’s body transfers the string’s vibrations to the air
     more efficiently, which increases the intensity of the sound.
[29] 3 Hz  
[30] To change the length of the air column, thereby changing the
     fundamental frequency.
[31] Yes.  This difference will equal the fundamental frequency if
     the pipe is open at both ends but will equal twice the
     fundamental frequency if the pipe is closed at one end.
[32] The first possible wavelength is 2L for the flute and 4L for the
     clarinet.  Because the speed of sound is the same in each and
     v = λf, the flute’s fundamental frequency is twice the
     clarinets.
[33] As temperature increases, the speed of sound in air increases. 
     Because f1 is proportional to V, fundamental frequency likewise
     increases.
[34] 443 Hz, 886 Hz, 1330 Hz   
[35] 3.0x103 Hz

Mixed Review, pg 436

     [36a] 52 cm  [b] 640 Hx, 960 Hz  [40a] 70.1 Hz     [b] 285
[37] 5 beats per second           [41] Lclosed = 1.5Lopen
[38] 20 m, 2x10-2 m               [42] 1.9x10-2 m
[39] 0.20 s                       [43a] 5.0x104 W  [b] 2.8x10-3

Standardized Test Prep, pg 438


1] B  [2] J  [3] D  [4] H  [5] C  [6] F  [7] B  [8] G   [9] D  [10] G 11] 7 Hz
[12] 750 Hz   [13] 0.33 m   [14] 0.47 W/m2  [15] 5.0x10-5W

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Ch 12 Test Practice:  Sound Waves

12.1 Sound Waves

     1 mi = 1609 m     Speed of Light = 3.0 x 108 m/s     Io = 1x10-12 W/m2

1    Define:  [a] Wavelength           [f] Hertz
         [b] Frequency            [g] Doppler Effect 
         [c] Period               [h] Transverse Wave
         [d] Amplitude            [i] Longitudinal Wave
         [e] Cycle               

2    a] State two uses of the Doppler Effect
b] Identify all terms in the equation V/c = Δf/f

3    Draw & label the diagram for a:
     a] Transverse Wave           b] Longitudinal Wave

4    Diagram & label the following situations:  Use tuna can & washer. 
     a] Both the source and listener are stationary.
     b] The listener is stationary and the source is approaching.
     c] The listener is stationary and the source is receding.    
     d] The source is stationary and the listener is approaching.
     e] The source is stationary and the listener is receding.
         1 pt for correct labeling of Source & Listener
         1 pt for diagram with incorrect placement of source dots.    
         1 pt for correct placement of source dots.                   
         1 pt for labeling diagram 3 second snapshot                  
         1 pt for labeling the waves as 1st-3 sec, 2nd 2 sec, 3rd 1 sec

5    Find the speed (mi/h) of a car if the radar gun (9.375 GHz) measures a frequency
     change of 2000 Hz.

12.2 Intensity & Resonance

6    Define:  [a] Intensity   [b] Resonance   [c] Decibel

7    Write the equation for intensity in words & symbols.

8    Find the intensity of sound if you are located 3 m from a person speaking with a
0.50 W voice.                                                         A1 & A2, pg 415

9    Find the power of a source if your audiometer reads 8.0x10-5 W/m2 when you are 2.5 m away from the source.                                                 A3 & A4, pg 415

10   Find the distance from a 6 watt sound if the audiometer reads
2.0x10-4 W/m2.                                                             A5, pg 415

11   When the decibel level in the auditorium goes from 70 dB to 110 dB how much greater is the intensity?                                     12.1 Rev Q1, pg 420, #17 pg 434

12   You shout at your friend 3.0 m away. 
     If your shouting power is 6.0x10-3 W, how loud is your voice when it reaches your
     friend?                                                                   #22, pg 435

12.3 Harmonics

13   Define:  [a] Fundamental Frequency     [c] Timbre
         [b] Harmonic Series           [d] Beat

14   Draw & label the diagram for
     a] a string vibrating at its fundamental frequency.
     b] an open pipe vibrating at its fundamental frequency.
     c] a closed pipe vibrating at its fundamental frequency.
     d] a closed pipe vibrating at its 2nd harmonic.
     e] a closed pipe vibrating at its 3rd harmonic.

