13 March, 2003
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
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
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
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
This, however, is only an idea of how to explain a phenomenon I was unable to prove due to human
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.
Rossing, Thomas D., Moore, F. Richard & Wheeler, Paul A. The Science of Sound, Third Edition. San
Francisco: Addison Wesley, 2002.
Raichel, Daniel R. The Science and Applications of Acoustics. New York: AIP Press, 2000.