Take the vibrating string satisfying
PDE: $\quad u_{tt} = \alpha^2 u_{xx} , \qquad 0 < x < L , \quad t > 0$
BC: $\quad u(0,t) = u(L,t)= 0$
The constant $\alpha^2 = \frac{T}{\rho}$ where $T$ is tension and $\rho$ is linear density of the string.

Suppose the string vibrates at base frequency $\omega$.

a) If we lengthen the string to $3 L$ the frequency $\omega$ gets multiplied by .

b) If we increase tension by a factor of $36$ the frequency $\omega$ gets multiplied by .

help (numbers)