sound ap physics: m. blachly nature of sound wave sound is a mechanical, longitudinal, pressure wave
TRANSCRIPT
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
Speed of Sound
Bulk modulus
fluids
Bv
B
05
Medium Speed (m/s)
Air 343
Helium 972
Water 1500
Steel 5600
string
Fv
Recall that the bulk modulus is the ratio of the stress to the strain. It is an effective “spring constant” for the fluid
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:
331 m/s 1273
Tv
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
area
PI
A 2
WattsUnits:
m
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 meters from the source.
2
2
2
4
4
0.884 W/m
A r
P PI
A r
I
Intensity TnRRecall 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
27
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 of
• A single battery
• Entire Nuclear Power Plant
23
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.
10logo
I
I
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
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 dBPerforation of Eardrum 1x104 W/m2 160 dB
Intensity
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, obnoxious student at a swim meet (let’s call him Ryan*) 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.
*Note: this is a hypothetical student and any resemblance to any actual student you may or may not know is purely coincidental.
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
36
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
38
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
40
Doppler Effect, combined
0
velocity of source
velocity of observer
velocity of sound
o
s
s
v vf f
v v
v
v
v
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
44
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 soundVisualizations: http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=21