Vibrating Strings String Instruments In many musical instruments
Vibrating Strings
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) ¡
Standing Wave Two interfering waves have the same amplitude and wavelength but opposite directions ¡ Wave produced remains relatively stationary ¡
Definitions Node – points of standing wave that remain at rest – where destructive interference is occurring ¡ Loop or Antinode – double crest or double trough – where constructive interference occurs ¡
Natural Frequency Only certain frequencies of waves produce standing wave patterns ¡ Frequencies that produce standing wave patterns are called Natural Frequencies ¡
First Harmonic Lowest frequency of standing wave ¡ Also called fundamental freq. ¡ One loop and two nodes ¡ L = ½ ¡
Overtones ¡ Other natural frequencies of vibration
2 nd Harmonic Two loops and three nodes ¡ L = ¡
3 rd Harmonic Three loops and four nodes ¡ L = 3/2 ¡
Frequency of given harmonic is a multiple of the fundamental frequency ¡ Fn = n F 1 ¡
¡ ¡ A. 32 m long violin string is tuned to play a note at 440 Hz what is the wavelength of the fundamental? What are the frequencies of the next three harmonics?
Resonance on Strings • The speed of a wave on a string depends on the tension of the string, as well as its mass per unit length. • More tension – greater velocity so higher frequency • Shorter string – higher frequency
Quality ¡ ¡ How you can tell one sound source from another even when playing the same note Depends on the presence of overtones
Tuning Fork Guitar
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