Answer
The wavelength on the string depends only on the length of the string.
The wavelength of the sound wave depends on the length of the string, the mass per unit length of the string, and the tension.
Work Step by Step
We can write an expression for the wavelength of the fundamental standing wave on a string:
$\lambda = 2L$
The wavelength on the string depends only on the length of the string.
We can write an expression for the wavelength of a sound wave moving through the air:
$\lambda = \frac{v}{f}$, where $v$ is the speed of sound through the air
The frequency $f$ in the air is the same as the frequency $f$ of the wave moving on a string. The frequency on a string depends on the length of the string, the mass per unit length of the string, and the tension.
Therefore, the wavelength of the sound wave depends on the length of the string, the mass per unit length of the string, and the tension.
