A body sends a wave $150$ mm long through medium P and $0.30$ m long in medium Q. If velocity of the wave in medium P is $80\,\text{cm s}^{-1}$, the velocity of wave in medium Q is

The third overtone of a closed pipe of length '$L_c$' has the same frequency as the third overtone of the open pipe of length '$L_0$'. Both the pipes have same diameters. The ratio $L_c : L_0$ is equal to

A tuning fork gives $5$ beats per second with a $33$ cm length of sonometer wire. If the length of the wire is shortened by $1$ cm, the number of beats is still the same. The frequency of the fork is

A set of $14$ tuning forks is arranged in a series of increasing frequencies. Each fork produces '$x$' beats per second with the preceding fork and the last fork is an octave of the first fork. If the seventh fork has the frequency of $114$ Hz, the value of $x$ is