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

- A
$110$

- B
$114$

- C
$113$

- D
$106$

In order to double the frequency of the fundamental note emitted by a stretched string, the length is reduced to $\frac{3}{4}$$^{th}$ of the original length and the tension is changed. The factor by which the tension is to be changed, is

The fundamental frequency of a sonometer wire increases by $6$ $Hz$ if its tension is increased by $44\%$ keeping the length constant. The change in the fundamental frequency of the sonometer wire in $Hz$ when the length of the wire is increased by $20\%$, keeping the original tension in the wire will be :-

If you set up the ninth harmonic on a string fixed at both ends, its frequency compared to the seventh harmonic

A sonometer wire oflength $1.5\ m$ is made of steel. The tension in it produces an elastic strain of $1 \%$. What is the fundamental frequency of steel if density and elasticity of steel are $7.7 \times 10^3 $ $kg/m^3$ and $2.2 \times 10^{11}$ $N/m^2$ respectively?

- [JEE MAIN 2013]

In an experiment with sonometer when a mass of $180\,g$ is attached to the string, it vibrates with fundamental frequency of $30\,Hz$. When a mass $m$ is attached, the string vibrates with fundamental frequency of $50\,Hz$. The value of $m$ is $.........\,g$.

- [JEE MAIN 2023]