Sound
Extra Practice: C14.1, 14.1, 14.3, 14.5, 14.9,
14.11, 14.13, 14.15, 14.17, 14.19
Reminders!
• WebAssign:
Better your grade by requesting manual
extensions on old assignments (50% recovery).
• Last homework:
Due tomorrow night!
• Final:
May 4, 8-11pm
Study by fixing old homeworks, practicing old
tests, doing practice test!
Peer Pressure Extra Credits
• Student evaluations
• Fill out online
• If 60% of class fills it out
EVERYONE gets +1% on their class grade.
• Class this Wednesday
• If 80% of the class participates
EVERYONE gets +1% on their class grade.
FCI will also be good review for final.
I will email you when I
know where the final is.
(They haven’t told me yet!
Sorry!)
Last time…
(λ)
(λ)
v = λf =
F string tension
µ mass density
Important things today
Sound as a wave
How does it work?
Calculating the speed of sound
in gasses, liquids, and solids.
Quantifying loudness.
How loud is 11?
What makes sound?
v = λf =
Pitch: determined by wavelength or frequency of vibration.
High pitch: high frequency.
F
µ
This sounds like a silly question but I’m asking it to make you think about how that sound is produced, and how it gets to your ears. Every single thing that makes sound
is making some kind of vibration. The pitch of that sound is determined by its frequency of vibration. A sound-maker is a vibrating object. And that vibration causes
changes in the molecules around them that propagate outward. NOTE here’s a tuning fork. It makes sound by vibrating at a fixed frequency.
Thinking about sound…
Pitch: determined by wavelength or frequency of vibration.
High pitch: high frequency (short wavelength).
Middle G:
f = 392 Hz
Pitch (vibration frequency)
v = λf =
F
µ
Tuning forks work by vibrating, a little bit like a guitar string. I have two tuning forks here. If you put it in water you can see that it’s vibrating (it splashes water around!)
Thinking about sound…
Pitch: determined by wavelength or frequency of vibration.
High pitch: high frequency (short wavelength).
Which fork will make the higher pitch (assuming
they’re made from the same material)?
A. Longer fork
B. Shorter fork
C. Both will make the
same pitch
D. Not enough info
Q123
Pitch (vibration frequency)
v = λf =
F
µ
ANSWER: B.
The shorter tuning fork will, generally, have a higher pitch if the two forks are made of the same thickness and material!
What this means…
Sound moves via compression of molecules!
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sio
s
e
Co
m
pr
Ra
r
ti
ac
ef
ion
on
s
es
Co
m
pr
Ra
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tio
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ac
ef
Note: propagation speed of sound is
independent of wave properties!
Speed depends ONLY upon the material sound is in.
You say… but v = λf ?!?
Raise pitch f, and wavelength λ will decrease!
Important to realize: HOW FAST sound moves doesn’t depend on the wave itself. It depends ONLY ON THE MATERIAL THE SOUND IS MOVING THROUGH.
What can be confusing is this equation - the wavelength and frequency are related!
http://www.physicsclassroom.com/mmedia/waves/gsl.cfm
Density of air:
1 kg/m3
Density of outer space:
0.0000000000000000000000000001 kg/m3
Why is this a great tagline or even a real physical thing? It’s because there are so few molecules in space that sound has trouble propagating. A density wave relies on
having molecules to compress. Sound is pretty much lost as soon as it hits the vacuum of space. Another film faux pax, by the way! Come on star wars!
Speed of Sound in a Solid
• The speed of sound in a solid depends on the
material’s compressibility and density
Y
v=
ρ
ρ
Remember
last time:
wave on a
string!
• Y is the Young’s Modulus of the material
• ρ is the density of the material
TensileStress =
Relate to string: tension (how compressible it is) over mass density!
YOUNG’S MODULUS SHOULD LOOK FAMILIAR!
F
ΔL
=Y
A
Lo
v=
F
µ
Ydirt ~ 4x107 Pa
Ysteel ~ 2x1011 Pa
ρdirt ~ 1250 kg/m3
ρsteel ~ 8050 kg/m3
Don’t do this for safety’s sake!
A train turns on < mile away and heads down the line
toward you. Will you hear the train first with your ear to the
steel tracks, or to the ground (made of loose dirt)?
Q124
Steel is stiffer —> higher Y.
Steel is denser—> higher rho.
Dirt: v = 178.9 m/s
Steel: v = 4984 m/s
ANSWER: B
A. Ground
B. Tracks
C. Not enough info
Y
v=
ρ
Speed of Sound in a Liquid
• In a liquid, the speed also depends on the
liquid’s compressibility and density
B
v=
ρ
ρ
ΔV
Volume Stress = − B
Vo
• B is the Bulk Modulus of the liquid
• ρ is the density of the liquid
BUT REMEMBER!!!
Temperature affects the volume
and density of materials.
Speed of Sound in Air
For Earth’s atmosphere, the speed of sound is
331 m/s at 0oC (273 K)
Note: for all the materials so far, sound speed
goes as 1/sqrt(density)!
