The length of a sonometer wire tuned to a frequency of $250 Hz$ is $0.60$ metre. The frequency of tuning fork with which the vibrating wire will be in tune when the length is made $0.40$ metre is .... $Hz$

Figure, shows a stationary wave between two fixed points $P$ and $Q$. Which point$(s)$ of $1, 2$ and $3$ are in phase with the point $X?$

A string in musical instrument is $50 cm$ long and its fundamental frequency is $800 Hz.$ If a frequency of $1000 Hz$ is to be produced, then required length of string is ..... $cm$

A massless rod of length $L$ is suspended by two identical strings $AB$ and $CD$ of equal length. A block of mass $m$ is suspended from point $O$ such that $BO$ is equal to $‘x’$. Further it is observed that the frequency of $1^{st}$ harmonic in $AB$ is equal to $2^{nd}$ harmonic frequency in $CD$. $‘x’$ is

Two wires $W_1$ and $W_2$ have the same radius $r$ and respective densities ${\rho _1}$ and ${\rho _2}$ such that ${\rho _2} = 4{\rho _1}$. They are joined together at the point $O$, as  shown in the figure. The combination is used as a sonometer wire and kept under tension $T$. The point $O$ is midway between the two bridges. When a stationary waves is set up in the composite wire, the joint is found to be a node. The ratio of the number of an tin odes formed in $W_1$ to $W_2$ is

To increase the frequency from $100 Hz$ to $400 Hz$ the tension in the string has to be changed by ..... $times$