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

An observer moves towards a stationary source of sound with a speed $\frac{1}{5}$ th that of sound. The frequency of ${ }^{\text {th }}$ sound emitted by the source of $f$. The apparent frequency recorded by the observer is