$56$ tuning forks are arranged in increasing order of frequencies in a series such that each fork gives $4 \text{ beats per second}$ with the previous one. The frequency of the last fork is the octave of the first. The frequency of the first fork is ..... $Hz$.

Two sound waves of wavelengths $\lambda_1$ and $\lambda_2$ $(\lambda_2 > \lambda_1)$ produce $n$ beats per second. The speed of sound is:

$A$ set of $20$ tuning forks is arranged in a series of increasing frequencies. If each fork gives $4 \; Hz$ beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first,then the frequency of the last fork is $\dots \; Hz$.

$A$ tuning fork gives $3$ beats with $50 \ cm$ length of sonometer wire. If the length of the wire is shortened by $1 \ cm$,the number of beats is still the same. The frequency of the fork is (in $Hz$)

Two identical straight wires are stretched so as to produce $6$ beats per second when vibrating simultaneously with tensions $T_1$ and $T_2$ respectively. On changing the tension slightly in one of them,the beat frequency remains unchanged. This will happen when (Given $\rightarrow T_1 > T_2$)

Three sound waves of equal amplitudes have frequencies $(n - 1)$,$n$,and $(n + 1)$. They superimpose to produce beats. The number of beats produced per second is: