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Problem from yesterday.What are the answers?
• What is the decibel level of the lowest “hearable” noise?
• What is the decibel level of the threshold of pain?
10 log
o
II
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More on Intensity
• Remember the Units for I– Watts / Meter2
– What is “Watts” a measure of?
– What is “Meter2” a measure of?
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A sound source is doing work on the air.
It’s generating power.
That power spreads outward in a sphere, spread out on it’s surface.
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Sound waves carry energy.
Energy per second is the power of the wave.
The sound intensity is defined as the power that passes through a surface divided by the area of that surface.
A
PI
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24 r
PI
s
area of sphere
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Problem• A person stands 3 meters away from a speaker
generating 45 watts of power.
– What is the intensity heard by the person?
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Problem• A person stands 3 meters away from a speaker
generating 45 watts of power.
– What is the intensity heard by the person?
– What is the dB level?
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Problem• A person stands 3 meters away from a speaker
generating 45 watts of power.
– What is the farthest a person can stand from this speaker and still hear it?
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Diffraction
• Question – – Light and sound are both waves. – If I shine a flashlight out the door, the light
goes in a straight line. – If I shout out the door, the sound waves will
curve both direction down the hall.
• Why is this?
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Diffraction
• If a wave (any wave) passes through a gap, it will spread out as if the gap were a point source of the wave.
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Diffraction
• Works best when the gap matches the wavelength of the wave.
• Tapers off if the gap gets significantly wider than the wavelength.
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Diffraction
• Back to the question – – Light – ~ nanometers– Sound - ~ meters
• Which will diffract most effectively through a doorway?
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Phase
• What is the difference between these two waves?
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Phase
• Same amplitude.
• Same wavelength.
• The only difference is the phase.
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Phase
• Phase is the fraction of the wave cycle that has elapsed.
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Phase
• What are some units for “fraction of a cycle?”
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Phase
• What are some units for “fraction of a cycle?”
• Radians, Degrees, and Revolutions.
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Phase difference
• Often times, we will want to compare the difference in phase of two waves to see how they will combine.
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Phase difference.
• Two waves completely in phase.
• Crests Line up.
• Phase difference = 0
• Two waves completely out of phase.
• Crest lines up with trough.
• Phase difference = 180˚, or ∏ rads, or 1/2 revolution.
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Phase difference
• If two waves with different phases interfere, the amplitude of the combined wave will be between the sum of the original two and the difference of the original two.
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Interference of sound waves
• The phase of a wave as it reaches a point depends on the distance from that point to the source.
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Interference of sound waves
• The phase of a wave as it reaches a point depends on the distance from that point to the source.
• The phase difference between sound from two sources depends on the path difference between those two sources.
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Interference of Sound Waves• Constructive interference occurs when compressions
from both sources hit simultaneously.– Or the two sources are in phase at that point.
• Path difference between two waves’ motion is some integer multiple of wavelengths
• Path difference = nλ (n= 0, 1, 2, 3 etc…)
• Destructive interference occurs when compression lines up rarefaction.– Or the two sources are out of phase at that point.
• Path difference between two waves’ motion is an odd half wavelength
• Path difference = (n + ½)λ
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What does this look like?• Two sources
– Red is compression– Blue is rarefaction
– Light blue lines are nodes where sound level is 0 or quiet. (Destructive Interference). They get equal and opposite compressions and rarefactions.
They are “dead zones” and never hear either source.
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Beats
• Two waves, with slightly different frequencies, interfere. What will this sound like?
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Beats
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Beats• Beats are alternations in loudness, due to interference• Alternates between constructive and destructive
interference.• The beat frequency equals the difference in frequency
between the two sources:
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