How does tightening the string of a violin change its vibration?

When you turn the tuning pegs of a violin to tighten the strings, the tension in the strings increases. That leads to a higher frequency at which the strings vibrate. So, turning the tuning pegs to tighten the violin strings raises their pitch.

The relationship between the tension of a string and the frequency can be understood through the formula:

$$f = \sqrt{\frac{T}{\mu L}}$$

- \(f\) is the frequency of the vibration

- \(T\) is the tension of the string

- \(\mu\) (mu) is the mass per unit length of the string

- \(L\) is the length of the string vibrating

From the formula, we see that the frequency is directly proportional to the square root of the tension, meaning as the tension increases, so does the frequency of vibration.

Additionally, tightening the string also increases its stiffness. A stiffer string resists deformation more, leading to a higher restoring force when it is plucked or bowed. This increased restoring force causes the string to oscillate at a higher frequency.

The interplay between tension and stiffness determines the pitch and timbre of the violin's sound. By adjusting the tension of the strings, violin players can achieve precise intonation and produce a rich variety of tones and expressions in their music.