Ans:  [5] 143 mi/h     [8] 4.42x10-3     [9] 6.28x10-3 W     [10] 48.9 m
[11] 10,000       [12] 77 dB

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Definitions

1    Define:  [a] Wavelength:  Distance between corresponding points on consecutive
                          waves      
         [b] Frequency:   The number of events per unit time.
                          Ex:  70 heart beats per minute           
         [c] Period:      The time per cycle. 
                          Ex: Count the cycles 10 sec
                              Period = 10 sec/#Cycles              
         [d] Amplitude    The Maximum displacement from rest.
                          Ex:  The height of a crest or trough.
         [e] Cycle        One complete back & forth motion.
         [f] Hertz        One cycle per second (sec-1)
         [g] Doppler Effect  The apparent change in frequency (not amplitude)
                             due to the motion of the source or the listener.
         [h] Transverse Wave  A wave whose vibration is perpendicular to wave travel. 
         [i] Longitudinal Wave  A wave whose vibration is parallel to wave travel. 
         [j] Intensity    Power per unit area (W/m2).
                          Ex:      Power       =  P   
                              Area of a Sphere   R2  
         [k] Resonance    A large vibration caused by a small periodic stimulus at
                          the system's natural frequency.
                          Ex:  A child moves mover her legs two feet in rhythm with a
                          swing and the swings in a 10 ft arc.
         [l] Decibel      The loudness of sound perceived by humans. 
                          It is a logarithmic function of intensity: 
                          dBHi - dBLo = 10Log(IHi/ILo)
                         

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Estimated Solutions Ch 12 Test Practice

No Calculator

1 mi = 1609 m     Speed of Light = 3.0 x 108 m/s     Io = 1x10-12 W/m2

5    Find the speed (mi/h) of a car if the radar gun (9.375 GHz) measures a frequency
     change of 2000 Hz.
     V = Δf =      V      =   2000 Hz                                  
     c    f   3.0x108m/s     10x109 Hz

V  =   2000 Hz x 3.0x108m/s = 6000x10-1  = 600 m/s = 60 m/s
       10x109 Hz                10         10

60 m x 3600 s x  1 mi  = 6x36 = 3x36 = 108 mi  (Calculator Ans: 143)
   s     1 h    2000 m     2               h

8    Find the intensity of sound if you are located 3.0 m from a person speaking with a 0.50 W voice.
I =  P   = 0.50 W = 0.50 W = 0.50 = 0.50x10-2 = 5.0x10-3 W/m2
    4πR2    4π32m2    12x9     108   
(Calculator Ans:  4.42x10-3 W/m2)

9    Find the power of a source if your audiometer reads 8.0x10-5 W/m2 when you are 2.5 m away from the source.
I =  P   ---> 8.0x10-5 W/m2 =    P     
    4πR2                      4π2.52m2  

8.0x10-5 W/m2 x 4π2.52m2 = P

8.0x10-5x12x32m2 = 8x10-5x12x9 = 72x10-5x10 = 720x10-5 = 7.2x10-3 W = P
(Calculator Ans:  P = 6.28x10-3 W)

10   Find the distance from a 6 watt sound if the audiometer reads
2.0x10-4 W/m2.

I =  P   ---> 2.0x10-4 W/m2 =  6      
    4πR2                      4πR2  

2.0x10-4 W/m2 x R2 =  6           
                     4π

 R2 =       6      = 6x104 = 60000 = 60000 = 10000 = 2500 m2 
     4π x 2.0x10-4    4π2     (8π)     24       4
     ____
R = √2500 = 50 m (Calculator:  48.9 m)

11   When the decibel level in the auditorium goes from 70 dB to 110 dB how much greater is the intensity?
dBHi - dBLo = 10 Log(IHi/ILo)  OR  dBHi - dBLo = X & IHi/ILo = 10x 
                                      10
110 - 70 = X --->X = 4 & IHi/ILo = 104 ---> IHi = ILox104 = ILox10,000
   10

12   You shout at your friend 3.0 m away.  If your shouting power is
6.0x10-3 W, how loud is your voice when it reaches your friend?

