A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is $$\left(\frac{a-1}{a}\right)$$ then the value of $$a$$ is _________.

Two open organ pipes of lengths $$60 \mathrm{~cm}$$ and $$90 \mathrm{~cm}$$ resonate at $$6^{\text {th }}$$ and $$5^{\text {th }}$$ harmonics respectively. The difference of frequencies for the given modes is _________ $$\mathrm{Hz}$$. (Velocity of sound in air $$=333 \mathrm{~m} / \mathrm{s}$$)

A sonometer wire of resonating length $$90 \mathrm{~cm}$$ has a fundamental frequency of $$400 \mathrm{~Hz}$$ when kept under some tension. The resonating length of the wire with fundamental frequency of $$600 \mathrm{~Hz}$$ under same tension _______ $$\mathrm{cm}$$.