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 the occurrence of $6\, beats/s$ when both the wires oscillate together would be:

Two sound waves with wavelengths $5.0\, m$ and $5.5\, m$ respectively,each propagate in a gas with velocity $330\, m/s$. We expect the following number of beats per second.

$A$ wire having tension $225 \ N$ produces six beats per second when it vibrates with a tuning fork. When the tension changes to $256 \ N$,it vibrates with the same fork,and the number of beats per second remains unchanged. The frequency of the fork is: (in $Hz$)

When an air column at $15 ^\circ C$ and a tuning fork are sounded together, $4$ beats per second are produced. The frequency of the fork is less than that of the air column. When the temperature falls to $10 ^\circ C$, the beat frequency decreases by one. The frequency of the fork will be ..... $Hz$ $[V_{sound}$ at $0 ^\circ C = 332, m/s]$.

$A$ tuning fork vibrates with $2$ beats in $0.04$ seconds. The frequency of the fork is .... $Hz$.

The frequency of a tuning fork is $220 \,Hz$ and the velocity of sound in air is $330 \,m/s$. When the tuning fork completes $80$ vibrations, the distance travelled by the sound wave is: (in $\,m$)