Vibrating Strings and Resonance in Air Columns. String Instruments  In many musical instruments, the source sets a string into vibration  Standing waves.

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Presentation transcript:

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 25 o C?

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/ 1 st Harmonic/ 1 st Resonant L = ¼

3 rd Harmonic/ 2 nd Resonant L = ¾

5 th Harmonic/ 3 rd Resonant L = 5/4

Open Ended Tube  Fundamental/ 1 st Harmonic/ 1 st Resonant L = ½

Second Harmonic/ 2 nd Resonant L =

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

What is the frequency of the 2 nd overtone for a 26cm open ended organ pipe at 20 o C?

What is the frequency of the 2 nd resonant for a 26cm long closed end organ pipe at 20 o C?

A flute is designed to play a middle C (262 Hz) as the fundamental when all holes are covered. Assuming 20 o C, how long is the flute?

If the same flute was played at 10 o C, what frequency will the note be?