Natural
Frequency &
Resonance
AP Physics 1
Natural Frequency
• Nearly all objects when hit or struck or plucked or
strummed or somehow disturbed, will vibrate.
o if you drop a pencil or a meter stick on the floor is will vibrate.
o If you pluck a guitar string, it will begin to vibrate.
o If you blow over the top of a soda bottle, the air inside will vibrate.
• When each of these objects vibrate they tend to vibrate
at a particular frequency or a set of frequencies known
as the natural frequency.
• All objects have a natural frequency or set of
frequencies at which they vibrate.
Timbre
• The quality or timbre of a sound produced by a
vibrating object is dependent upon the natural
frequencies of the sound waves produced by the
objects.
Pure Tone
• Some objects tend to
vibrate a single
frequency are are said
to produce a pure
tone.
• Example: Flute
• 200 Hz
Rich Tone
• Other objects vibrate
and produce more
complex waves with a
set of frequencies that
have a whole number
mathematical
relationship between
them and are said to
produce a rich sound.
• A tuba tends to vibrate
at a set of frequencies
that are
mathematically related
by whole number
ratios; it produces a
rich tone.
Noise
• Still other objects will
vibrate at a set of
multiple frequencies
that have no simple
mathematical
relationship between
them. These objects
are not musical at all
and the sounds that
they create could be
described as noise.
• When a meter stick or
pencil is dropped on
the floor, it vibrates with
a number of
frequencies, producing
a complex sound wave
that is clanky and noisy.
Natural Frequencies
Produced
Factors Affecting Natural
Frequency
• The actual frequency at which an object will vibrate
at is determined by a variety of factors. Each of
these factors will either affect the wavelength or the
speed of the object. Since
frequency = speed/wavelength
Consider a guitar as an example. There are six strings
,each having a different linear density (the wider
strings are more dense on a per meter basis), a
different tension (which is controllable by the guitarist),
and a different length (also controllable by the
guitarist).
Guitar example
• The speed at which waves move through the strings is
dependent upon the properties of the medium - in this case
the tightness (tension) of the string and the linear density of
the strings. Changes in these properties would affect the
natural frequency of the particular string.
• The vibrating portion of a particular string can be shortened by
pressing the string against one of the frets on the neck of the
guitar. This modification in the length of the string would affect
the wavelength of the wave and in turn the natural frequency
at which a particular string vibrates at. Controlling the speed
and the wavelength in this manner allows a guitarist to control
the natural frequencies of the vibrating object (a string) and
thus produce the intended musical sounds. The same
principles can be applied to any string instrument - whether it
is the harp, harpsichord, violin or guitar.
Wind Instrument
Example
•
Consider the trombone with its long cylindrical tube that is bent upon
itself twice and ends in a flared end. The trombone is an example of a
wind instrument. The tube of any wind instrument acts as a container for
a vibrating air column. The air inside the tube will be set into vibration by
a vibrating reed or the vibrations of a musician's lips against a
mouthpiece. While the speed of sound waves within the air column is not
alterable by the musician (they can only be altered by changes in room
temperature), the length of the air column is.
•
For a trombone, the length is altered by pushing the tube outward away
from the mouthpiece to lengthen it or pulling it in to shorten it. This causes
the length of the air column to be changed, and subsequently changes
the wavelength of the waves it produces. And of course, a change in
wavelength will result in a change in the frequency. So the natural
frequency of a wind instrument such as the trombone is dependent upon
the length of the air column of the instrument. The same principles can
be applied to any similar instrument (tuba, flute, wind chime, organ pipe,
clarinet, or soda bottle) whose sound is produced by vibrations of air
within a tube.
Forced Vibration
•
•
•
If you were to take a guitar string and stretch it to a given length
and a given tightness and have a friend pluck it, you would hear
a noise; but the noise would not even be close in comparison to
the loudness produced by an acoustic guitar.
On the other hand, if the string is attached to the sound box of
the guitar, the vibrating string is capable of forcing the sound box
into vibrating at that same natural frequency. The sound box in
turn forces air particles inside the box into vibrational motion at
the same natural frequency as the string. The entire system (string,
guitar, and enclosed air) begins vibrating and forces surrounding
air particles into vibrational motion.
The tendency of one object to force another adjoining or
interconnected object into vibrational motion is referred to as a
forced vibration. In the case of the guitar string mounted to the
sound box, the fact that the surface area of the sound box is
greater than the surface area of the string means that more
surrounding air particles will be forced into vibration. This causes
an increase in the amplitude and thus loudness of the sound.
Resonance with Tuning
Forks
• Video: Resonance with tuning forks
• In this demonstration, one tuning fork forces another
tuning fork into vibrational motion at the same natural
frequency. The two forks are connected by the
surrounding air particles. As the air particles surrounding
the first fork (and its connected sound box) begin
vibrating, the pressure waves that it creates begin to
impinge at a periodic and regular rate of 256 Hz upon
the second tuning fork (and its connected sound box).
The energy carried by this sound wave through the air is
tuned to the frequency of the second tuning fork. Since
the incoming sound waves share the same natural
frequency as the second tuning fork, the tuning fork
easily begins vibrating at its natural frequency.
Resonance
• resonance - when one object vibrating at the same
natural frequency of a second object forces that
second object into vibrational motion.
Resonance Videos
Water Glass Resonance
Mechanical Universe: Resonance