The velocity of sound in a gas,in which two wavelengths $4.08\,m$ and $4.16\,m$ produce $40$ beats in $12\,s$,will be ..............$m\,s^{-1}$.

$5\, \text{beats/second}$ are heard when a tuning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either $0.95\, \text{m}$ or $1\, \text{m}$. The frequency of the fork will be ... $\text{Hz}$.

When two tuning forks (fork $1$ and fork $2$) are sounded simultaneously,$4$ beats per second are heard. Now,some tape is attached to the prong of fork $2$. When the tuning forks are sounded again,$6$ beats per second are heard. If the frequency of fork $1$ is $200 \, Hz$,then what was the original frequency of fork $2$ (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 $0 ^\circ C = 332, m/s]$.

Two tuning forks $A$ and $B$ produce $8 \, Hz$ beats per second when sounded together. $A$ gas column $37.5 \, cm$ long in a pipe closed at one end resonates in its fundamental mode with fork $A$,whereas a column of length $38.5 \, cm$ of the same gas in a similar pipe is required for resonance with fork $B$. The frequencies of these two tuning forks are:

Two wires are in unison. If the tension in one of the wires is increased by $2\%$,$5$ beats are produced per second. The initial frequency of each wire is .... $Hz$.