91Ó°ÊÓ

The speed of a wave is given by the following equation.

$\mathbf{v}\mathbf{=}\sqrt{\frac{\mathbf{T}}{\mathbf{μ}}}$

Here, v is the speed of a wave, T is the tension, and$\mathit{μ}$is the mass density.

Given that all four strings have the same tension. As a result, the linear density of the string will be the only factor that affects the wave's speed. According to the equation above, the wave speed is inversely proportional to linear density. Thus, the thicker the string more the mass density hence the slower the velocity of sound on the string. Thus, waves will travel faster in thin strings.

The fundamental frequency is given by,

$$\begin{gathered} \mathrm{f}=\frac{\mathrm{v}}{2\mathrm{L}} \\ =\frac{1}{2\mathrm{L}}\sqrt{\frac{\mathrm{T}}{\mathrm{μ}}} \end{gathered}$$

Here, L is the length of the string.

So, it is clear that frequency is inversely proportional to the mass density. Hence, thinner strings will have a higher frequency or thicker strings will have lower notes.