Frequency and Distance
By: Jose Barragan, Bona Kim, Anke
Scheller, and Ashley Thiessen
January 22, 2010
Introduction.:.
Method.:. Diagram.:.
Results and Discussion.:.
Acknowledgments.:. Links.:.
Bibliography.:. Go Up
Introduction
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Background
In orchestras or bands, flutes are always placed at the front of the wind sections and the tubas are placed in the very back. According to conductors, the reason for this is because higher pitched instruments, like the flute, produce pitches that do not carry as far as the sounds of a lower instrument. This could be a surprise for many people because the flute produces a tone that is focused and gives an impression of being loud. But, there are several examples in nature and in our society that illustrate that low pitches do carry further distances. For example, elephants use low frequencies to communicate with one another over long distances. Also, “AM radio signals, in the range of 520 to 1,710 KHz, can often be picked up at distances of 100-300 miles, while FM frequencies of 88 MHz to 108 MHz are limited to what's known as line-of-sight transmission, topping out at around 50-60 miles, at best.”3 In addition, foghorns are used to communicate over long distances because it produces low sounds that can carry far.2
Statement of the Problem
The purpose of this investigation is to determine the relationship between frequencies of a sound wave and the distance that the sound wave can travel, if such relationship exists.
Hypothesis
If different frequencies of sound are projected at a given decibel and the decibel is measured at a certain distance away from the sound source, then the lower frequencies will have higher decibels at distance
than the higher frequencies, because lower frequencies travel farther better than higher frequencies.
Variables
Independent Variable: Different frequencies
Dependent Variable: Decibel measured at a certain distance away from the sound source
Control: The volume (decibel) at which the different pitches are played.
The music instrument used to produce the pitch.
The person who plays the instrument.
Distance at which the decibel is measured.
Decibel at which the different pitches are played.
Place and setting – no wind, no outside noises.
Method
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First, find a tunnel or tube-like hallway that
can keep the sound contained. If this is done in a hallway, find one with the
least amount of openings. Also, the location must be at least 25 meters long in
order to get a more accurate change in decibels from one end of the hallway to
the other. Next, a person with a musical instrument (Person A) stands on one
end of the hallway and the data recorder (Person B) waits on the other end. The
person playing the instrument has to stay in the same spot to the best of her
abilities because otherwise, it will alter the decibel measurements. Pick one
decibel that the sound source (Person A) will play for all of the different
pitches. In this particular experiment, we started out with only the flute and
then added on the clarinet to broaden the range of pitches we could test out,
but other musical instruments or other devices can be used as the sound source.
The third person with the decibel meter (Person C) waits until person A plays a
steady pitch at the selected decibel value then quickly runs to the other end
of the hallway to measure the decibel of the sound. Person C has to make sure
to always stand in the same places when measuring the decibel values. Repeat
this five times with each pitch. Test five to six pitches throughout the range
of the instrument. If two decibel meters are available, simply set up one
decibel meter next to Person A and one on the other end of the hallway to keep
the measurements more consistent and free of errors that will occur from
measuring the decibel from slightly different locations. Since we were using a
musical instrument, we converted music notes to frequency from a pitch vs
frequency chart. 5
List of Materials
-
A group with a minimum of three people
-
Instruments
-
Tuner
-
One or two decibel meter with full batteries
-
A long tube-like hallway or something similar
-
Paper and Pencil
-
Meter stick
Diagram
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Results
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Averaged Data
(62+60+63+62+62)/5 = 61.8
(57+55+57+55+58)/5 = 56.4
(53+58+56+54+57)/5 = 55.6
(62+63.9+64+64+64.2)/5 = 63.62
(38+35+44+50+46)/5 = 42.6
(60+59.8+56+61+57)/5 = 58.76
(53+52+47+52+54)/5 = 51.6
(62+63+59+63+57)/5 = 60.8
(62+69+65+68+69)/5 = 66.6
(62+69+63+54+52)/5 = 60
|
Frequency
|
Decibel
|
|
146.832
|
61.8
|
|
195.998
|
56.4
|
|
261.626
|
55.6
|
|
293.665
|
63.62
|
|
349.228
|
42.6
|
|
391.995
|
58.76
|
|
466.164
|
51.6
|
|
698.457
|
60.8
|
|
932.328
|
66.6
|
|
1244.508
|
60
|
Clarinet data was separated out
for further study alone because only the notes played on the clarinet followed
our predicted trend, unlike the rest of the data, and therefore was a point of
interest.
