A source and an observer move away from each other with same velocity of $10 \mathrm{~ms}^{-1}$ with respect to ground. If the observer finds the frequency of sound coming from the source as 1980 Hz , then actual frequency of the source is (speed of sound in air $=340 \mathrm{~ms}^{-1}$ )

A wave is given by $y=5 \times 10^{-3} \sin \left(12.5 \pi x-\frac{\pi}{2} t\right)$. Then its wavelength and time period are respectively ( $y$ and $x$ are in metres and $t$ is in seconds)

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