A tuning fork $A$ of frequency 250 Hz and another tuning fork $B$ of frequency $x$ produced 5 beats per second when vibrated together. If the fork $B$ is waxed and vibrated together with $A$, then 3 beats per second are produced. Then, $x=$

If the seventh harmonic of a closed pipe is in unison with fourth harmonic of an open organ pipe, then the ratio of length of closed pipe to that of open pipe is

An observer moves towards a stationary source of sound, with a speed of one fifth of the speed of sound. The apparent increase in the frequency heard by the observer is

A rod of length $L$ and negligible mass is suspended by two identical strings $A B$ and $C D$ as shown in the figure A mass $M$ is suspended from point $O$ which is at a distance $x$ from $B$. If the frequency of the first harmonic of $A B$ is equal to the frequency of the second harmonic of $C D$, then the value of $x$ is