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Lecture 17October 29, 2004
On Wednesday - Thumping
The Drum
Each of these modes are usually excited.The tension of the drum determines the frequency of each mode.The modes may NOT be harmonicEach mode dies out at a different rate.The player can change the basic “tone” of the drum by changing the tension of the drum head.
Kettle Drum INITIAL Spectrum
Drum Frequencies
The Sonogram
Modes
All modes are excited at first strike.These vibrations may excite others … resonance. Each mode decays in a different time. Amplitude
time
So … back to the tuning forks
Objects will resonate when
They are in contact with something that vibrates at its resonant frequency. Buzz in cars is a good example
Sound can cause resonance if it is at a frequency that is the resonant frequency of another object nearby. It must have enough energy.
Back to the trip from the instrument into our heads
The Trip
CREATIONOf Sound
TRAVELAND
ROOM ACOUSTICS
Sound Travels
ENERGY
Something is Missing
As time progresses, the amount of energy received by the ear increases.We need a measure of energy per unit time.
ENERGY
ENERGY PER UNIT TIME
sec
Joule1 watt 1
Second
JoulesPOWER
TimeUnit
Energy
Example = The Light Bulb
Consider a 60 Watt light bulb.It requires 60 Joules of energy each second.One Joule = 1 Newton Meter Joule=1( N-m)x (1 lb/4.45N) x
(3.28ft/m) Joule=0.738 ft-lbs
Thinking about light bulbs
60 Joules = 44.2 ft-lbsLift a ~4 pound weight 10 ft. or about one story of a building.Do this every second for 60 watts.
Joule=0.738 ft-lbs
A 100 lb woman would have to run up about 2 floorsof a building per second to generate this much power!
About Spheres ….
2
3
4
3
4
rAreaSurface
rVolume
r
Energy Spreads Out
These AREAS increase with r2.
Power per unit area therefore DECREASES with r2.
Let’s go to a concert.50 Meters
30 watts Ear Canal ~ 0.5 cm = 0.005 m
Area = (0.005)2=0.000025 m2
Houston we have another problem
Ear Area = (0.005)2=0.000025 m2
30 watts, 50 meters
To the ear ….
50m
30 watt
Area of Sphere =r2
=3.14 x 50 x 50 = 7850 m2
Ear Area = 0.000025 m2
In the ear…
wattsmm
watt
Ear
m
watt
m
watt
areaunit
power
000000095.0000025.00038.0
:
0038.07850
30
22
22
How do we deal with all of these zeros???
Answer: Scientific NotationChapter 1 in Bolemon, Appendix 2 in Johnston
0.000000095 watts = 9.5 x 10-8 watts
NOTE
10a/10b=10a-b
Example 1000/10=103/101=10(3-1)=102=100 10000/0.005=104/5 x 10-3=(1/5)x10(4-(-3))
=(1/5)x 107 =(10/5) x 106 = 2,000,000
You can actually get used to doing it this way! But you probably won’t!
Q:Can we hear 9.5 x 10-8 watts?
?
Acoustic Power (Watts)
INSTRUMENT Acoustic Power
Clarinet 0.05
Double Bass 0.16
Trumpet 0.31
Cymbals 9.5
Bass Drum 25
Entire Orchestra 67
Decibels - dB
The decibel (dB) is used to measure sound level, but it is also widely used in electronics, signals and communication.
Decibel continued (dB)Suppose we have two loudspeakers, the first playing a sound with power P1, and another playing a louder
version of the same sound with power P2, but
everything else (how far away, frequency) kept the same.
The difference in decibels between the two is defined to be
10 log (P2/P1) dB
where the log is to base 10.
?
What the **#& is a logarithm?
Bindell’s definition:
Take a big number … like 23094800394
Round it to one digit: 20000000000Count the number of zeros … 10The log of this number is about equal to the number of zeros … 10.Actual answer is 10.3Good enough for us!
Back to the definition of dB:
The dB is proportional to the LOG10 of a ratio of intensities.Let’s take P1=Threshold Level of Hearing which is 10-12 watts/m2
Take P2=P=The power level we are interested in.
10 log (P2/P1)
An example:
The threshold of pain is 1 w/m2
1201210)10log(1010
1log 10
:PAIN of thresholdfor the rating dB
1212-
Take another look.
The sensitivity range for human hearing depends on the loudness and pitch. Noises along each black line would be heard with the same volume.