Why Does Strumming Force Not Alter the Pitch of a Guitar String?

[jaumzaum]

Guitar strings behave like a spring when tuned:

F = k.x is the tension in the string, where k is the contant of the string and x the displacement (when tuned). So by the equation :

$v = \sqrt{ F/u}$

where u is the linear density of the string.$v = \lambda.f -> f = \sqrt{ F/u}/\lambda$

The first string of a guitar is E and has a frequency f1, when tuned, that is proportional to the square root of the string tension.

But when we play the first string weakly, we seem to hear the same E note (sure, more weak) and when we play strongly, we seem to hear this same E stronger. So the force we apply in the string does not seem to change the frequency, only the amplitude. But in a spring, when we make a vertical displacement

[PLAIN]http://img716.imageshack.us/img716/6427/sgfhdf.jpg

The tension do change

So why don't we have a change in the frequency?

 

[Philip Wood]

Even for quite large displacements, the string tension doesn't change enough to affect the wave speed significantly. Indeed, constant tension is one of the assumptions we make when deriving the wave speed formula you've quoted. The derivation involves the transverse acceleration of the string due to transverse components of the tension which arise when the string is displaced.

For very large displacements, you're absolutely right: the note will change. It will also be far from pure!

 

[Ken G]

That's the right answer, but just to make it perfectly clear, there's a big difference between a spring that is not stretched, for which plucking causes all the stretching, versus a spring that is already stretched when you pluck it. The guitar string is the latter case, so that plucking really doesn't increase the already significant tension. Indeed, you know that when you "tune" the guitar, you do so by altering the initial tension, so that's what is key in producing the tone.

 

[olivermsun]

The tension do change

So why don't we have a change in the frequency?

Actually you do hear a slight frequency shift when you pluck hard on a stringed instrument.

 

[PJC01]

I would like to clarify that the SHM (Simple Harmonic Motion) of a guitar string is a complex phenomenon that involves multiple factors, including tension, linear density, and the material of the string itself. The equation v = √(F/u) is a simplified version of the wave equation that only applies to ideal strings with no damping or other external forces acting on it. In reality, guitar strings are not ideal and therefore the equation may not accurately represent the behavior of the string.

In regards to the observation that the frequency of the string does not seem to change with different levels of force applied, it is important to note that the human ear is not a precise instrument for measuring frequency. The perceived pitch of a sound is influenced by many factors, including the amplitude of the sound wave, the harmonics present, and even the listener's own auditory system. Therefore, it is possible that the frequency of the string does change with different levels of force, but it is not noticeable to the human ear.

Additionally, the force applied to a guitar string is not solely responsible for the frequency of the sound produced. The length of the string, the tension, and the linear density all play a role in determining the frequency. Therefore, it is not surprising that the frequency does not seem to change with different levels of force, as the other factors may be compensating for the change in tension.

In conclusion, the SHM of a guitar string is a complex phenomenon that cannot be fully explained by a simple equation. While the equation v = √(F/u) may provide a basic understanding of the relationship between tension and frequency, there are many other factors at play that influence the behavior of the string. Further research and experimentation are necessary to fully understand the intricate dynamics of guitar strings.