Amplitude of transmitted wave, $A_{t}=\frac{2 Z_{1}}{Z_{1}+Z_{2}} A=\frac{2 \sqrt{\mu T}}{\sqrt{\mu T}+\sqrt{4 \mu T}} A=\frac{2}{3} A$

Thus, $P=\frac{1}{2} \mu \omega^{2} A^{2} v$

$=\frac{1}{2} \times 4 \mu \times \omega^{2} \times \frac{4 A^{2}}{9} \times \sqrt{\frac{T}{4 \mu}}=\left(\frac{1}{2} \times \mu \times \omega^{2} \times A^{2} \times \sqrt{\frac{T}{\mu}}\right) \times \frac{8}{9}$

$=\frac{8}{9} \times$ Initial power

Thus power transmitted $=\frac{8}{9} \times 100=89 \%$