How does the frequency of sound given by a stretched string depend on its (a) length, (b) tension?

(a) As we know,

frequency (f) = $\dfrac{1}{2l} \sqrt\dfrac{T}{πr^2d}$

Hence, the frequency of sound given by a stretched string is inversely proportional to the length of the string.

f ∝ $\dfrac{1}{l}$

(b) The frequency of sound given by a stretched string is directly proportional to the square root of the tension in the string.

f ∝ $\sqrt T$