Sound
What is sound?
If a tree falls in the middle of a forest, and there is no
one there to hear it, did it make a sound?
Plot of Air
Pressure over
Distance
Sound: ___________________________
Representation
of Air
Molecules
Speed of sound in air: (T in °C)
v ≈ (331+ 0.60T )m / s
For T = 20°C (68°F), v = 343 m/s
= 1125 ft/sec = 767 mph
Ruben’s Tube
General Sherman
World’s Largest Tree
52,500 ft3
1.3 Estabrook 111s
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Example: Travel Time
Sound: Speed, Pitch, and Intensity
How long does it take for sound to travel the length of this
room (100 ft)?
•
Pitch is related to frequency
•
Lowest pitch humans can hear: ______
•
Highest pitch humans can hear: ________
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How long does it take for sound to travel 1 mile?
You see a flash of lightning. 3.4 seconds later you
hear the thunder. How far away is the storm?
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Sound: Intensity and Loudness
•
_________: sensation in human beings
•
_________: Power per unit area perpendicular to wave
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Sound Level
•
Sound intensity levels usually specified on a
___________ scale
•
Common unit: bel, after Alexander Graham Bell
Humans can detect sounds approximately in range
of _______ to ____ W/m2
•
Higher intensity levels can be heard, but are painful
•
Loudness _____________ proportional to intensity
•
To produce a sound twice as loud requires about
____ times the intensity
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•
•
More common is
•
__________, or 1/10 bel
β (in dB) = 10 log
I
I0
I0 is a reference intensity, usually taken as the
threshold of hearing, 1x10-12 W/m2
Threshold of hearing:
Level of pain:
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Wind Instruments: Open tubes
Displacement
λn =
2L
n
f n = nf1 =
nv
2L
n = 1, 2, 3, …
Natural Frequencies of Open Tubes
First
λ = 2L
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Sound: Wind Instruments, Resonance in Pipes
•
Set the frequency of the speaker to 230 Hz. Determine
when resonance occurs.
•
Set the open tube to 160 cm in length. Determine the
various resonant frequencies. What can you say about
the ratio between them?
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Second
λ=
2L
2
Third
λ=
3L
2
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Example: Flute
A flute is an open pipe designed to play middle C (262
Hz) when all the holes are covered. Assume the
temperature is 20°C. Find the distance from mouthpiece
to far end of flute.
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Example: Bugle
Wind Instruments: Closed tubes
λn =
Displacement
A bugle is simply an tube of fixed length that behaves as if it
is open at both ends. A bugler, by adjusting their lips
correctly and blowing with proper air pressure, can cause a
harmonic (usually other than the fundamental) of the air
column within the tube. For certain tunes, only four notes
are required, 565, 678, 791, and 904 Hz.
f n = nf1 =
nv
4L
n = 1, 3, 5, …
What is the fundamental frequency?
What is the required length of the bugle (m)?
Natural Frequencies of Open Tubes
First
What harmonic is the 565 Hz note?
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4L
n
Second
λ = 4L λ =
16
4L
3
Third
λ=
4L
5
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Sound: Wind Instruments, Resonance in Pipes
Example: Closed-closed tube
•
A pipe closed at both ends can have standing waves
inside it, but you normally don’t hear them because so
little of the sound can get out. You can hear the standing
waves if you are inside the pipe, such as when you sing
in the shower.
Set the closed tube to 80 cm in length. Determine the
various resonant frequencies. What can you say about
the ratio between them?
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Determine the wavelengths of standing waves in a pipe
closed at both ends.
Find the fundamental frequency for a shower stall that is
2.5 m tall.
Is this frequency audible?
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