Motion in One Dimension by 87D52HjJ


  AP Physics: M. Blachly
Nature of Sound Wave

 Sound is a mechanical, longitudinal, pressure
Nature of Sound Wave
 What, exactly, is oscillating?

 Air molecules are compressed together by the
 mechanical motion of some solid matter.
 The compressions and rarefactions propagate
 through the medium

 Compressions are areas of increased molecular
 Rarefactions are regions of decreased density
Pressure Graph
Speed of Sound

                               Medium           Speed (m/s)
vstring                       Air              343
                              Helium           972

             B                 Water            1500
v fluids 
                              Steel            5600
B  Bulk modulus

       Recall that the bulk modulus is the ratio of the
       stress to the strain. It is an effective
       “spring constant” for the fluid

 How would you expect the speed of sound in air
 (v) to depend on the temperature (T) of the air?
  • 1. v will increase as T increases
  • 2. v will decrease as T increases
  • 3. v will not depend on T
Temperature Dependence
 As the air heats up, the molecules move faster and
 the pressure wave passes through the medium
 The functional relationship is given by the empirical

          v   331 m/s      1
Paint Bomb

 Suppose a paint bomb exploded. How would the
 thickness of the paint on your face depend on
 how far you were from the bomb?
Energy and Intensity
 Waves transmit energy
 The rate that energy is transmitted is the power.
 What is intensity?
 Intensity is the “concentration” of power on a particular
 Intensity is the rate at which energy flows to a given
 area, perpendicular to the direction of wave travel.

   power P                                 Watts
I                                 Units:
    area   A                                m2
Example of Spherical Waves
 Assume that a 100 W
 speaker radiates energy
 outwards in a sphere.
 What is the intensity of
 this sound a distance of 3
                              A  4 r   2

 meters from the source.
                                  P     P
                              I 
                                  A 4 r  2

                              I  0.884 W/m 2
Intensity TnR
  Recall Intensity = P/A. If you are standing 6 meters
  from a speaker, and you walk towards it until you are 3
  meters away, by what factor has the intensity of the
  sound increased?

  A: 2
  B: 4
  C: 8
  D: ½
  E: ¼

Graph This Data:

    Source                   Intensity
    Gentle Breeze            1E-11 W/m2
    Whisper                  5E-9 W/m2
    Conversation             2E-6 W/m2
    Orchestra                6E-3 W/m2
    iPod on Max w/ earbuds   0.02 W/m2
    F-16 at Takeoff          100 W/m2
Your Ear

   Your Ear is sensitive to an amazing
   range! (1dB – 100 dB)
    • Lowest limit: 10-12 Watts/m2
    • Upper limit: 1 Watt/m2
   Like a laptop that can run using all power
    • A single battery
    • Entire Nuclear Power Plant

The Ear

 We (humans) do not have a linear response to
 When the intensity doubles, we do not register
 that the sound is twice as loud.
 Our response is actually more logarithmic
 It makes sense then to define an intensity scale
 that is more matched to what we experience
Intensity Scale
 Intensity scale is a log scale, called the decibel scale.
 It measures the intensity relative to a reference level,
 known as the threshold of hearing.
 Io = 1 x 10-12 W/m2.

                        I 
                10log  
                         Io 
 A speaker emits 600 Joules of energy each second.
 Assuming a spherical wave, calculate the intensity (in
 decibels) a distance of 5 meters away from the source.
  = 122.8 dB
 Find the power of a source if the intensity at a distance
 of 120 meters is 65 dB.
The Decibel Scale
             Source               Intensity
      Threshold of Hearing  1x10-12 W/m2    0 dB
         Rustling Leaves    1x10-11 W/m2 10 dB
             Whisper        1x10-10 W/m2 20 dB
      Normal Conversation    1x10-6 W/m2 60 dB
       Busy Street Traffic   1x10-5 W/m2 70 dB
        Vacuum Cleaner       1x10-4 W/m2 80 dB
         Large Orchestra    6.3x10-3 W/m2 98 dB
          iPod on Loud       1x10-2 W/m2 100 dB
       Front Row, Concert    1x10-1 W/m2 110 dB
        Threshold of Pain    1x101 W/m2 130 dB
       Military Jet Takeoff  1x102 W/m2 140 dB
     Perforation of Eardrum 1x104 W/m2 160 dB
Example Problem #1

 A sound wave has an intensity of 0.0533 W/m2.
 What is the intensity of this sound in db?
 A pair of headphones reduce the noice level by
 25db. What intensity would reach your ears if
 you were wearing these headphones?
Example Problem #2

 A loud student (let’s call him Travis) can produce
 a sound level of 90 db at a distance of 2 meters.
 Find the intensity of this wave.
 What power is required to produce this wave,
 assuming that it is spherically distributed.
  As a police car passes you with its siren
  on, the frequency of the sound you hear
  from its siren

1) Increases           2) Decreases   3) Same

  Doppler Example Audio
  Doppler Example Visual

Doppler Effect, moving source

 When source is coming toward you (vs > 0)
 • Distance between waves decreases
 • Frequency increases
 When source is going away from you (vs < 0)
 • Distance between waves increases
 • Frequency decreases

Doppler Effect , moving observer

 When moving toward source (vo < 0)
 • Time between waves peaks decreases
 • Frequency increases
 When away from source (vo > 0)
 • Time between waves peaks increases
 • Frequency decreases

Doppler Effect, combined

           v  vo 
    f f         
           v vs 
    vs  velocity of source
    v0  velocity of observer
     v  velocity of sound
  Doppler TnR
A: You are driving along the highway at 65 mph, and behind you a police
car, also traveling at 65 mph, has its siren turned on.
B: You and the police car have both pulled over to the side of the road, but
the siren is still turned on.
In which case does the frequency of the siren seem higher to you?
1. Case A
2. Case B
3. same                correct

Sonic Effects

 What if vs > v ?
Sonic Boom

 When the velocity is greater than the speed of
 sound, the pressure waves build up along a cone
 that trails the source.
 Mach = velocity of source / velocity of sound

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