# Vibrating Strings and Resonance in Air Columns

Vibrating Strings and Resonance in Air Columns String Instruments

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

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

Begins to vibrate itself Wind Instruments

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 Fundamental/ 1st Harmonic/ 1st

Resonant L= 3rd Harmonic/ 2nd Resonant L=

5th Harmonic/ 3rd Resonant L = 5/4 Open Ended Tube

Fundamental/ 1st Harmonic/ 1st Resonant L= 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?

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