The frequency of a wave equivalent to string vibration is determined by the tension, mass per unit length, and length of the string. Here's the breakdown:

Factors Affecting Frequency:

* Tension (T): Higher tension results in a higher frequency. Imagine tightening a guitar string – it vibrates faster and produces a higher pitch.

* Mass per unit length (µ): Lower mass per unit length (thinner string) results in a higher frequency. A thinner string vibrates faster than a thicker one.

* Length (L): Shorter length results in a higher frequency. Imagine shortening a guitar string – it vibrates faster and produces a higher pitch.

Formula:

The frequency (f) of a vibrating string is given by:

```

f = (1/2L) * √(T/µ)

```

Where:

* f: frequency (Hz)

* L: length of the string (m)

* T: tension in the string (N)

* µ: mass per unit length of the string (kg/m)

In simpler terms:

* Higher tension = Higher frequency

* Thinner string = Higher frequency

* Shorter string = Higher frequency

Example:

If you have two identical guitar strings, one tuned to a higher pitch (higher frequency) than the other, the higher-pitched string will have either:

* Higher tension

* Lower mass per unit length (thinner)

* Shorter length

Note: This formula applies to the fundamental frequency (the lowest frequency at which the string can vibrate). Higher harmonics (overtones) also exist at multiples of the fundamental frequency.