Given:  P = 6.0x10-3 W   Since dB = 10Log(I/Io)
        R = 3.0 m       We need to find I
       Io = 1x10-12 W/m2  I =  P   = 6x10-3 = 6x10-3 = 6.0x10-5 
Find:  dB = ?               4πR2     4π32     12x9
                        (Calculator Ans:  5.31x10-5)
                       
     dB = 10Log(I/Io)
     dB = 10Log(6.0x10-5/10-12)
     dB = 10 Log(6.0x107)
     dB = 10(Log(6) + Log(107)
     dB = 10(0.6 + 7) = 10(7.6) = 76 dB  (Calculator Ans:  77 dB)

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Calculator Solutions Ch 12 Test Practice

     1 mi = 1609 m     Speed of Light = 3.0 x 108 m/s     Io = 1x10-12 W/m2

5    Find the speed (mi/h) of a car if the radar gun (9.375 GHz) measures a frequency
     change of 2000 Hz.
      V = Δf =      V      =   2000 Hz                                  
      c    f   3.0x108m/s    9.375x109 Hz

      V =   2000 Hz x 3.0x108m/s = 6000x10-1  = 600 m/s = 64 m/s
          9.375x109 Hz              9.375       9.375

     64 m x 3600 s x  1 mi  = 143 mi 
        s     1 h    1609 m       h

8    Find the intensity of sound if you are located 3 m from a person speaking with a 0.50 W voice.
I =  P   = 0.50 W = 4.42x10-3 W/m2
    4πR2    4π32m2             

9    Find the power of a source if your audiometer reads 8.0x10-5 W/m2 when you are 2.5 m away from the source.
I =  P   ---> 8.0x10-5 W/m2 =    P     
    4πR2                      4π2.52m2   

8.0x10-5 W/m2 x 4π2.52m2 = P

P = 6.28x10-3 W

10   Find the distance from a 6 watt sound if the audiometer reads
2.0x10-4 W/m2.

I =  P   ---> 2.0x10-4 W/m2 =  6      
    4πR2                      4πR2   

2.0x10-4 W/m2 x R2 =  6           
                    4π

 R2 =       6      = 6x104 = 60000 = 2387 m2  Be sure to put 8π in ()
     4π x 2.0x10-4    4π2     (8π)  
     ____
R = √2387 = 48.9 m

11   When the decibel level in the auditorium goes from 70 dB to 110 dB how much greater is the intensity?
dBHi - dBLo = 10 Log(IHi/ILo)  OR  dBHi - dBLo = X & IHi/ILo = 10x 
                                      10
110 - 70 = X --->X = 4 & IHi/ILo = 104 ---> IHi = ILox104 = ILox10,000
   10

12   You shout at your friend 3.0 m away.  If your shouting power is
6.0x10-3 W, how loud is your voice when it reaches your friend?

Given:  P = 6.0x10-3 W   Since dB = 10Log(I/Io)
        R = 3.0 m       We need to find I
       Io = 1x10-12 W/m2  I =  P   = 6x10-3 = 0.006  = 5.31x10-5  
Find:  dB = ?                4πR2    4π32     113

                        dB = 10Log(I/Io)
                        dB = 10Log(5.31x10-5/10-12)
                        dB = 10 Log(5.31x107)
                        dB = 77.2 Decibels--SigFig-->77 dB

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