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THE FREQUENCIES OF
SOUND WAVES IN PHYSICS
ON MUSICAL NOTES
BY EZGI SÖNMEZ
Imagine if someone suddenly tells you the word "wave", what would be
the first thing that pops into your mind? Sea, sand, sun, holiday ... Well,
what would you think if the person told you that the word he’s talking
about is related to physics and music? I know that it is a bit hard to wrap
your head around it but waves are the elements that play an effective
role in the fields of physics and music. In this article, I will explore the
frequencies of sound waves in physics on musical notes and find the
frequency of the basic tones in music with you.
Sounds are a set of vibrations that travel around like waves. These sound
waves are vibrating particles that are reflected off surfaces. In this essay,
I am going to examine the sound of musical chords. Every music has a
frequency which is the rate per second of a vibration constituting a wave
or simply Hertz (Hz). When the note gets higher also frequency gets
higher periodically. To find the frequency of a note we should know the
A4 note’s frequency as a reference which is 440 Hz. A4 note is known
as the Pitch Standard (Stuttgart Pitch) which is the reference frequency
used to calibrate acoustic equipment and to tune musical instruments.
We have the formula to find any note’s frequency which is:
fn = f0 * (a)n
f0 = the frequency of one fixed note which must be defined. A common
choice is setting the A above middle C (A4) at f0 = 440 Hz.
n = the number of half steps away from the fixed note you are. If you are
on a higher note, n is positive. If you are on a lower note, n is negative.
fn = the frequency of the note n half steps away.
a = (2)1/12 = the twelfth root of 2 = the number which when multiplied
by itself 12 times equals 2 = 1.059463094359...
Now let’s look at the three notes above:
A5 = 880 Hz A4*2 = 440*2
A4 = 440 Hz
A3 = 220 Hz A4/2 = 440/2
These three notes are various octaves of the A note, and we observe that the frequency of the note doubles
as each octave goes up, or the frequency of the note decreases by half when each octave goes down. Inside
every octave, we have 12 half notes. For every time we increment the number we divide by 12 we get a note
half step above the previous note. But if we want to calculate the frequency of the note below our reference
note we should use negative numbers. So by doing that we will get the frequency of the note a half step
below the previous note every time we reduce the number by one. This is why the variable “a ” in the
formula is equal to the twelfth root of two which takes us from our reference note to an octave higher or
lower by raising or lowering a note by a semitone. So we can understand that “a ” is a constant number
which is approximately equal to 1.059463094359.
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