The frequency of the third overtone of a pipe of length ' $L_{\mathrm{c}}$ ', closed at one end is same as the frequency of the sixth overtone of a pipe of length ' $L_0$ ', open at both ends. Then the ratio $\mathrm{L}_{\mathrm{c}}: \mathrm{L}_0$ is

A wire of length ' $L$ ' and linear density ' $m$ ' is stretched between two rigid supports with tension ' $T$ '. It is observed that wire resonates in the $\mathrm{P}^{\text {th }}$ harmonic at a frequency of 320 Hz and resonates again at next higher frequency of 400 Hz . The value of ' $p$ ' is

The frequency of two tuning forks A and B are respectively $1.4 \%$ more and $2.6 \%$ less than that of the tuning fork C . When A and B are sounded together, 10 beats are produced in 1 second. The frequency of tuning fork C is

A resonance tube closed at one end is of height 1.5 m . A tuning fork of frequency 340 Hz is vibrating above the tube. Water is poured in the tube gradually. The minimum height of water column for which resonance is obtained is (Neglect end correction, speed of sound in air $=340 \mathrm{~m} / \mathrm{s}$ )