Transcript Waves and Sound

Sound Part II
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Music
What is the study of sound called?
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Acoustics
What is the difference between
music and noise?
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Music: Sound that follows a regular
pattern; a mixture of frequencies which
have a clear mathematical relationship
between them.
Noise: Sound that does not have a
regular pattern; a mixture of
frequencies whose mathematical
relationship to one another is not
readily discernible.
SOURCES OF SOUND
Sound comes from a vibrating object. If an object
vibrates with frequency and intensity within the
audible range, it produces sound we can hear.
MUSICAL
INSTRUMENTS
String Instruments:
guitar, violin and piano
Wind Instruments:
Open Pipe: flute and some organ pipes
Closed Pipe: clarinet, oboe and saxophone
Percussion Instruments:
Drums, bells, cymbals
As a string vibrates, it sets surrounding air molecules
into vibrational motion. (called forced vibrations) The
frequency at which these air molecules vibrate is
equal to the frequency of vibration of the guitar
string.
Forced vibrations: the vibration of an object
caused by another vibrating object. AKA
Resonance
Standing Waves
reflection resulting in
A type of ____________
interference
____________ .
Created when periodic waves with equal
amplitude and wavelength reflect and
superimpose on one another.
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http://www.walterfendt.de/ph14e/stwaverefl.htm
Cont’d
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stationary and are due
Nodes: appear __________
destructive
to ______________
interference.
vibrate
Antinodes: appear to ___________
and
constructive
are due to _______________
interference.
Standing Wave: A result of
interference. Occurs at harmonic
frequencies
only created within the medium
at _______
_________ of
specific frequencies
vibration (harmonic frequencies)
 as frequency of the wave
increases
_____________,
number of
nodes and antinodes
___________
in the same
increases
amount of space
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Ruben’s Tube
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Ruben's Tube - YouTube
Standing Waves
The nodes and antinodes remain in a fixed
position for a given frequency.
There can be more than
one frequency for
standing waves in
a single string.
Frequencies at which
standing waves can be
produced are called the
natural (or resonant) frequencies.
A guitar or piano string is fixed at both ends
and when the string is plucked, standing waves
can be produced in the string.
Standing waves
are produced by
interference
Resulting in nodes
an antinodes
2-antinode
Demo mini-wiggler
When an instrument produces sound, it
forms standing waves and resonates at
several related frequencies.
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Fundamental Frequency(1st harmonic):
lowest
the ___________
frequency that an
instrument vibrates at. Defines it’s
pitch
________
Overtones: Other frequencies the
instrument resonates at
Harmonics= Overtones that are whole
number multiple of the fundamental
frequency.
The harmonics enhance the quality
Sound Spectrum
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Intstruments do not produce a
single sound wave
Superposition of many sine waves
sawtooth wave
f = 500 Hz
f + 2f + 3f
(A = 1)
(A3 = 1/3)
10 harmonics
f + 2f
(A2 = 1/2)
f + 2f + 3f + 4f + 5f (A5 = 1/5)
Piano
Fundamental only
Harmonics 1 & 2
Harmonics 1, 2, 3
Harmonics 1 - 4
Harmonics 1 - 5
Harmonics 1 - 6
Full sound
A sound is the
sum of its parts.
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Physical Science: Sound | Discovery
Education THe Piano
Boundary Conditions on a
String
Since the ends are fixed, they
will be the nodes.
The wavelengths of the
standing waves have a simple
relation to the length of the
string.
The lowest frequency called
the fundamental frequency
(1st harmonic)has only one
antinode. That corresponds to
half a wavelength:
The other natural frequencies are called overtones.
They are also called harmonics and they are integer
multiples of the fundamental.
The fundamental is called the first harmonic.
The next frequency has two antinodes and is called
the second harmonic.
The equation for strings is
f – frequency in hertz
n – number of harmonic
L – length of string in meters
V – velocity in medium in meters/sec
λ - wavelength in meters
-n
can be any integer value greater than one.
A wave travels through a string at 220m/s.
Find the fundamental frequency (1st
Harmonic) of the string if its length is
0.50m.
 v=
220 m/s
 L = 0.5 m
n = 1
 f = nv/2L
 f =(1)(220 m/s) /(2)(0.5m)
 f = 220 Hz
Find the next two frequencies (2nd and
3rd harmonics) of the string.
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Second Harmonic
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Third Harmonic
A wave travels through a string at 220m/s.
Find the fundamental frequency (2nd
Harmonic) of the string if its length is
0.50m.
 v=
220 m/s
 L = 0.5 m
n = 1
 f = nv/2L
 f =(2)(220 m/s) /(2)(0.5m)
 f = 440 Hz
A wave travels through a string at 220m/s.
Find the fundamental frequency (3rd
Harmonic) of the string if its length is
0.50m.
 v=
220 m/s
 L = 0.5 m
n = 1
 f = nv/2L
 f =(3)(220 m/s) /(2)(0.5m)
 f = 660 Hz
What is the pattern that you are
seeing? What do you think the
frequency is for the 4th harmonic?
