Transcript Resonance - Titan Physics 2009

Sound and Music
A Deliciously Delightful Discussion of
Resonance, Harmonics, Beats, and Periods and
Frequencies
Presented by Giuliano Godorecci, Lisa Schalk, Patrick Woodbury, and Sean Perry (respectively)
Resonance
•Resonance is defined as “The
reinforcement or prolongation of
sound by reflection from a surface
or by the synchronous vibration
of a neighboring object”.
•An example of resonance can
easily be found in musical
instruments of all kinds, ranging
from woodwinds to stringed
instruments.
•The mass of a string, the length,
and the tension of the string, all
dictate what frequency the string
will vibrate at and, thus, what
pitch of sound will be emitted.
•The strongest resonance of an
instrument is located at the
natural harmonics of the
instrument, such as the 5th, 7th,
and 12th fret of a guitar.
Resonance (Cont.)
•Resonance is the movement up
and down or back and forth of an
object. This motion is called an
oscillation.
•The higher up on a guitar’s neck
one plays, the higher the pitch of
the notes will become because
the strings length becomes
shorter and shorter, causing the
oscillations of the strings to
increase in rate.
•Some strings can start oscillating
at their fundamental frequencies
when other strings are played,
just as an E string on a guitar will
sound after an A string is plucked.
References
• “The ABC’s of Resonance.” Intuitor.com. April 2, 1996. web. 2007.
<http://www.intuitor.com/resonance/abcRes.html>


A harmonic is a sinusoidal
component of a periodic wave or
quantity having a frequency that is
an integral multiple of the
fundamental frequency by definition.
Harmonics are all periodic at the
fundamental frequency, which means
the sum of harmonics is also periodic
at that frequency. In other words,
the second harmonic always has
exactly half the wavelength (and
twice the frequency) of the
fundamental; the third harmonic
always has exactly a third of the
wavelength (and so three times the
frequency) of the fundamental, and
so on. This is pictured on the right.
Harmonics

When a guitar string is plucked, the string
vibrates most notably at its fundamental
frequency, but simultaneously it also vibrates
at all integer multiples of that frequency. The
vibration along the entire length of the string
is known as the fundamental, while vibrations
occurring between points along the string
(known as nodes) are referred to as
overtones. The fundamental and overtones,
when sounded together, are perceived by the
listener as a single tone.
Guitar Harmonics
Beats
• A beat is an effect that occurs when two waves of opposite form and slightly different
frequency occur simultaneously. This should not be confused with the very different concept of
musical beats.
(Image sourced from http://www.aaroncake.net/
Beats (cont.)
•
When the waves first meet, they are exactly opposite one another. This results in complete
destructive interference – the waves cancel each other out completely, and no sound is
produced.
Here, the red line represents the sound generated by the combined waves.
Beats (cont.)
•
As the waves become increasingly desynchronized, however, they gradually move from
destructive interference to constructive interference. When the waves cause complete
destructive interference, they are said to be out of phase; when they cause complete
constructive interference, they are in phase.
• As this pattern continues, the combined waves form a third wave. The listener perceives this wave as a
gradual rise from softness to loudness and back.
Beats (cont.)
•
A beat occurs at the moment the two waves are completely in phase – that is, synchronized –
and thus are at their loudest.
• The magnitude of the difference between the waves’ frequencies determines how often beats
occur.
• For waves whose frequencies differ by 1 Hz, a beat will occur once every second because the
combined waves have a period of 1.
• If the difference in frequency is 2 Hz, then a beat will occur every 1/2 second.
•A difference of 3 Hz will result in a beat every 1/3 second.
•In the same vein, a difference of 4 Hz results in a beat every 1/4 second, 5 Hz results in a beat
every 1/5 second, and so on.
• In other words, the period of each beat is equal to the reciprocal of the difference in frequency
between the waves in question.
•As the difference between the waves’ frequencies increases, the speed of the transition from
softness to loudness increases until eventually, the listener perceives two distinct tones.
Beats (cont.)
•
•
The distinctive effect created by a very small difference in frequency is sometimes taken
advantage of to create an unusual sound.
The supplementary video at http://titan-physics.wikispaces.com/The+Music+Group
demonstrates the sound created by beats with increasingly large differences in frequency.
References
•
•
That good ol’ physics textbook you’ve been hauling around most of the last year.
Also, http://www.aaroncake.net/ for an image of a single sine wave, which I painstakingly
copied, pasted, and manipulated to create my illustrations.
Period and Frequency
Painstakingly created by Sean Perry
Period
• The period of an object moving in
a set pattern is the time it takes
the object to move from its point
of origin to the furthest part of it’s
path, and back the point of origin.
• This is usually measured in
seconds.
Frequency
• The frequency of an object moving
in a set pattern is the number of
complete cycles (A cycle is from
origin to end back to origin.) it
makes in a set amount of time.
• This is usually measured in hertz.
Switching back and forth
between the two, just like
a pendulum.
• To find the period of a moving
object from its frequency, you
invert the frequency, dividing 1 by
it.
• To find the frequency of a moving
object from its period, you invert
the period, dividing the number 1
by it.
How I can possibly relate
this to music.
• The higher the frequency of a
moving object, such as a string,
the higher pitched the sound is.
The lower the frequency, the lower
we perceive the sound.
• Inversely, the lower the period of a
moving object, the higher the
sound is that we perceive, and the
higher the period, the lower the
sound is that we perceive.
My… numerous references
• http://www.engineeringtoolbox.co
m/sound-frequency-wavelengthd_56.html
And that’s it.