The pitch of a vibrating string depends on various factors, including the tension in the string, its length, and the material it is made of. However, the medium in which the string vibrates also plays a role in determining the pitch.
When a string vibrates, it creates waves that travel through the medium. The speed at which these waves travel depends on the density and elasticity of the medium. In general, the denser the medium, the slower the waves travel. This is because the molecules in a dense medium are more tightly packed, so they have to move more slowly to make way for the waves.
The speed at which the waves travel also affects the wavelength of the waves. Wavelength is the distance between two adjacent peaks or troughs of a wave. The longer the wavelength, the lower the pitch of the sound.
So, if a string vibrates in a denser medium, the waves will travel slower and have a longer wavelength, which will result in a lower pitch. Conversely, if the string vibrates in a less dense medium, the waves will travel faster and have a shorter wavelength, resulting in a higher pitch.
In summary, the medium in which a string vibrates can affect its pitch by changing the speed at which the waves travel and the length of the wavelength. This is why strings vibrate differently in different materials and also why the pitch changes when you play the same note on a string that is stretched or relaxed.