Vibrating Strings and
Resonance in Air Columns
String Instruments
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In many musical instruments, the
source sets a string into vibration
Standing waves are produced at the
fundamental frequency as well as
the other natural frequencies
(overtones)
A .32m long violin string is tuned to play a
note at 440 Hz what is the wavelength of
the fundamental?
For the violin string played in the previous
problem, what would the wavelength of the
sound wave produced in air be at 25oC?
Intensity Increased
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Stringed instruments would not be
very loud if just a string
They have a sounding board or
sounding box to amplify the sound
The box (and air in it) resonates
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Begins to vibrate itself
Wind Instruments
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Standing waves produced in a column of
air in a pipe
Stream of air is directed against on edge
which creates turbulence and sets the air
into vibration
Only frequencies which create standing
waves persist
At points in the standing wave pattern
produces a loop, sound intensity is
amplified
Closed Ended Tube
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Fundamental/ 1st Harmonic/ 1st
Resonant
L=¼
3rd Harmonic/ 2nd Resonant
L=¾
5th Harmonic/ 3rd Resonant
L = 5/4 
Open Ended Tube
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Fundamental/ 1st Harmonic/ 1st
Resonant
L=½
Second Harmonic/ 2nd Resonant
L=
3rd Harmonic/ 3rd Resonant
L = 3/2 
What is the frequency of the 2nd
overtone for a 26cm open ended organ
pipe at 20oC?
What is the frequency of the 2nd
resonant for a 26cm long closed end
organ pipe at 20oC?
A flute is designed to play a middle C (262 Hz) as the
fundamental when all holes are covered. Assuming
20oC, how long is the flute?
If the same flute was played at 10oC,
what frequency will the note be?