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 to3 L
the frequency \omega gets multiplied by
.

b) If we increase tension by a factor of36
the frequency \omega gets multiplied by
.

help (numbers)

PDE:

BC:

The constant

Suppose the string vibrates at base frequency

a) If we lengthen the string to

b) If we increase tension by a factor of

help (numbers)

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