As the temperature increases, the speed of
sound in air
A.
B.
C.
increases.
decreases.
stays the same.
If you don’t know, you can think
about what should happen to a
typical material that’s heated.
Q125
WHAT HAPPENS IF YOU HEAT UP THE AIR? I want you to think and guess: what happens to the sound speed?
ANSWER: A.
Speed of Sound in Air
For Earth’s atmosphere, the speed of sound is
331 m/s at 0oC (273 K)
T
v = 331m / s
≈ 343mT/ sis in
Kelvin!!
273K
Speed of sound ~343m/s
at room temperature (293 K ~ 20 oC)
This equation is calibrated to Earth’s atmosphere. I’ve swept under the rug some factors of molecular density.
T
v = 331m / s
≈ 343m / s
273K
A man shouts and hears his
echo off a mountain 5 seconds
later. How far away is the
mountain?
Speed of sound in air at room
temperature ~343m/s.
343m/s times 2.5 seconds is about 0.5 miles (1mile=1.6 km)
[see lightboard notes]
How loud is loud?
The Intensity of Sound
• Sound energy moves
outward in all directions
• Energy spread over a
bigger and bigger sphere!
• Surface area of sphere
= 4 π r2
I=
power
P
=
area
4πr 2
Units of power: Watts (W)
Units of intensity: W/m2
Sound propagates in all directions, and it gets weaker as you move away. We measure the POWER of sound transferred from the source (so how much power is it
producing) and we divid that by the AREA OVER WHICH IT’S SPREAD AT OUR DISTANCE R.
Power is in Watts. Intensity is in W/m2 although we also measure this in decibels, which I’ll speak about shortly.
The Intensity of Sound
• Sound energy moves
outward in all directions
• Energy spread over a
ar
bigger and bigger sphere! r, you’ll he
fa
s
a
y!
x
t
i
2
s
t
of sphere
• Surfaceuarea
n
e
e
g
t
n
si
s
I=f4yπor2
e
l
x
4
with
d
n
u
o
s
a
I=
power
P
=
area
4πr 2
Units of power: Watts (W)
Units of intensity: W/m2
Sound propagates in all directions, and it gets weaker as you move away. We measure the POWER of sound transferred from the source (so how much power is it
producing) and we divid that by the AREA OVER WHICH IT’S SPREAD AT OUR DISTANCE R.
Power is in Watts. Intensity is in W/m2 although we also measure this in decibels, which I’ll speak about shortly.
Quietest sounds we can hear:
10-12 W/m2
Sounds that hurt:
1 W/m2
Difference of 1012! This is huge!
So why don’t loud sounds sound 10^12 louder than the quietest sounds?
Alternate Measurement
of Intensity
Decibels (dB)
β = 10 log(I/I0)
I0 = 10-12 W/m2
“How many times 10 louder is this sound
than the faintest hearable sound?”
Our ears hear in a non-linear way; decibels are a better way to describe this. You can see it as simply a different scaling of Intensity.
ARGH!
10-2 W/m2
10-4 W/m2
10-6 W/m2
10-8 W/m2
10-10 W/m2
Intensity (W/m2)
100 W/m2
10-12 W/m2
What u say?
Here are intensity using both scales compared with levels of hearing over freq range of hearing. You will have a problem on your homework to practice the use of
decibels!
Jet takeoff (25m away):
150 dB
ARGH!
100 W/m2
Intensity (W/m2)
10-2 W/m2
Typical rock concert:
115 dB
10-4 W/m2
10-6 W/m2
10-8 W/m2
Restaurant: 60 dB
Quiet suburb: 50 dB
10-10 W/m2
10-12 W/m2
Breathing: 10 dB
What u say?
You will have a problem on your homework to practice this but you shouldn’t need to know it for the test.
The rods on the xylophone below generate different
frequencies. Why?
A) The rods have different densities
B) The velocity of sound changes through the rods
of differing length.
C) The wavelengths vary.
D) More than one of the above.
Q126
Y
v=
= λf
ρ
Same
material
used
Answer: C. Speed of wave depends only on the type of material; the wavelength and frequency are related to keep the velocity the same in a single material!
The Frequency of
Sound
• Audible waves
• Lay within the normal range of hearing of the human
ear
• Normally between 20 Hz to 20,000 Hz
• Infrasonic waves
• Frequencies are below the audible range
• Earthquakes are an example
• Ultrasonic waves
• Frequencies are above the audible range
• Dog whistles are an example
Which one of these do we use for medical purposes? Why?
Applications of Ultrasound
High frequency means small wavelength, thus
can be used to produce images of small objects
v = λf
Widely used as a diagnostic and treatment tool
• Ultrasounds to observe babies in the womb
• Ultrasonic flow meter to measure blood flow
• Cavitron Ultrasonic Surgical Aspirator (CUSA) used
to surgically remove brain tumors