$A$ set of $24$ tuning forks is arranged in a series of increasing frequencies. If each fork gives $4 \, Hz$ beats per second with the preceding one and the frequency of the last tuning fork is two times that of the first fork,find the frequency of the $5^{th}$ tuning fork in $Hz$.

$A$ prong of a vibrating tuning fork is in contact with the water surface. It produces concentric circular waves on the surface of the water. The distance between five consecutive crests is $0.8 \ m$ and the velocity of the wave on the water surface is $56 \ m/s$. The frequency of the tuning fork is: (in $Hz$)

$A$ source of sound gives five beats per second when sounded with another source of frequency $100 \, s^{-1}$. The second harmonic of the source together with a source of frequency $205 \, s^{-1}$ gives five beats per second. What is the frequency of the source in $s^{-1}$?

Two harmonic waves moving in the same direction superimpose to form a wave $x = a \cos(1.5 t) \cos(50.5 t)$ where $t$ is in seconds. Find the period with which they beat (close to the nearest integer). (in $s$)

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:

The wavelengths of two sound notes in air are $\frac{40}{195} \,m$ and $\frac{40}{193} \,m$. Each note produces $9$ beats per second separately with a third note of fixed frequency. The velocity of sound in air in $m/s$ is