Why does the pitch get higher if you tighten string of guitar?

The frequency of a vibrating string is determined by its length, tension and mass per unit length. Increasing the tension of the string increases its frequency, causing the pitch to get higher. This is because the string is stretched tighter when it is tensioned, which causes it to vibrate faster. The faster vibration produces a higher pitch.

The formula for the frequency of a vibrating string is:

$$ f = \frac{1}{2L}\sqrt{\frac{T}{\rho}} $$

where:

- f is the frequency in hertz (Hz)

- L is the length of the string in meters (m)

- T is the tension in newtons (N)

- $\rho$ is the mass per unit length of the string in kilograms per meter (kg/m)

As the tension, \(T\), increases, the frequency, \(f\), also increases, resulting in a higher pitch.