$A$ wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of $25 \ Hz$. The mass of the wire is $2 \ g$ and its linear mass density is $4 \times 10^{-3} \ kg/m$. What is the tension in the string (in $N$)?

The correct graph between the frequency $n$ and the square root of density $(\rho)$ of a wire,keeping its length,radius,and tension constant,is:

$A$ sonometer wire '$A$' of diameter '$d$' under tension '$T$' having density '$\rho_1$' vibrates with fundamental frequency '$n$'. If we use another wire '$B$' which vibrates with the same frequency under tension '$2T$' and diameter '$2d$',then the density '$\rho_2$' of wire '$B$' will be:

In an experiment with a sonometer,a tuning fork of frequency $256 \ Hz$ resonates with a length of $25 \ cm$ and another tuning fork resonates with a length of $16 \ cm$. If the tension of the string remains constant,the frequency of the second tuning fork is .... $Hz$

$A$ sonometer wire is vibrating in resonance with a tuning fork. Keeping the tension applied same,the length of the wire is doubled. Under what conditions would the tuning fork still be in resonance with the wire?

$A$ uniform string resonates with a tuning fork at a maximum tension of $32 \,N$. If it is divided into two segments by placing a wedge at a distance one-fourth of the length from one end,then to resonate with the same frequency,the maximum value of tension for the string will be ........... $N$.