For waves propagating in a medium, identify the property that is independent of the others

Two tuning forks having frequency $256\, Hz \,(A)$ and $262\, Hz \,(B)$ tuning fork. $A$ produces some beats per second with unknown tuning fork, same unknown tuning fork  produce double beats per second from $B$ tuning fork then the frequency of unknown tuning fork is :- ............ $\mathrm{Hz}$

A sound-source is moving in a circle and an observer is outside the circle at $O$ as shown in figure. If the frequencies as heard by the listener are $\nu _1, \nu _2$ and $\nu _3$ when the source is at $A, B$ and $C$ position, respectively, then

A tuning of fork of frequency $392\, Hz$, resonates with $50\, cm$ length of a string under tension $(T)$. If length of the string is decreased by $2\%$, keeping the tension constant, the number of beats heard when the string and the tuning fork made to vibrate simultaneously is

If $L_1$ and $L_2$ are the lengths of the first and second resonating air columns in a resonance tube, then the wavelength of the note produced is

Two identical piano wires, kept under the same tension $T$ have a fundamental frequency of $600\, Hz$. The fractional increase in the tension of one of the wires which will lead to occurrence of $6\, beats/s$ when both the wires oscillate together would be