Dulku – Physics 20 – Unit 4 – Topic K
Dulku – Physics 20 – Unit 4 – Topic K
Specific Outcome:
i. I can explain, qualitatively, the conditions for constructive and
destructive interference of waves and for acoustic resonance.
Acoustic Resonance
Musical Resonance
Acoustic resonance makes the different
frequencies possible for a musical instrument
At its resonant frequency, a musical
instrument vibrates with high amplitude!
Musical Resonance
Vibrating Strings
Air Column Resonators
Acoustic Resonance
Musical Resonance
For musical objects, a wave is two-sided
because it is symmetrical
ex. the following waveform corresponds to
1.5 wavelengths, not 3 wavelengths!
A musical instrument usually has multiple
resonant frequencies, organized into a
fundamental frequency and its overtones
Dulku – Physics 20 – Unit 4 – Topic K
Dulku – Physics 20 – Unit 4 – Topic K
1
Vibrating Strings
The lowest resonant frequency of a string is
called the fundamental frequency
This resonant frequency (f) is for λ/2
Vibrating Strings
The second resonant frequency is also called
the first overtone:
This resonant frequency (f) is for λ
This string vibrates as one whole segment
Dulku – Physics 20 – Unit 4 – Topic K
Vibrating Strings
The third resonant frequency is also called
the second overtone:
Dulku – Physics 20 – Unit 4 – Topic K
Air Column Resonators
If a sound source is held near a column of air,
it can make the air column resonate
The air column may resonate in more than
one place
There are two types of column resonance:
1. open tube (or open pipe)
This resonant frequency (f) is for 3λ/2
Dulku – Physics 20 – Unit 4 – Topic K
2. closed tube (or closed pipe)
Dulku – Physics 20 – Unit 4 – Topic K
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Air Column Resonators
Lengths of an air column at which this occurs
are called resonant lengths
The frequency heard or measured depends on
the length of column used
Air Column Resonators
Resonance will occur only if there is
constructive interference between the sound
source and the column
The column of air:
always has a sound source (ex. speaker,
tuning fork) at one end
either be left open (exposed) or closed
(sealed) at the other end
Dulku – Physics 20 – Unit 4 – Topic K
Dulku – Physics 20 – Unit 4 – Topic K
Air Column Resonators
A closed-pipe (closed-tube) resonator is a
cylindrical tube of air with one end closed
Constructive interference (resonance) occurs
if there is an antinode at the sound source
At resonant lengths of the column,
constructive interference (resonance) occurs
Air Column Resonators
The shortest (fundamental) resonant length
of a closed-tube column is ¼λ (or λ/4):
l1 =
λ
4
where:
l1 = first resonance length (m)
λ = wavelength of sound (m)
For each additional half wavelength (λ/2 or
2λ/4), there is another resonant length
Dulku – Physics 20 – Unit 4 – Topic K
Dulku – Physics 20 – Unit 4 – Topic K
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Air Column Resonators
Air Column Resonators
The resonant lengths of a closed-tube
resonator are λ/4, 3λ/4, 5λ/4, etc.
l2 =
3λ
4
5λ
l3 =
4
where:
l2 = second resonance length (m)
l3 = third resonance length (m)
λ = wavelength (m)
MEMORIZE or KNOW HOW TO SOLVE FOR THESE!!
Dulku – Physics 20 – Unit 4 – Topic K
Dulku – Physics 20 – Unit 4 – Topic K
Air Column Resonators
ex. If the shortest (first) resonant length for a closed
pipe resonator is 16.5 cm when a 500 Hz tuning fork
is used, what is the speed of sound?
l1 =
λ
4
l1 = 16.5 cm/100 = 0.165 m
Air Column Resonators
ex. If the first resonant length in a closed air column is
18.5 cm when sounded with a 480 Hz tuning fork,
what is the speed of sound?
l1 =
λ
4
l1 = 18.5 cm/100 = 0.185 m
λ = 4l1 = 4(0.165 m) = 0.660 m
λ = 4l1 = 4(0.185 m) = 0.740 m
v = fλ = (500 Hz)(0.660 m) = 330 m/s
v = fλ = (480 Hz)(0.740 m) = 355 m/s
Dulku – Physics 20 – Unit 4 – Topic K
Dulku – Physics 20 – Unit 4 – Topic K
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Air Column Resonators
Air Column Resonators
An open-pipe (open-tube) resonator is a
cylindrical tube of air with both ends open
Each additional half wavelength (λ/2) yields
other resonant lengths
Same as before: constructive interference
(resonance) occurs if there is an antinode at
the sound source (at resonant lengths)
The resonant lengths of an open-tube column
are λ/2, 2λ/2, 3λ/2, 4λ/2, 5λ/2, etc.
The shortest resonant length for an opentube resonator is ½λ or λ/2
Dulku – Physics 20 – Unit 4 – Topic K
Air Column Resonators
The first three resonant lengths
l1 =
l2 =
λ
2
2λ
2
3λ
l3 =
2
where:
l1 = 1st resonance length in m
=λ
l2 = 2nd resonance length in m
l3 = 3rd resonance length in m
λ = wavelength of sound in m
Simplified, this gives us resonant lengths of:
λ/2, λ, 3λ/2, 2λ, 5λ/2, etc.
Dulku – Physics 20 – Unit 4 – Topic K
Air Column Resonators
Let’s do a side-byside comparison of
the resonant
lengths in closedtube and opentube resonance
columns:
MEMORIZE THE LAST TWO OR KNOW HOW TO SOLVE!!
Dulku – Physics 20 – Unit 4 – Topic K
Dulku – Physics 20 – Unit 4 – Topic K
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Air Column Resonators
ex. Find the shortest length of an open tube air
column that will resonate at 400 Hz with a
speed of sound of 341 m/s.
λ=
v = fλ
l1 =
λ
2
=
v
=
f
341 m/s
400 Hz
0.8525 m
2
= 0.8525 m
Vibrating Strings
A vibrating string will be governed by the
first resonance equation for an open-pipe:
l1 =
λ
2
where:
l1 = length of the string (m)
λ = wavelength of sound (m)
= 0.426 m
Dulku – Physics 20 – Unit 4 – Topic K
Dulku – Physics 20 – Unit 4 – Topic K
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