Physics is all around us, and yet we always overlook it. We see, hear or feel
something happen but never stop to question why. Physics will tell us why. Music plays
a part in everyone's lives. So much so that it is often overlooked and the technicalities of
it are unappreciated. Sure there are times when we listen carefully to the music behind
the songs we hear, we may focus on the rhythm or the harmonies, but we never think of
what it took to make the sounds that we are hearing. As a musician and electrical
engineer student, sounds around us make me think why and how they are produced in
certain pitch or certain frequency. I’ve been playing musical instruments since a very
young age and not always the desire to know more was in me but, since I started the
university and took physics class a whole new world was open right in front of me.
When I learned that physics explains the “how something occurs” and the “why
something occurs” then started to wonder how when plucking my guitar’s strings a
pleasant sound comes out of it. By doing some research I discovered some basic
physics principles that show me how the sound is made.
Sounds in general are produced when something vibrates and when something
vibrates in the air it is called, traveling longitudinal wave and when a string vibrates it is
called a transverse wave, which can be heard by the human ear. Sound waves consist
of areas of high and low pressure called compressions and rarefactions, respectively.
The wavelength and the speed of the wave determine the pitch, or frequency of the
sound. Wavelength, frequency, and speed are related by the equation speed =
frequency * wavelength. Since sound travels at 343 meters per second at standard
temperature and pressure (STP), speed is a constant. Using the same equation we can
solve for frequency and get that it is determined by speed / wavelength. The longer the
wavelength, the pitch will be lower. The 'height' of the wave is its amplitude. The
amplitude determines how loud a sound will be. Greater amplitude means the sound will
be louder. When I learned these basic principles, I began to understand my guitar.
Accordingly to the tension on the guitar string the wavelength is going to be longer or
shorter. With more tension we will have less wavelengths, and with less tension we will
have more wavelengths. This is an indirectly proportional relation. The amplitude term
can be heard in the guitar by how hard the string is plucked. The harder the string is
plucked the bigger the amplitude, meaning that the sound will be louder. The softer the
string is plucked the amplitude will be much less, giving us a directly proportional
relation between the amplitude and the sound produced by the guitar string.
Learning these principles helped me understand my guitar a little bit more, but
made me ask myself more, which lead me to think about the tension involved in guitar
strings. In class we have learn that normal tension force may be defined as T=ma, in
the 2nd Law of Newton, but for a guitar string it involves other quantities. The equation I
said earlier for speed changes when talking about the tension. Now we define it as V =
fλ = √(T/μ), T being the tension, μ being the mass per unit length and λ being the
wavelength. Solving for T gives us, T = μV2= μλ2f2 . The tension is now in terms of the
mass per unit length, the frequency and the wavelength. All three of these quantities are
easily solved for. The mass per unit length is the only variable that needs to be
determined experimentally. It is a straightforward measurement of the mass of a certain
length of string divided by the length. The frequency is determined by which of the six
strings on the guitar is being analyzed. The guitar has six strings and their frequencies
in (Hz) respectively are 82.41, 110.00, 146.83, 196.00, 246.94, 329.63 and the
wavelength depends on the scale-length (Ls)of the guitar which it is λ = 2Ls.
I think this is the beginning of much more research and discoveries that I will be
doing with music and sound. Analyzing music with your ear may be pleasing and fun but
analyzing it with physics opens a whole new world that never thought of. This feeling I
just described made me think of the multiverse theory first coined by William James in
the year 1895. I’m not saying I believe in that theory but who knows. With physics many
things can be discovered.
Bibliography:
Hollis, Benjamin. "Physics of Sound." The Method Behind the Music. 1 Jan. 1999.
Web. 3 Apr. 2015. .
Achilles, Daryl. "Tension of Guitar Strings." Https://courses.physics.illinois.edu.
12 Dec. 2000. Web. 3 Apr. 2015.
Guitar_String_Tension_Experiment.pdf>.
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