Re: When rarefactions are closer together, why is vibrations interpreted clear?

Your question involves four concepts; longitudinal waves, rarefactions 
close to each other, rarefactions close to the sound source, and how clear 
a sound is to the listener.  These are four separate concepts so let me 
comment on each separately.

You are correct in noting that a vibrating source produces longitudinal 
waves.  In a longitudinal wave the rarefactions (and condensations too) 
move in the same direction as the vibrating source, rather than at 90 
degrees to the vibrating source.  All sounds are longitudinal waves so we 
do not have to consider this concept for the rest of your question.

You also refer to how close the rarefactions are to each other.  This 
relationship affects the musical pitch of the sound.  Rarefactions that are 
close together mean that the rate of vibration is faster compared to when 
the rarefactions are farther apart.  Fast vibrations have a higher musical 
pitch compared to slow vibrations.  The higher-pitched notes played from 
the right side of a piano keyboard will have rarefactions closer together 
compared to rarefactions that are farther apart for the lower-pitched notes 
played from the left side of the keyboard.

You also refer to the distance of the rarefactions from the sound source.  
As the sound moves away from the sound source, the distance between the 
rarefactions does not change, though the strength of the rarefactions 
gradually diminish.  The strength of the rarefactions is interpreted by the 
listener as the loudness of the sound.  High-strength rarefactions are 
louder than low-strength rarefactions.  Rarefactions close to the sound 
source will start out at a certain loudness.  As they move away from the 
sound source the rarefactions lose their strength and the loudness 
decreases.  Note however, that because the distance between the 
rarafactions stays the same the pitch stays the same. Loudness and pitch 
are largely independent.  An example of a loud, high-pitched sound would be 
a smoke detector alarm and an example of a quiet, high-pitched sound would 
be the beep from a digital watch.

Whether a sound is "clear" or not may depend on two considerations, one 
related to the overall loudness of the sound, and one related to the 
loudness of just the high-pitched portions of the sound.

The overall loudness of a sound decreases as you move away from the source 
because the rarefactions (and condensations too) lose their strength.  This 
loudness decrease will occur even sooner if other sounds are present in the 
surrounding environment.  These other sounds are called ambient noise, 
noise that often comes from many sources at many different locations.  
Ambient noise in our radio example may be the rustling of leaves, traffic 
noise, wind noise, etc.  Ambient noise is usually evenly distributed in the 
surrounding environment because it comes from so many different sources.  
Let's say that the ambient noise level outside is 60 decibels.  This noise 
level will be approximately the same everywhere in the environment so it 
will remain at 60 dB even at different locations.  Now let's say that the 
loudness of the radio at a distance of one foot in front of the speaker is 
80 decibels.  At this distance of one foot, the radio is 20 decibels louder 
than the ambient noise (80 dB vs 60 dB).  You will hear the radio very 
"clearly" because the radio sound is much louder than, and not affected by, 
the ambient noise.  If you move far enough away from the radio so that the 
loudness of the radio drops to 65 dB, the overall sound from the radio 
starts to get covered up by the 60 dB ambient noise level, making the sound 
from the radio less clear.

The loudness of the high-pitched portions of a sound also affect how 
"clear" a sound is.  Many of the sounds we listen to such as speech, most 
music, etc. contain sounds that are louder for the lower pitches (long 
distances between rarefactions) compared to the loudness of the sounds for 
the higher pitches (short distances between rarefactions).  Let's say that 
you are listening to a Shania Twain song from the radio.  The lower pitches 
of her music (the vowel sounds in her voice, the bass guitar, notes from 
the left side of the piano keyboard, etc.) will be rather loud (lets say 80 
dB).  The higher pitches of her music (the consonants in her voice, 
symbols, notes from the right side of the piano keyboard, etc.) will be 
less loud (say 70 dB).  Standing close to the radio, you easily will hear 
both the low and the high pitches of her music because they both are louder 
than the ambient noise.  However, as you walk away from the radio, the high 
pitches will be covered up by the ambient noise much sooner compared to the 
low-pitched sounds because the high-pitched sounds are less loud to begin 
with.  At one point you will still hear the vowels, the bass guitar, etc, 
but will not hear the consonants, the symbols, etc.  You can still tell 
that it is a Shania Twain song
but it will sound less clear, or muffled.

Gerald R. Popelka, Ph.D.
Director, Communication Sciences Lab