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If you had a string that was 10
m long and it was vibrating in
the 5th harmonic, how would
you solve for wavelength?
v/λ = nv/2L
Rearrange to solve for λ
2Lv/nv = λ
λ = 2L/n
λ = 20m /5 = 4m
When string is longer, the
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Wavelength is
Longer
Therefore the frequency is
Lower
The sounds produced by vibrating strings are not very loud.
Many stringed instruments make use of a sounding board or
box, sometimes called a resonator, to amplify the sounds
produced. The strings on a piano are attached to a
sounding board while for guitar strings a sound box is used.
When the string is plucked and begins to vibrate, the
sounding board or box begins to vibrate as well (forced
vibrations). Since the board or box has a greater area in
contact with the air, it tends to amplify the sounds.
On a guitar or a violin, the length of the
strings are the same, but their mass per
length is different. That changes the
velocity and so the frequency changes.
Frequency in string depends on
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Length of string: inverse or direct?
Inverse
As string length goes up frequency decreases
Tension: inverse or direct?
Direct
As tension increases frequency increases (shortening
string)
Thickness: inverse or direct?
Inverse
As thickness increases frequency decreases
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The speed v of waves on a string depends on the string tension T and linear mass
density (mass/length) µ, measured in kg/m. Waves travel faster on a tighter string and
the frequency is therefore higher for a given wavelength. On the other hand, waves
travel slower on a more massive string and the frequency is therefore lower for a given
wavelength. The relationship between speed, tension and mass density is a bit difficult
to derive, but is a simple formula:
v = T/µ
Since the fundamental wavelength of a standing wave on a guitar string is twice the
distance between the bridge and the fret, all six strings use the same range of
wavelengths. To have different pitches (frequencies) of the strings, then, one must
have different wave speeds. There are two ways to do this: by having different tension
T or by having different mass density µ (or a combination of the two). If one varied
pitch only by varying tension, the high strings would be very tight and the low
strings would be very loose and it would be very difficult to play. It is much
easier to play a guitar if the strings all have roughly the same tension; for this
reason, the lower strings have higher mass density, by making them thicker
and, for the 3 low strings, wrapping them with wire. From what you have learned
so far, and the fact that the strings are a perfect fourth apart in pitch (except between
the G and B strings in standard tuning), you can calculate how much µ increases
between strings for T to be constant.
WIND INSTRUMENTS Wind instruments produce sound
from the vibrations of standing waves occur in
columns
air
_________of
_______
inside a pipe or a
Open Pipe Boundary: Antinode to antinode
Closed Pipe Boundary: Node to antinode
Open at both ends pipe
Closed at one end pipe
So for an Open tube, since each harmonic
increases by ½ a wavelength, calculation is
same as for string. However use velocity of
sound in air (usually 340 m/s)
1st Harmonic is ½ of a wavelength
For a half-closed tube
Different than open pipes due to boundary. Start
at ¼ λ and build by ½ a λ. Use velocity of sound
in air (usually 340 m/s)
4
1st Harmonic is ¼ of a wavelength
Why a 4?
HARMONICS
a) For open pipe
The harmonics will be all multiples of the fundamental
n = 1, 2, 3, 4 , 5 …
b) For closed pipe
The harmonics will be the odd multiples of the
fundamental
n = 1, 3, 5, 7, …
Ex 6: A pipe that is open at both ends is 1.32 m long, what is
the frequency of the waves in the pipe?
v = 340 m/s
L = 1.32 m
f = nv
2L
= (1) (340)
2 (1.32m)
= 128.79 Hz
Ex 7: What if it was closed at one end?
f = nv
4L
= (1) (340)
4 (1.32m)
= 64.39 Hz
Ex 8: An organ pipe that is open at both ends has a
fundamental frequency of 370.0 Hz when the speed of
sound in air is 331 m/s. What is the length of this pipe?
f' = 370 Hz
v = 331 m/s
f = nv
2L
370 = (1)(331)
2 L
L = (1)(331)
2(370)
= 0.45 m
How can you change the fundamental
frequency of a wind instrument?
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Change the length of the air column:
open and close valves
As the length shortens, the wavelength
gets
Shorter
Which means the frequency gets
Higher
And the pitch is
higher
Beats…..or how to tune a guitar!
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frequency
Beat _____________
refers to the
rate at which the volume is heard to
be ____________from
high to low
oscillating
volume.
It is due to the interference effect
resulting from the
superposition
____________________
of two
waves of slightly different
frequencies propagating in the
same direction
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The beat frequency between two sound waves is
the absolute difference in the frequencies of the
two sounds.
f beat = | f A- f B |
Ex I: Given a sound at 382 Hz and a sound at
388 Hz:
f beat = 6Hz
The human ear cannot detect beat frequencies
of greater than 10Hz.
Musical instruments are tuned to a single note
when the beat frequencies disappear.
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The Beat...
Beats
Auditory Illusion
Palm Pipes Activity
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An example of a closed pipe