A pipe open at both ends and a pipe closed at one end have same length. The ratio of frequencies of their $P^{\text {th }}$ overtone is

The fundamental frequency of sonometer wire increases by 9 Hz , if its tension is increased by $69 \%$, keeping the length constant. The frequency of the wire is

A sonometer wire is in unison with a tuning fork, when it is stretched by weight $w$ and the corresponding resonating length is $L_4$. If the weight is reduced to $\left(\frac{w}{4}\right)$, the corresponding resonating length becomes $L_2$. The ratio $\left(\frac{L_1}{L_2}\right)$ is

For formation of beats, two sound notes must have