How does pitch change when you tighten the instrument?

The pitch of an instrument changes when you tighten it because the tension of the strings increases. When the strings are tighter, they vibrate at a higher frequency, producing a higher pitch. Conversely, when the strings are looser, they vibrate at a lower frequency, producing a lower pitch.

This relationship between tension and pitch is fundamental to the tuning of stringed instruments. By adjusting the tension of the strings, musicians can bring their instruments into tune with each other and with the desired pitch standard.

The specific relationship between tension and pitch is given by the following formula:

```

f = (1/2L)√(T/m)

```

where:

* f is the frequency of the vibrating string

* L is the length of the vibrating string

* T is the tension of the string

* m is the mass of the string

As this formula shows, the frequency of a vibrating string is directly proportional to the square root of the tension of the string. This means that if you double the tension of a string, its frequency will increase by a factor of √2. Conversely, if you halve the tension of a string, its frequency will decrease by a factor of √2.