Motion in One Dimension by 87D52HjJ

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```									Sound
AP Physics: M. Blachly
Nature of Sound Wave

Sound is a mechanical, longitudinal, pressure
wave.
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
Terminology

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

Medium           Speed (m/s)
F
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
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TnR

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
faster.
The functional relationship is given by the empirical
formula:

T
v   331 m/s      1
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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
area
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
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

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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 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
of
• A single battery
• Entire Nuclear Power Plant

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The Ear

We (humans) do not have a linear response to
sound.
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 
Examples
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
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.
TnR
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

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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

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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

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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

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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
Visualizations: http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=21

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