Conclusion
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From
the experiment, we found that part of the lower range of notes had a negative
relationship between frequency and decibel and that the rest of the higher
notes showed no pattern or correlation at all. For example, when the frequency
of the note played was 146.832Hz, the average decibel measured at twenty-five
meters away was 61.8dB and when the frequency was 349.228Hz, the average
decibel was 42.6dB. And later, when this negative correlation was disrupted,
391.995Hz measured 58.76dB while 1244.508Hz measured 60dB.
From
the data collected during the experiment, our hypothesis was weakly supported.
Only part of the data supported our hypothesis that higher frequencies would
travel less far and therefore give smaller decibel values at the other end of
the hallway. The of rest of the data, starting for 391.995Hz onward, did not
support our hypothesis and did not show any pattern at all.
There
are two factors that contribute to this experiment. First, it is said that
lower frequency sound waves do travel further because they do not lose as much
energy to the medium – in this case, air –that they are moving through. 1 This can explain the downward
trend we saw with the frequencies; 146.832Hz, 195.998Hz, 261.626Hz, and
349.228Hz. Second, the square of a frequency of a sound wave is directly
proportional to its intensity (W/m˛ or converted into dB). 4 This explains why the high
frequencies produced higher decibel/intensity values. This two idea contrast
each other, but if we take into account that the square of the distance from
the sound source is inversely proportional to the sound wave’s intensity, 4 we can predict that as distance
increases, the intensity of high frequencies will be decreasing exponentially.
This means that the first factor (that lower frequency sound waves do travel
further because they do not lose as much energy to the medium) will overrule
the directly proportional relationship between frequency and intensity at some
point if we make the distance greater.
Dealing
with sound waves, there was a lot of error. For example, the person playing the
note on the instrument did not hold the note steady, volume and pitch wise.
Without an extra decibel meter, the player had to rely on her ears to keep the
sound as steady as possible. Also, we did not take into account the refraction
of the sound waves when they hit the wall or the diffraction of the waves when
they hit the person running through the hallway. Lastly, there were slight
differences in the location of the decibel meter for each trial, but the
differences were not significant.
In
order to improve this experiment, we would use two decibel meters to eliminate
the running back and forth, and with it, the uncertainties and follow this
action. Also, we would use a speaker or a steady sound source instead of live
playing of musical instruments in order to produce more steady sound waves. In addition,
we would want to find a longer hallway in order to test out whether or not a
longer distance would have made a difference in the kind of data we collected.
Lastly, we would look into whether or not having non-reflective surfaces would
provide better control of the sound waves’ echoes for the experiment.
Acknowledgements
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top
First off, we would like to thank Corey
Cushing for running back and forth on the football field when he was not part of
our group. Also, we would like to thank the amazing Mr. Murray for his
interesting story and memorable Mohawk.
Links
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http://dev.physicslab.org/Document.aspx?doctype=3&filename=WavesSound_IntroSound.xml
- Very good site about the movement of sound waves. It has an example of a
moving wave from a pitch fork on the home page as well showing how longitudinal
waves move.
http://www.physlink.com/education/askexperts/ae557.cfm
- This question and answer talks about how frequency travels. The discussion is
about the relationship between distance and frequency.
http://answers.google.com/answers/threadview/id/772249.html
- Another question and answer in thread form concerning the idea of distance
between frequency.
http://sound.westhost.com/articles/fadb.htm#s12
- This website talks about frequency, amplitude, and dB. It concerns wavelengths
and sound in general.
http://www.phy.mtu.edu/~suits/notefreqs.html
- Gives a frequency for musical notes in Hz and in cm.
Bibliography
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Works Cited
1Colwell, Catherine H. "PhysicsLAB: Introduction to
Sound." Welcome to PhysicsLAB! Web. 22 Jan. 2010.
<http://dev.physicslab.org/Document.aspx?doctype=3&filename=WavesSound_IntroSound.xml>.
2DiBonaventuro, Frank. "I was told that lower frequency
sound waves (like from a bass guitar) travel lower to the ground that higher
frequencies. Is this true?" Physics and Astronomy Links - PhysLink.com.
Web. 22 Jan. 2010. <http://www.physlink.com/education/askexperts/ae557.cfm>.
3"Distance waves can travel based on frequency." Google
Answers. Web. 22 Jan. 2010.
<http://answers.google.com/answers/threadview/id/772249.html>.
4Elliot, Rod. "ESP - Frequency, Amplitude and dB."
Elliott Sound Products - The Audio Pages (Main Index).
Leonard Audio, 01 Dec. 2006. Web. 22 Jan. 2010.
<http://sound.westhost.com/articles/fadb.htm#s12>.
5Suits, B. H. "Frequencies of Musical Notes." Michigan Technological University - Department of Physics. Web. 22 Jan. 2010.
<http://www.phy.mtu.edu/~suits/notefreqs.html>.
