# Genevieve Ernst

Document Sample

```					                                                                                                     Genevieve Ernst
13 March, 2003
Physics H90
How to Best Annoy Your Neighbors

Abstract: According to the equation for the transmission loss of sound through a solid (TL)0 = 10log(1 +

πMF/400), low frequencies should transmit better through walls than high frequencies. This experiment tested the

effectiveness of different frequencies to transmit through a wooden door at different amplitudes, but was

inconclusive due to the human inconsistency in producing sound on an amplified acoustic guitar.

Introduction: When a car drives by and the music it is blaring catches your attention, it is not the wailing high

notes of a violin that you hear from down the street, but the rhythmical thumping of the lowest bass tones. High

frequency techno music was never enough to keep me awake at night, but I was immediately aware when my

downstairs neighbor purchased a sub-woofer that powerfully pumped a low frequency beat up to disturb my sleep.

Low frequencies clearly transmit better through walls, doors, floors and ceilings and my goal was to see how the

transmission of sound varied between high and low frequency notes on an amplified acoustic guitar.

Theory: When sound waves in the air come in contact with solids, such as a wall or door, much of the sound wave

is reflected back, some is absorbed by the solid and some is transmitted through the solid by bending it, shaking it,

or by doing both. At relatively low frequencies, transmission loss of sound through a solid is indirectly

proportional to frequency, as shown by the equation for transmission loss (TL)0 = 10log(1 + πMf/400).

A standard acoustic guitar, with six strings and 72 possible fret positions can produce an incredible range

of frequencies and, when plugged into an amplifier, an incredible range of amplitudes as well. This versatility

makes the guitar useful for measuring variable frequencies. In order to ensure an accurate frequency reading, the

equation for frequency ratio R = 10I log2/1200 was used to take into account by how many cents each note was

off of its standard frequency.

Experiment: Using an amplified acoustic guitar as my sound source, I selected ten different frequencies to be

measured, as well as three different decibel levels—three different volume settings of the guitar’s amplifier. I

measured the frequencies the guitar produced using a frequency meter approximately one foot from the amplifier

of the guitar and also made initial decibel readings with a decibel meter at this range with the amplifier set to level
6. I then measured all ten frequencies at this level from outside of the room, with a distance of about ten feet and

a 2.5 cm thick painted wood door between the decibel meter and the amplifier. For each of the ten frequencies,

the guitar player plucked the string three times and I used the average of the decibel readings as my amplitude for

the given note. I also selected four different frequencies to measure with the amplifier set at levels 6, 4 and 2

from outside the room. The ten frequencies I used were the notes E2, B2, A3, B3, G4, G4#, B4, C5#, E5 and C6,

which included the lowest (the first string, open) and highest (the sixth string held at the last fret) notes

conventionally produced with the selected guitar. These notes represented a frequency range of over three

octaves. From the frequency meter’s reading of how many cents each played note was off by, I was able to

calculate the actual frequencies for the notes on the guitar I was using, as opposed to the standard frequency for

each note. When graphing my experimental results, the actual frequencies determined by these calculations were

used.

Table 1: Sounded notes, their standard frequencies and their actual frequencies, as calculated using the equation
for frequency ratio R = 10I log2/1200.

Note            Standard Frequency in Deviation from Standard Actual Frequency in Hertz
Hertz                 in Cents
E2                                     82.407                      -15                  81.696
B2                                     123.47                       +5                 123.826
A3                                        220                     +10                  221.274
B3                                     246.94                     +15                  249.089
G4                                        392                        0                     392
G4#                                     415.3                       +5                 416.496
B4                                     493.88                     +10                   496.74
C5#                                    523.25                       +5                 524.757
E5                                     659.26                     +10                  663.077
C6                                     1046.5                     +20                1058.639
Sound Transmission at Varied Frequencies
110
105
100
95
90
85
80
75
70
65
60
81.696   123.83    221.27   249.09    392        416.5   496.74   524.76   663.08   1058.7

Frequency of Note in Hertz

Amplitude in Room                      Amplitude Through Door

Fixed Frequencies Measured at Different Amplifier Levels Through
a Door
80
75
70
65
60
55
50
45
40
6                                                4                                               2
Amplifier Volume Level

Analysis: The notes on the guitar used for my experiment were fairly well in tune, deviating from standard

frequency by an average of 9.5 cents. Most of the frequencies were slightly too high, with only one at standard

and one slower than the standard. My experimental data showed no steady trend in sound transmission when

varied frequencies were compared at fixed amplitude. Instead, there was considerable fluctuation from one

frequency to the next, but not in an inverse relationship between frequency and amplitude, as predicted. While at

high amplitude levels there was no logical correlation between frequency levels and ability to transmit sound

through a door, at low decibel levels, they were inversely proportional, as predicted.
Conclusions: More than anything else, my data showed that controlling all possible aspects of human

inconsistency is crucial in conducting an experiment with logical, conclusive results. While equations and my

own experience both predicted that the lower the frequency of the note, the louder it would be on the other side of

the door, the experiment did not produce this result until the sound was played at very low decibel levels. This

may indicate that the difference in transmission ability does not become apparent until barely any sound is being

transmitted, but more likely, considering the rest of the data, which was scattered, this remains a hypothesis. My

explanation for the results of my experiment, which did not show what was expected, lay in the sound production.

While an amplifier can be set at a constant volume level, a human cannot pluck a guitar string with the exact same

force ten times in a row. In an attempt to minimize this effect on the experimental results, I had the guitar player

produce each of the ten notes three times in a row and took a mean as the decibel level. However, rather than

eliminating the factor of human inconsistency, it merely showed me how much variability I was facing, as the

three readings for any given note would fluctuate by as many as fifteen decibels, which was about 14-18% of the

total decibel level, a fairly large portion of the total.

In my research, I hoped to find out why exactly low frequency sounds are transmitted better through

solids than high frequency sounds. Unfortunately, I was unable to find this information. My only idea is that

since high frequency sounds travel in shorter wavelengths, they are more easily disturbed and scattered by

encountering a solid when transmitting pressure through the air. Since they occur at higher frequencies (meaning

more individual periods are being transmitted through the wall in a given period of time), there are more

opportunities for the wave to be diminished, as there are more periods. The pressure of longer waves however,

seems more stable in that small disturbances to the wave would only reduce its pressure slightly, but with less

periods to act on, it would not diminish it as effectively.
Figure 1: Transmission of sound waves through a solid

Low Frequency
Sound Wave

High Frequency
Sound Wave

Solid

This, however, is only an idea of how to explain a phenomenon I was unable to prove due to human

inconsistency.

If I were to redo this experiment, I would select frequencies at more regular intervals and use at least four

or five different amplifier levels when measuring the sound through a door. I would probably also test through

one door and two doors, or through some other solid, such as a car door (this was not feasible as the amplifier of

the guitar must be plugged into an electrical outlet). Most importantly though, I would use a sound source that

did not rely on human force to produce sound. This would ensure that different decibel levels transmitting

through the given solid would be due to differences in the excited frequencies, not in how hard the guitarist had

plucked the string.

In conclusion, while I was unable to confirm that lower frequency sounds are more successful at

transmitting pressure, and therefore sound, through solids, my experiment reinforced the importance of

eliminating all possible elements of human inconsistency when conducting an experiment.

Bibliography:

Rossing, Thomas D., Moore, F. Richard & Wheeler, Paul A. The Science of Sound, Third Edition. San