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 = ¼

3rd Harmonic/ 2nd Resonant

L = ¾

5th Harmonic/ 3rd Resonant

L = 5/4

Open Ended Tube

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?